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Robust Surface Matching for Automated Detection of Local Deformations Using Least-Median-of-Squares Estimator
Abstract
Automated detection of the local deformation of a suqface involves the detection of the differences between an original and a deformed digital suI.face model without the aid of control points. The process is normally automated by matching two digital suqace models. This technique is desirable for many industrial applications. With the existence of local deformation, conventional suI.face matching algorithms with least-squares conditions will fail because the estimated parameters are influenced by local deformation. As a result, some robust estimators can be applied-to robustify sudace matching algorithms. In addition to a re-evaluation of the pedormance of the M-estimator, two other robust estimators-the GM-estimator and the LMS-esti-mator (least median of squares)-have been explored in this study for the purpose of detecting local deformation. Test results show that the LMS-estimator is superior to both the M-estimator and the GM-estimator for detecting local deformation in three respects: (1) it is not sensitive to the location of local deformation; (2) the largest tolerable deformation percentage is improved to a level of almost 50 percent; and (3) when the deformation percentage is less than 40 percent, deformations of very small magnitude can be detected. It has also been found that the largest tolerable deformation percentage is related to the magnitude of the deformation.
... However, not all well-distributed GCPs can be found in high mountain areas and it is even impossible to establish GCPs prior to debris flow hazards. Thus, debris flow investigation on the basis of multi-temporal DEMs without GCPs has to be investigated (Borga et al. 1998, Kää b 2000, Li et al. 2001, Huggel et al. 2003. Such a technique, which applies seven parameters, according to the rigid transformation model, to describe the relationship between two DEMs, can improve efficiency greatly and reduce fieldwork. ...
... This method can detect deformation areas of up to 25%. Li et al. (2001) integrated the LMS-estimator with a random sample scheme and then proposed a new algorithm, called the LMS-LZD method. This algorithm can detect nearly 50% of deformation areas. ...
... , u i 5r i /s i , and r i and s i are residuals and its standard deviation, respectively, k 0 , k 1 are constants. Li et al. (2001) improved this method using least median of squares estimator (LMS). We named this the LMS-LZD method. ...
Automatic DEM deformation detection without ground control points (GCPs) with its application in debris flow change analysis is an attractive but very difficult research topic. Based on the existing methods of M‐LZD and LMS‐LZD, this paper presents an improved method that takes both magnitude and relationship into account through allocating an appropriate weight to each observation and evaluating the contribution of each observation to deformation with the allocated weight. Such improvement enhances greatly the ability of DEM deformation detection. Compared with the M‐LZD and LMS‐LZD algorithm, using the multi‐temporal DEMs of the Puwaigou valley, along the Hengduan mountain ranges in the southwest of China, where debris flows occur frequently during each summer due to heavy rainfall and each Autumn due to rapid snowmelt, the experimental results demonstrate that our method has the highest detection accuracy (RMS) and detection percentage (capability) of over 50%. The advantages of our method are (1) it does not need GCPs and prior information and knowledge of the terrain surface, and (2) it can calculate simultaneously the volume and determine the spatial distribution of terrain surface changes of multi‐temporal DEMs.
... Karras and Petsa (1993) adopted date snooping, and proposed a new method for matching DEMs with some existing outliers. Pilgrim (1996a,b) improved LZD by using an M-estimator to replace the least squares (LS) technique, Li et al. (2001) integrated LMS-estimator with the random sample scheme and then proposed a new robust LZD algorithm, called LMS-LZD. The algorithm can detect deformation areas of no more than 50%. ...
... Although LTS has many advantages over LMS, LMS is more often investigated (Masuda and Yokoya, 1995;Li et al., 2001). What hinders LTS's application is mainly its relatively low computational efficiency. ...
... After pairing points located on the reference and the deformed DEMs, the height difference (the difference in z-direction, dz) between the two points of each pair can be calculated. It should be noted that all points located outside the overlapped region will be dropped by setting their weight (w) to zero (also refer to Li et al., 2001). Therefore, the optimal transformation T can be derived by minimizing the sum of least h squared dzs according to the LTS estimator, while the traditional LZD algorithm finds the transformation by minimizing the sum of all squared dzs. ...
Robust DEM co-registration for detecting terrain changes is an attractive but unresolved problem in both Remote Sensing and the Prevention and Mitigation of Hazards. Since robust DEM co-registration is an inherently very difficult problem, the algorithms developed are becoming more and more complicated. In this paper, a robust method for DEM co-registration is proposed, which integrates the least trimmed squares (LTS) estimator with the least Z-difference (LZD) algorithm. Moreover, a self-adaptive threshold based on the histogram of height differences is employed to identify the terrain changes automatically, which are the fundamental data for landslide assessment. The results of simulated experiments illustrate the robustness and accuracy of the new algorithm.
... Pilgrim (1996) implemented robust surface matching, using a modified M-estimator, for detection of simulated growths and swellings in a medical photogrammetric application, noting improved performance over the non-robust version of the algorithm. Li et al. (2001) evaluate the performance of several robust estimators, through application to simulated datasets. However, while these two studies highlight the potential of the technique, they are based on simulated datasets for close range applications. ...
... In this research, Tukey's Biweight was selected for application. The Biweight is one of the most commonly-utilised M-estimators, and as highlighted by Li et al. (2001) in the context of robust surface matching, offers strong robustness characteristics. The weight function for the Biweight is defined as: ...
... This involves the application of weighted least squares, which is a straightforward extension of the normal case. Through IRLS, the weight matrix is recomputed as a function of the standardised least squares residuals after each iteration (Li et al., 2001). Consequently, the weights are not held fixed, but alter in response to the fluctuating residuals. ...
With the increasing availability of a diverse range of datasets from sources such as airborne and terrestrial laser scanning, InSAR, and high resolution satellite remote sensing, there are improved opportunities for dataset integration and the synergistic benefits which this can offer. However, accurate registration is a fundamental pre-requisite for data fusion, and an issue which is often overlooked. This paper presents a strategy for improving the effectiveness of coastal geohazard monitoring through the integration of airborne and terrestrial laser scanning datasets. This approach is based upon a robust least squares surface matching technique, which enables the reliable reconciliation of disparate datasets, overcoming disparities between the input surfaces. The development of the matching algorithm, which incorporates a robust M-estimator function, is detailed. Application of this approach to a test site located on the east coast of England highlights the effectiveness of the robust matching algorithm for data integration, improving the quality of the resultant surface models, and facilitating subsequent analysis of change over a four month period. Robust surface matching is a flexible technique, which shows significant potential for a range of data fusion tasks, particularly where there is also a requirement for reliable change detection.
... This is true, even where vegetation has been removed through filtering algorithms, as there will always be residual effects due to the differing and inconsistent vegetation penetration properties of these two techniques. The introduction of local surface discrepancies will influence the estimation of the transformation parameters, and where the effects are significant, conventional least squares approaches may fail, or may converge to an erroneous solution (Li et al., 2001; Pilgrim, 1996). Although minor differences between the surfaces can be tolerated, the assumption that the surfaces are overwhelmingly similar is critical for attaining a successful solution. ...
... This incorporates a weighting function based on a modified maximum likelihood estimator (M-estimator), which identifies, and down-weights high-residual observations which can effectively be considered as outliers in the matching. This strategy was further investigated by Li et al. (2001). However, these studies were motivated by medical and industrial applications, and although they demonstrated the superior results which could be obtained through a robust approach, both studies were restricted to simulated datasets. ...
... Given more time, it would be desirable to investigate this aspect in order to optimise robust functionality, and evaluate sensitivity to such parameters. Furthermore, it may be useful to explore alternative functions, such as the LMS-estimator (least median of squares), which is recommended by Li et al. (2001) for its excellent robustness qualities. However, the LMS function is not as straightforward to resolve as M-estimator functions, and incorporating this is likely to entail major modifications to the existing algorithm. ...
Coastal change is a major issue in many regions of the world, and is often driven by geohazard processes such as landslides and rockfalls. Effective assessment of such phenomena is essential for successful management of coastal ecosystems, and is often reliant on GIS-based analysis. However, while it is crucial that multi-temporal datasets can be accurately registered to a common reference system, traditionally, the dynamic nature of the coastal environment has hampered this process. This paper presents a robust surface matching technique which overcomes the requirement for physical control points, and instead derives control directly from the DEM surfaces. Although surface matching procedures are well established, performance can be sub-optimal where the surfaces contain regions of difference, such as those associated with geohazard activity or vegetation effects. The crucial aspect of the least squares matching approach developed here, is the incorporation of a robust estimation function which allows the effects of surface discrepancies to be mitigated through outlier handling. Aerial photogrammetry is an established technique for coastal monitoring, and extensive archival collections exist. However, archival datasets are particularly affected by the difficulties associated with acquisition of ground control. Conversely, the maturing technique of airborne laser scanning is less influenced by such problems, and instead is capable of producing a high quality representation of coastal terrain. This paper describes the application of the robust surface matching technique to test sites located on the east coast of England. Photogrammetric DEMs are approximately oriented, before being matched to control surfaces derived from higher order datasets, including airborne laser scanning DEMs. The robust matching algorithm is shown to produce significantly improved results over ordinary surface matching. Analysis indicates the effectiveness of this technique for exploitation of archival datasets, revealing a signature of extensive geohazard activity over the twenty-five year study period. Robust matching of airborne laser scanning datasets has also enabled the quantification of short-term geohazard activity, demonstrating the flexibility of this strategy.
... However, not all well-distributed GCPs can be found in high mountain areas and it is even impossible to establish GCPs prior to debris flow hazards. Thus, debris flow investigation on the basis of multi-temporal DEMs without GCPs has to be investigated (Borga et al. 1998, Kää b 2000, Li et al. 2001, Huggel et al. 2003. Such a technique, which applies seven parameters, according to the rigid transformation model, to describe the relationship between two DEMs, can improve efficiency greatly and reduce fieldwork. ...
... This method can detect deformation areas of up to 25%. Li et al. (2001) integrated the LMS-estimator with a random sample scheme and then proposed a new algorithm, called the LMS-LZD method. This algorithm can detect nearly 50% of deformation areas. ...
... , u i 5r i /s i , and r i and s i are residuals and its standard deviation, respectively, k 0 , k 1 are constants. Li et al. (2001) improved this method using least median of squares estimator (LMS). We named this the LMS-LZD method. ...
An attractive, but very difficult research topic is automatic DEM deformation detection without control points. The technique is essential for multi-temporal remote sensing applied in, e.g., soil-erosion and debris flow disaster monitoring. This paper presents a differential model and a fully automatic method for multi-temporal DEMs deformation detection without control points based on Least Z-Difference (LZD) algorithm. Firstly, the corresponding points on both original DEM and ready matching DEM are paired using the criterion in the LZD algorithm, and then differential model can be constructed by arraying all Z-coordinate differences between corresponding points in line with their position. The weight of each observation (Z-difference) is set using the characteristics of differential model. The observation, whose weight is set to zero, is dropped from the matching process. Afterwards, all isolated observations are also removed. After processed through the above two steps, almost all of suspicious deformed observations, including some good observations, would be able be discarded from the objective function. Therefore, the DEM surface deformation can quantificationally be detected by the matched DEMs. A comparison study using multi-temporal DEMs on PUWAIGOU debris-flow valley shows that the presented method in this paper is more robust and has higher accuracy than ones of M-LZD and LMS-LZD algorithms. Moreover, the new method can detect that DEM data, whose deformation area is over 50%.
... The terrestrial change is the basic data for Earth's hazards study, which can be quantitatively measured using multi-templar DEMs [1,2]. The technique of DEM deformation detecting without control points is much useful, and is developed from the DEM co-registration theory and algorithm. ...
... The least z-difference method (LZD) [3] is one of the mostly used algorithms for DEM co-registration. By treating the terrestrial change as gross error in LZD algorithm, its spatial distribution and magnitude can be detected with robust estimator [2,4]. ...
DEM matching algorithm without control points is the base for detecting deformation method, the deformation existing in DEMs is treated as gross error. The detectability and locatability of multiple gross errors is very critical according to the surveying error and reliability theory. The interactive observations number (ION) derived from gross error judgement matrix is adapted in this paper. The relationship between zero-column vectors in judge matrix and the rank of the coefficient matrix of DEM matching is discussed in theory, and prove none zero-column vectors exist with real date sets. ION Equal to the number of redundant observations. Experimental results show that DEM matching algorithm has the detectability and locatability of multiple gross errors, and the deformation can be correctly detected by robust estimators in prearranged confidence level.
... Moreover, in dynamic environments, such as that under study here, there is potential for more significant differences to arise as a result of processes such as glacier melt. The introduction of local discrepancies between the surfaces will influence the estimation of the transformation parameters, and where the effects are significant, conventional least squares approaches may fail, or may converge to an erroneous solution [34]. To overcome this, a weighting function based on a maximum likelihood estimator (M-estimator) was embedded in the software. ...
... Thus, the influence of outlying points, or regions of surface difference, can be mitigated and a more accurate solution is likely to be achieved. Similar approaches, based on the incorporation of robust estimation functions, have been shown to produce good results with experimental datasets [34], [36]. It is beyond the scope of this paper to provide a detailed account of the algorithm utilised here. ...
Glaciated regions are known to be particularly sensitive to climate change. Historical archives of glacier volume change are important, as they provide context for present-day changes. Although photogrammetric archives exist for many regions, their usefulness is often limited by a lack of contemporary ground control. High quality digital elevation models (DEMs) underpin a range of change analysis activities. This paper presents a cost-effective solution which utilizes Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) DEMs as control for the scaling and orientation of archival data sets. Instead of relying upon ground-control points, a robust surface matching algorithm is employed to automatically determine the transformation required to register two overlapping DEMs. Through application to the Slakbreen glacier system in Svalbard, Norway, the strategy is assessed by first matching an ASTER DEM to a fixed lidar reference surface. This demonstrates that ASTER DEMs are effectively correct in scale, supporting their use as a control surface. The second stage of the research implements this by matching an aerial photogrammetric DEM to an ASTER reference surface. Resultant volumetric and annual elevation change rates are compared to those derived from lidar data, which are considered in this paper as a truth data set. ASTER-based matching produced a mean annual elevation change rate of -4.12 ma-1, compared to a value of -4.11 ma-1 derived from the lidar data. In volumetric terms, this equates to a difference of 0.6%. A major advantage of this approach is the near-global coverage offered by ASTER data and the opportunity that this presents for remote glacial change analysis over regional extents.
... Through cross-correlation techniques the vertical and horizontal shifts of selected sections of the " slave DTM " with respect to the " master-DTM " can be measured so that the vertical differences between the DTMs to be co-registered become minimal for the stable terrain sections. From these shift vectors (Fig. 9) an optimal horizontal and vertical shift, rotation, scale, etc., between the DTMs to be compared can be computed and the " slave DTM " transformed accordingly (Pilgrim, 1996a, b; Li et al., 2001; Weidmann, 2004 ). The crosscorrelation focuses on stable terrain with sufficient relief (i.e. ...
... Through cross-correlation techniques the vertical and horizontal shifts of selected sections of the " slave DTM " with respect to the " master-DTM " can be measured so that the vertical differences between the DTMs to be co-registered become minimal for the stable terrain sections. From these shift vectors (Fig. 9) an optimal horizontal and vertical shift, rotation, scale, etc., between the DTMs to be compared can be computed and the " slave DTM " transformed accordingly (Pilgrim, 1996a, b;Li et al., 2001;Weidmann, 2004). The crosscorrelation focuses on stable terrain with sufficient relief (i.e. ...
Process interactions and chain reactions, the present shift of cryospheric hazard zones due to atmospheric warming, and the potential far reach of glacier disasters make it necessary to apply modern remote sensing techniques for the assessment of glacier and permafrost hazards in high-mountains. Typically, related hazard source areas are situated in remote regions, often difficult to access for physical and/or political reasons. In this contribution we provide an overview of air- and spaceborne remote sensing methods suitable for glacier and permafrost hazard assessment and disaster management. A number of image classification and change detection techniques support high-mountain hazard studies. Digital terrain models (DTMs), derived from optical stereo data, synthetic aperture radar or laserscanning, represent one of the most important data sets for investigating high-mountain processes. Fusion of satellite stereo-derived DTMs with the DTM from the Shuttle Radar Topography Mission (SRTM) is a promising way to combine the advantages of both technologies. Large changes in terrain volume such as from avalanche deposits can indeed be measured even by repeat satellite DTMs. Multitemporal data can be used to derive surface displacements on glaciers, permafrost and landslides. Combining DTMs, results from spectral image classification, and multitemporal data from change detection and displacement measurements significantly improves the detection of hazard potentials. Modelling of hazardous processes based on geographic information systems (GIS) complements the remote sensing analyses towards an integrated assessment of glacier and permafrost hazards in mountains. Major present limitations in the application of remote sensing to glacier and permafrost hazards in mountains are, on the one hand, of technical nature (e.g. combination and fusion of different methods and data; improved understanding of microwave backscatter). On the other hand, better dissemination of remote sensing expertise towards institutions involved in high-mountain hazard assessment and management is needed in order to exploit the large potential of remote sensing in this field.
... The squared loss in the ICP algorithm has been replaced with the LMS criterion in [301] and [171], and with the LTS criterion for example in [45] and [199]. [201] proposed the so-called fractional root mean squared distance as distance measure for ICP, which is essentially an LTS criterion, up to taking the square root. ...
Autonomous vehicles have to interact with their environment with the goal to fulfill their tasks while respecting all desired constraints such as not causing dangerous situations, driving comfortable maneuvers, enabling a smooth traffic flow, or avoiding overly polluting driving behavior. All steps require a suitable perception of the environment conditions, such as the estimation of the own position, a prediction of the trajectories of other traffic participants, or the assessment of parameters corresponding to vehicle dynamics. However, classical estimation algorithms are known to be easily distorted by outliers in the data. In addition, apart from rule-based systems , it becomes more convenient to train autonomous agents by machine learning algorithms. Again, such algorithms need to be robust in order to cope with model misspecification or outliers in the data. Robust Statistics is a discipline of statistics which exactly addresses these challenges. The goal of this paper is to provide an extensive overview of current applications of Robust Statistics in autonomous driving in a unified notation and to extract possible directions for future work.
... However, when airborne LiDAR operations are carried out in the field, if there is no building point cloud data, such algorithms will be ineffective. Traditional strip adjustment methods such as least squares 3D surface matching (LS3D) [29] and the least Z-difference (LZD) algorithm [31], shown in Figures 6 and 7, may also produce mismatch errors between the established tie points due to the mismatch errors in the original point cloud data, and this may lead to strip adjustment failure. From the comparative test results (Figure 13), it can be seen that the accuracy of the LS3D method is the poorest among the various strip adjustment methods. ...
Airborne light detection and ranging (LiDAR) data are increasingly used in various fields such as topographic mapping, urban planning, and emergency management. A necessary processing step in the application of airborne LiDAR data is the elimination of mismatch errors. This paper proposes a new method for airborne LiDAR strip adjustment based on point clouds with planar neighborhoods; this method is intended to eliminate errors in airborne LiDAR point clouds. Initially, standard pre-processing tasks such as denoising, ground separation, and resampling are performed on the airborne LiDAR point clouds. Subsequently, this paper introduces a unique approach to extract point clouds with planar neighborhoods which is designed to enhance the registration accuracy of the iterative closest point (ICP) algorithm within the context of airborne LiDAR point clouds. Following the registration of the point clouds using the ICP algorithm, tie points are extracted via a point-to-plane projection method. Finally, a strip adjustment calculation is executed using the extracted tie points, in accordance with the strip adjustment equation for airborne LiDAR point clouds that was derived in this study. Three sets of airborne LiDAR point cloud data were utilized in the experiment outlined in this paper. The results indicate that the proposed strip adjustment method can effectively eliminate mismatch errors in airborne LiDAR point clouds, achieving a registration accuracy and absolute accuracy of 0.05 m. Furthermore, this method’s processing efficiency was more than five times higher than that of traditional methods such as ICP and LS3D.
... Previous researchers have focused on improving the performance of one aspect of registration algorithms. For example, various improved ICP algorithms [30][31][32] cannot significantly improve the convergence speed. Some registration algorithms [21,26] based on new distance function focus on improving convergence speed and ignore the improvement of robustness. ...
One key issue in the optical measurement of free-form or complex surfaces is the point cloud registration procedure, which aligns the measurement data to the part model for a robust, fast and accurate inspection process. Therefore, a robust registration method for surface inspection is proposed based on an adaptive distance function (ADF) and the M-estimation method. The ADF as the basis error metric can accurately describe the shortest point-surface distance, and the M-estimation method is used to eliminate outliers and enhance the robustness of the registration performance. The registration problem using the M-estimation method can be interpreted as an iterative reweighted least squares (IRLS) minimization. Then, a nonlinear optimization model called IRLS-ADF is established to obtain the transformation parameters. The convergence of the proposed method is also analysed. Moreover, compared to the previous algorithms, the experiments confirm that the proposed method can achieve a combination of good robustness, fast convergence speed and high accuracy.
... Due to the relatively high noise level of many scans, particularly in the sectors illustrating long distance measurements, the Huber function [43] which attenuated the outlying measurement results (affected by gross errors) was also applied in the calculations. This function was arbitrarily selected from among many functions known and commonly used for this purpose [21,31,[44][45][46][47]. The robust function rejects or significantly reduces weights of the specific pairs due to robustness criterion (see Figure 5). ...
The purpose of this article is to present a study aimed at developing a method for the precise determination of unmanned surface vehicle (USV) movement parameters (heading (HDG), speed over ground (SOG) and rate of turn (ROT)) through appropriate processing. The technique employs a modified weighted ICP (Iterative Closest Point) algorithm and a 2D points layer arranged in the horizon plane obtained from measurements. This is performed with the help of Light Detection and Ranging (LIDAR). A new method of weighting is presented. It is based on a mean error in a given direction and the results of modified weighted ICP tests carried out on the basis of field measurement data. The first part of the paper characterizes LIDAR measuring errors and indicates the possibilities for their use in matching point clouds. The second part of the article deals with a method for determining the SOG and course over ground (COG), based on a modified weighted ICP algorithm. The main part of the paper reviews a test method aimed at evaluating the accuracy of determining the SOG and COG by the scan-matching method using a modified weighted ICP algorithm. The final part presents an analysis comparing the obtained SOG and COG results with reference results of GNSS RTK measurements and the resulting generalised conclusions.
... The latter approach can also be divided into two classes: feature-information based methods and geometricrelation based methods (Akca et al. 2006). Due to the lack of requirement of feature points and high matching precision and efficiency, geometric-relation based methods are the primary DEM coregistration methods, which include the minimum height difference algorithm (Least Z-difference, LZD) (Rosenholm et al. 1988;, Interactive Closest Points method (ICP) (Besl 1992), Least Squares 3D Surface algorithm (LS3D) and some improved algorithms (Karras et al. 1993;Zhllin et al. 2001). The ICP and LS3D algorithms are proposed for use on 3D terrain data with irregular distribution, such as 3D laser point cloud data; the LZD algorithm (which is the most commonly used DEM coregistration) is proposed for use on regular grid data, such as SRTM DEM data, because it provides an overall optimal performance (Yang 2012). ...
Due to the systematic error, especially the horizontal deviation that exists in the multi-source, multi-temporal DEMs (Digital Elevation Models), a method for high precision coregistration is needed. This paper presents a new fast DEM coregistration method based on a given SAR (Synthetic Aperture Radar) imaging geometry to overcome the divergence and time-consuming problem of the conventional DEM coregistration method. First, intensity images are simulated for two DEMs under the given SAR imaging geometry. 2D (Two-dimensional) offsets are estimated in the frequency domain using the intensity cross-correlation operation in the FFT (Fast Fourier Transform) tool, which can greatly accelerate the calculation process. Next, the transformation function between two DEMs is achieved via the robust least-square fitting of 2D polynomial operation. Accordingly, two DEMs can be precisely coregistered. Last, two DEMs, i.e., one high-resolution LiDAR (Light Detection and Ranging) DEM and one low-resolution SRTM (Shutter Radar Topography Mission) DEM, covering the Yangjiao landslide region of Chongqing are taken as an example to test the new method. The results indicate that, in most cases, this new method can achieve not only a result as much as 80 times faster than the minimum elevation difference (Least Z-difference, LZD) DEM registration method, but also more accurate and more reliable results.
... M-estimation, which originates from robust statistics [23,26,40], is a technique commonly used in robust regression but is also used in robust registration [27,30,47]. It is a generalization of least squares minimization where the squares are replaced with a robust criterion function giving less influence of strongly deviating data. ...
The problem of finding a rigid body transformation, which aligns a set of data points with a given surface, using a robust M-estimation technique is considered. A refined iterative closest point (ICP) algorithm is described where a minimization problem of point-to-plane distances with a proposed constraint is solved in each iteration to find an updating transformation. The constraint is derived from a sum of weighted squared point-to-point distances and forms a natural trust region, which ensures convergence. Only a minor number of additional computations are required to use it. Two alternative trust regions are introduced and analyzed. Finally, numerical results for some test problems are presented. It is obvious from these results that there is a significant advantage, with respect to convergence rate of accuracy, to use the proposed trust region approach in comparison with using point-to-point distance minimization as well as using point-to-plane distance minimization and a Newton- type update without any step size control.
... The accuracy of the calculated vertical changes is a function of the accuracy of the repeat DEMs that are used (Etzelmüller, 2000;Kääb, 2005). Pre-and post-processing procedures such as multi-temporal adjustment of photogrammetric blocks, or DEM co-registration, help to improve this accuracy (Pilgrim, 1996;Kääb and Vollmer, 2000;Li et al., 2001;Kääb, 2005;Nuth and Kääb, 2011). ...
Permafrost and frozen grounds are key elements of the terrestrial cryosphere that will be strongly affected by a warming climate. With widespread permafrost degradation likely to occur in this century, remote sensing of permafrost is seeking to unveil the processes and
causal connections governing this development, from the monitoring of variables related to the permafrost state to the mapping of the impacts of degradation and potential natural hazards on the ground.
However, remote sensing of permafrost is challenging. The physical subsurface variables which characterize its thermal state – ground temperature, ice content and thaw depth – are not directly measurable through current remote sensing technologies. Instead, there is a large diversity of target characteristics for remote sensing from which the
permafrost state can be indirectly derived. Mountain permafrost environments are characterized by a strong heterogeneity on small spatial scales, so that high-resolution remote sensors are generally required. Permafrost landforms and surface features, such as rock
glaciers, thermokarst lakes and push moraines, can be identified by image classification techniques in a variety of remote sensing products. Permafrost-related vertical and horizontal surface deformations can be identified by repeat digital elevation models, or
radar interferometry.
Similar techniques are applied in the Arctic lowland permafrost areas to identify and map indicators of thawing ice-rich permafrost, such as thermokarst, thaw slumps, or coastal erosion. In some areas, the presence of permafrost correlates with certain vegetation types or
surface covers, which can be mapped from satellite sensors. Furthermore, in the vast lowland permafrost areas, physical variables directly or indirectly related to thermal subsurface conditions are accessible through more coarsely resolved remote sensing techniques. These include the land surface temperature, the freeze-thaw state of the surface and subsurface, and the gravimetric signal from the ground.
Recently, there is progress towards quantitative monitoring of ground temperatures and thaw depths by employing remote sensing data in conjunction with thermal subsurface modeling. By exploiting the cumulative information content of several remote sensing data sets through data fusion strategies, the best possible estimate for the ground thermal state can be achieved.
... By adopting the M-estimator, Pilgrim [1996] proposed the M-LZD algorithm, which can detect no more than 25% deformation. Li et al. [2001] obtained the LMS-LZD algorithm by using the least median of squares (LMS) estimator. It can obtain matching with no more than 50% deformation. ...
The deformation detection method without control points is one of the key techniques for multi-temporal digital elevation model (DEM) analyses, and represents an attractive and difficult research topic. A novel method for improved DEM deformation detection is proposed in this paper, based on the Least Z-Difference algorithm with differential model (DM-LZD). In the new method, an additional parameter is employed to improve the weighting function for the observations in the matching algorithm. Three indexes are designed to give an in-depth and quantitative analysis of the performance, according to the possible two types of errors occurring in the weighting function. The experimental result, based on the simulated dataset, shows that with an appropriate additional parameter it will achieve a better balance between the deformation-detecting ability and the matchingaccuracy, and so generates better performance.
... A robust regression method with a breakdown point of 50 percent is capable of dealing with half of the data as outliers. Using a finite set of samples randomly-selected from the data (trial estimates) is among the popular methods for the detection of outliers and has been implemented in different ways by several researchers (Efron, 1979;Fischler and Bolles, 1981;Rousseeuw and Leroy, 1987;Li et al., 2001). The number of samples is calculated from: ...
Automated reconstruction of buildings from different data sources has been one of the most challenging problems in photogrammetry and computer vision. Systems for automated building reconstruction fail in many cases due to complexities involved in the data including image noise,
occlusion, shadow, and low contrast, as well as, low accuracy or density of height data. In this paper, the problem of overgrown and undergrown regions in the segmentation of aerial images is discussed, and a split-and-merge technique is presented to overcome this problem by making use of
height data. This technique is based on splitting image regions whose associated height points do not fall in a single plane, and merging coplanar neighboring regions. A robust plane-fitting method is used to fit planar surfaces to height points that are highly contaminated by gross errors.
Final roof planes are extracted out of the image planar regions by checking their slope and height over a morphologically opened DSM. An experimental evaluation is conducted, and its results indicate the capability of the proposed technique in splitting overgrown regions, merging undergrown
coplanar regions, and selecting the final roof planes. Also, the method is shown to be computationally efficient, and the reconstructed roof planes are of acceptable accuracy.
... The accuracy of the calculated vertical changes is a function of the accuracy of the repeat DEMs that are used (Etzelmüller, 2000;Kääb, 2005). Pre-and post-processing procedures such as multi-temporal adjustment of photogrammetric blocks, or DEM co-registration, help to improve this accuracy (Pilgrim, 1996;Kääb and Vollmer, 2000;Li et al., 2001;Kääb, 2005;Nuth and Kääb, 2011). ...
Permafrost and frozen grounds are key elements of the terrestrial cryosphere that will be strongly affected by a warming climate. This chapter presents an overview of the remote sensing methods for permafrost studies with current sensor technologies. It outlines the remote sensing methods in two permafrost environments that differ substantially in their character: mountain permafrost and lowland permafrost. For remote sensing of permafrost in mountain areas, evaluating surface features is the dominant remote sensing application. Remote sensing techniques employed in the vast arctic and subarctic lowland areas, however, include a wide range of sensors that allow both mapping of surface features and monitoring of physical surface variables that can be used to assess the permafrost state. The chapter concludes with an outlook on thermal permafrost modeling using remotely sensed data sets as input.
... Furthermore, DEM change detection within a certain time period may be also used to automatically quantify the coastal landscape changes. In this sense many researchers have adopted 3D surface matching techniques without control points to automatically co-register multi-temporal DEMs, usually using the newer DEM as the reference surface to achieve the 3D registration of an older and generally less accurate DEM [1], [2], [3], [4] and [5]. ...
Digital elevation models (DEMs) are widely used in GIS to predict the impact of coastal flooding and Sea Level Rise in coastal areas. Furthermore, DEM change detection within a certain time period may be also used to automatically quantify the coastal landscape changes. In this sense many researchers have adopted 3D surface matching techniques without control points (GCPs) to automatically co-register multi-temporal DEMs. In this paper a new approach based on robust surface matching for DEM 3D geo-referencing is proposed to avoid the costly and time-consuming necessity of GCPs. The algorithm starts from a coarse orientation of the historical DEM where the stereo model y-parallax is removed by means of an Automatic Relative Orientation. Additionally, it is necessary to manually mark three control points to apply a coarse Helmert 3D transformation, obtaining a preoriented stereo-pair which turned out to be helpful to improve and speed up the subsequent surface matching process. Absolute z-differences between reference and historical DEMs are calculated, allowing for the application of the widely known K-means algorithm to cluster up to four groups of homogeneous absolute differences. The two clusters showing the high values are considered as outliers or areas where terrain has significantly changed. The remaining areas are deemed as potentially matching areas where the robust surface matching can be applied using the M-estimator called Tukey's Biweight (TB). In this way the diagonal weight matrix, regarding TB function, is introduced in an iterative least square routine to compute the Helmert 3D transformation parameters. The proposed methodology was tested for geo-referencing a historical grid format DEM, comprising a little coastal area of Almeria (South Spain), obtained by digital stereo-photogrammetry from a B&W photogrammetric flight taken in 1977 at an approximated scale of 1:18000. The reference DEM was the 10 m grid-spacing digital elevation model produced by the Andalusia Regional Government (Spain) from a 1:20000 scale B&W photogrammetric flight taken in 2001. As well, we counted on two accurate DEMs based on LiDAR technology (ground truth) taken in 2005 and 2009 respectively. The results obtained from this work may be deemed as very promising, showing a high efficiency and accuracy for historical DEM 3D geo-referencing. After the application of the robust surface matching for non-altered or stable areas, the computed uncertainty, measured as standard deviation of DEM z-differences, turned out to be 1.08 m. That is quite similar to the estimated uncertainty for the reference model (around 1.03 m).
... [5,16,18,21,25,26,33]. If robust methods are not used, the registration runs the risk of being spoiled by deviant and incorrect data, since least squares algorithms are highly sensitive to gross errors in the data A least median of squares (LMS or LMedS) version of the ICP algorithm is used in [12,15,16]. The LMS estimates are very robust and are not affected by up to 50 % outliers. ...
Registration of point sets is done by finding a rotation and translation that produces a best fit between a set of data points and a set of model points. We use robust M-estimation techniques to limit the influence of outliers, more specifically a modified version of the iterative closest point algorithm where we use iteratively re-weighed least squares to incorporate the robustness. We prove convergence with respect to the value of the objective function for this algorithm. A comparison is also done of different criterion functions to figure out their abilities to do appropriate point set fits, when the sets of data points contains outliers. The robust methods prove to be superior to least squares minimization in this setting.
... However, the ICP algorithm has several drawbacks: (1) it is time consuming due to the exhaustive search for the closest points; (2) good initial approximations of the closest points are required for the convergence of the iteration calculations; (3) the closest point pairs are sometimes unreliable, especially for topographic models with low spatial resolutions; and (4) possible errors in point selection will lead to unfavorable surface matching results. Li et al. (2001) presented a surface matching technique to detect the local deformation of a surface using a least-median-of-squares estimator. Gruen and Akca (2005) described a least squares 3D surface matching method. ...
Various lunar digital topographic models (DTMs) have been generated from the data collected from earlier and recent lunar missions. There are usually inconsistencies among them due to differences in sensor configurations, data acquisition periods, and production techniques. To obtain maximum value for science and exploration, the multi-source lunar topographic datasets must be co-registered in a common reference frame. Only such an effort will ensure the proper calibration, registration, and analysis of the datasets, which in turn will permit the full comparative and synergistic use of them. This study presents a multi-feature-based surface matching method for the co-registration of multiple lunar DTMs that incorporates feature points, lines, and surface patches in surface matching to guarantee robust surface correspondence. A combined adjustment model is developed for the determination of seven transformation parameters (one scale factor, three rotations, and three translations), from which the multiple DTMs could be co-registered. The lunar DTMs derived from the Chang’E-1, SELENE, and LRO laser altimeter data in the Apollo 15 landing area and the Sinus Iridum area are examined in this study. Small offsets were found among the Chang’E-1, SELENE, and LRO DTMs. Through experimental analysis, the developed multi-feature-based method was proven able to effectively co-register multiple lunar DTMs. The performances of the multi-feature-based surface matching method were compared with the point-based method, and the former was proven to be superior to the latter.
... However, the identification and quality of ground control in archival photography is often problematic. As a result, much research has been carried out in order to reduce the need for these costly and difficult to measure GCPs by means of surface matching (see, for example, Li et al., 2001;Mills et al., 2003Mills et al., , 2005Miller et al., 2008;Akca, 2010;Aguilar et al., 2012), or extracting GCPs from lidar-derived digital elevation models (DEMs) (James et al., 2006). ...
The use of archival or historical photography for photogrammetric purposes often involves a lack of data concerning the aerial cameras employed, difficulties in identifying control points on the photos and inappropriate conservation of the photography. When camera calibration parameters are unknown, they should be estimated by means of a self-calibrating bundle adjustment. Several calibration models available in the Leica Photogrammetry Suite software have been tested on two archival datasets, captured in 1956 and 1977, covering the same working area. The accuracy of the dataset triangulation was found to depend significantly on the self-calibration method and the number of ground control points used; when the latter ranged from six to nine per stereopair, self-calibrating bundle adjustment techniques were found to slightly, but not always significantly, improve the photogrammetric capability of archival aerial photography. Thus, the adoption of self-calibration cannot guarantee the improvement of results when working on poorly conserved imagery. Results from such datasets are very dependent on numerous local variables which cannot be extrapolated to other areas for the same camera since each dataset is unique and may present systematic errors of a different nature. © 2012 The Remote Sensing and Photogrammetry Society and Blackwell Publishing Ltd.
... The distance between the point where i , the weight of i , 0 or 1, is used to deal with the question caused by the partial overlapping (Li, Xu et al. 2001). According to the principle of least square, the surface can then e matching with an iterative behavior. ...
Multi-temporal DEM co-registration provides an efficient technique for automatic analyzing the terrestrial changes caused by the geological hazards. Because this technique does not require any ground control points (GCPs), it can bring us many benefits: 1) avoid the GCP establishment, which is a cost and labor- intensive task; 2) quick response to the natural hazards, especially to the landslides and debris-flows; 3)make full use of remote sensing data obtained before the events. It is very difficult to obtain effective GCP owing to the terrestrial changes, even impossible; 4) analyze the region could not access. Iterative closest points (ICP) is the standard algorithm for surface matching in computer vision and pattern recognition. Its computational efficiency is slower and only suit for relative small data set. It adopts an exhaustive search strategy to find the point-to-point or point-to-normal corresponding pairs. It is very time-consuming, and consumes about 95% time of the whole matching process. Although many modifications have reported to speed up the corresponding pairs searching, it still could not meet the requirement for co-registering the large gridded DEM used in geosciences. This paper proposes an efficiency correspondence criterion for gridded DEM matching, called normal correspondence criterion (NCC), which finds the corresponding points alone the reference DEM normal vector and is optimized with a focus on the gridded date set. The experimental results show that the corresponding points can be determined within no more than 6 iterations in most cases, which yields high efficiency to DEM co-registration. According to the numerous experimental results based on the simulated data sets, DEM co-registration with NCC only use 1/10 time than that used by ICP, and slight larger convergence range.
... When reference points are not available, for the registration of DEM pairs a surface matching procedure can be applied to minimize the coordinate residuals of undeformed areas by means of a roto-translation transformation between the two reference systems. The iterative least square procedure can be used for detecting deformed and stable zones (Pilgrim, 1996;Mitchell and Chadwick, 1999;Li et al., 2001). ...
The application of GPS, Digital Photogrammetry and Laser Scanning to
landslide represent a powerfool tool for movement monitoring including
small deformation preceding the failure phase. These techniques are
applied leading to an integrated system to generate Digital Elevation
Models. The GPS gives the possibility of determining the relative
position of points at centimetric and/or millimetric accuracy by means
of fast survey operations. The application of this technique in the
so-called kinematic mode, that is moving continuously one receiver with
respect to a reference fixed station, allows the description of the
terrain surface measuring the coordinates of points distributed on a
high density irregular grid. Moreover Static and Fast Static GPS mode
provide an efficient means for determining the position at millimetric
level of precision of marker points distributed along the interested
area. Continuous observations of landslide surface displacement may be
performed by means of GPS permanent station monitored from a remote
control centre, and the possibility of automating the main GPS
operational steps (observation, collection, downloading and processing)
make it possible to control landslide activity in real time. The Digital
Photogrammetry provide the measurement of shape, position and dimension
of objects on a surface from stereo photographs. Combined with surveying
of control points, photogrammetric techniques can be applied to generate
DEMs. Aerial and terrestrial images are automatically processed by means
of correlation algorithms that work at sub-pixel level. The precision of
the computation of three dimensional coordinates of points depends
mainly on the scale and the resolution of the image. The Laser Scanning
technique is based on determining distances measuring the round trip
time of a laser wave: for each point shot by the laser beam, the
telemeter provide the distances, the reflectance and the coordinates of
a high number of surface points in a local reference system. In the
Emilia-Romagna Region (Northern Italy) the 26% of identified landslides
are classified as "active" and many of them are complex ones, including
roto-translational and earth flow movements. These rainfall-induced
landslides involving clay-rich soils are widely represented in the
Apennines. We tested the integrated methodology on two landslides: a
first comparison between GPS kinematic and aerial Digital Photogrammetry
was performed on the Ca' di Malta landslide, obtaining encouraged
results. In this work Terrestrial Laser Scanning is introduced and
tested together with GPS kinematic and terrestrial/aerial Digital
Photogrammetry on the Rocca Pitigliana landslide. DEMs of the landslide
can be obtained and internal accuracy estimated in the context of a cost
and time effective method. Models generated at different epochs can be
differenced to determine displacements in active parts of the landslide
and the real time monitoring can be well suited for integration with an
alert system for landslide hazard management.
... The robust estimation was used for detecting the change between surface models without the assistance of ground control points. (LI et al., 2001; Pilgrim, 1996) A " multimatch-mutimosaic " approach was used for matching and mosaicing TOPSAR DEM data. The cross-correlation was calculated to find the horizontal and vertical offsets. ...
To generate an accurate digital elevation model (DEM), Interferometric Synthetic Aperture Radar (InSAR) requires precise orbit data and baseline information, which are not always available. An alternative approach is to apply quality ground control points (GCPs) into the InSAR processing. However, locating high quality GCPs can also be difficult task, due to the low spatial resolution and radiometric response of synthetic aperture radar (SAR) images. This paper presents a method to register and align an InSAR DEM, generated from SAR images without precise orbit or baseline information and without GCPs, to an existing coarse reference DEM for refinement. The results showed this method achieves a comparable or even better accuracy than applying GCPs into InSAR processing. It was also found that the existing DEM with lower resolution than the InSAR DEM could be a good reference for this registration and alignment, i.e. refinement. ERS1/2 tandem SAR image pairs were used for 16-meter (post spacing) InSAR DEM generation. Both InSAR processing with and without applying GCPs were conducted for comparison purposes. The InSAR DEM was registered and aligned to SRTM 3 Arc Second data, a global reference DEM. The "truth" DEM used for accuracy evaluation is a higher accuracy DEM from aerial imagery with post spacing of 1.5 meters and vertical accuracy of 1.8 meters.
... To the southwest, a coherent flow field and almost constant thickness point to creeping permafrost in thermal equilibrium. The measurements were done in relation to hazard assessment associated with the larger thermokarst lake (seeFigure 1)formation between the DTMs can be computed and the 'slave DTM' transformed accordingly (Pilgrim, 1996; Li et al., 2001; Kääb, 2005b). DTM correlation focuses on stable terrain with sufficient relief (i.e. ...
Modern remote sensing techniques can help in the assessment of permafrost hazards in high latitudes and cold mountains. Hazard development in these areas is affected by process interactions and chain reactions, the ongoing shift of cryospheric hazard zones due to atmospheric warming, the large spatial scales involved and the remoteness of many permafrost-related threats. This paper reviews ground-based, airborne and spaceborne remote sensing methods suitable for permafrost hazard assessment and management. A wide range of image classification and change detection techniques support permafrost hazard studies. Digital terrain models (DTMs) derived from optical stereo, synthetic aperture radar (SAR) or laser scanning data are some of the most important data sets for investigating permafrost-related mass movements, thaw and heave processes, and hydrological hazards. Multi-temporal optical or SAR data are used to derive surface displacements on creeping and unstable frozen slopes. Combining DTMs with results from spectral image classification, and with multi-temporal data from change detection and displacement measurements significantly improves the detection of hazard potential. Copyright © 2008 John Wiley & Sons, Ltd.
... The best-fit procedure is designed to minimize the data representing the surface separation of DEM pairs, which are assumed to be noisy and distributed around null mean value, by estimating similarity transformation parameters. The presence of local deformations may affect parameter estimation, reducing the effectiveness of these conventional matching algorithms (Li et al., 2001). The major advantage of the least squares surface matching is that various statistical tests to assess the reliability of the results can be applied. ...
After a period of anomalous activity affecting the Volcano of Stromboli (Aeolian volcanic arc, Italy), the “Sciara del Fuoco” slope, situated on the north–east flank of the island, was affected by major landslides on December 30, 2002. Recent lava accumulations starting from the beginning of the eruption (December 28, 2002) and a portion of the subaerial and submarine deposits were detached. As a result, tsunami waves several meters high affected the coasts of the island. After the event, monitoring activities, coordinated by the Italian Civil Protection Department, included systematic photogrammetric surveys. The digital photogrammetric technique was adopted to extract high-resolution digital elevation models and large-scale orthophotos.The comparison between the data collected before the eruption and that acquired on January 5, 2003, together with bathymetric data, allowed to define the geometry and to estimate the volume of the surfaces involved in the landslides.The following 13 photogrammetric surveys (from January to September 2003) enabled the monitoring of the continuous and relevant morphological changes induced by both the lava flow and the evolution of the instability phenomena.The method adopted for the data analysis and the results obtained are described in the paper.
... This algorithm is based on the residual of each point derived from each iteration of the least squares adjustment. These residuals were inputted to an appropriate weight function to compute weights for each point, in which the points with large residuals were treated as blunders and their influence were mitigated through down-weighting (Pilgrim, 1996;Li et al., 2001;Miller et al., 2008). ...
Martian topographic data has been collected by various exploration missions over the last decade. These products provide detailed topographic information and are invaluable for scientists to interpret and understand the geological and climate evolution which has occurred on Mars. In order to fully utilise these multi-sensor, multi-resolution and multi-scale Martian topographic products, a co-registration process has been developed which allows co-registration of Digital Terrain Models (DTMs) to be performed to co-align these multiple datasets. Surface matching is the core technique to implement this task and it is here assessed to determine the parameters of the most robust algorithm for DTM co-registration. Once this task was finished, the matching tool was developed accordingly with a decision algorithm. This algorithm was then employed to align DTMs derived from Mars Orbiter Laser Altimeter (MOLA), High Resolution Stereo Camera (HRSC) and High Resolution Imaging Science Experiment (HiRISE). For MOLA and HRSC DTMs, the co-registration was performed directly as the MOLA DTM acted as a reference surface within a bundle adjustment process. DTMs from different versions covering three HRSC orbital strips were used for the assessment process. As a result the mean bias of the height differences of a preliminary version HRSC DTM was significantly reduced from 38.596 m to 2.233 m, when compared against MOLA while the bias of a newer DTM was improved from 1.616 m to 0.161 m after matching. Regarding the co-registration of HiRISE and MOLA DTMs, a hierarchical approach employing a HRSC DTM as an intermediate dataset was assessed. The results demonstrated that the method is feasible and that the three DTMs were co-registered effectively. Due to the success highlighted in this paper, a surface matching tool is recommended to be applied to DTMs derived from multiple sources before these data are further used. Moreover, surface matching can be considered as an additional step of any workflow for Mars DTM creation.
... Pilgrim (1996a, b) improved this method by using an M-estimator to replace the least squares (LS) technique used in LZD, naming it the M-LZD method. Li et al. (2001) integrated the LMS-estimator with a random sample scheme and then proposed a new algorithm, called the MS-LZD method. This algorithm can detect nearly 50% of the deformation area. ...
Digital elevation model (DEM) matching techniques have been extended to DEM deformation detection by substituting a robust estimator for the least squares estimator, in which terrain changes are treated as gross errors. However, all existing methods only emphasise their deformation detecting ability, and neglect another important aspect: only when the gross error can be detected and located, can this system be useful. This paper employs the gross error judgement matrix as a tool to make an in-depth analysis of this problem. The theoretical analyses and experimental results show that observations in the DEM matching algorithm in real applications have the ability to detect and locate gross errors. Therefore, treating the terrain changes as gross errors is theoretically feasible, allowing real DEM deformations to be detected by employing a surface matching technique.
... A possible approach involves the detection of the parameters for a rigid transformation in a common reference system of the two data sets, without the aid of control points (least square matching). The presence of local deformations may influence the estimation of the parameters, reducing the ability of these conventional matching algorithms to obtain the spatial registration, but some robust estimators can be applied (Li et al., 2001) to increase the tolerable percentage of deformed areas. As pointed out by many authors (Karras and Petsa, 1993; Pilgrim, 1996b), one of the major advantages of the least square matching is that the process allows for various statistical techniques which make the match procedure very robust; furthermore, it can be integrated with techniques for detecting changes of the surfaces due to real deformations or to statistical outliers. ...
Three-dimensional reconstruction of the ground surface (Digital Terrain Model, DTM), derived by airborne GPS photogrammetric surveys, is a powerful tool for implementing morphological analysis in remote areas. High accurate 3D models, with submeter elevation accuracy, can be obtained by images acquired at photo scales between 1:5000-1:20000. Multitemporal DTMs acquired periodically over volcanic area allow the monitoring of areas interested by crustal deformations and the evaluation of mass balance when large instability phenomena or lava flows have occurred. The work described the results obtained from the analysis of photogrammetric data collected over the Vulcano Island from 1971 to 2001. The data, processed by means of the Digital Photogrammetry Workstation DPW 770, provided DTM with accuracy ranging between few centimeters to few decimeters depending on the geometric image resolution, terrain configuration and quality of photographs. published
https://epic.awi.de/id/eprint/22315/
Die Arbeit beschäftigt sich mit Change Detection in arktischen Tundrengebieten. Das Untersuchungsgebiet, die Insel Kurungnakh, gehört zur dritten geomorphologischen Hauptterrasse des nordostsibrischen Lena Deltas, die von fluviale Sanden überlagernden, reliefbildenden eisreichen Permafrostsequenzen aufgebaut wird. Der Einleitung folgt eine Darstellung der durchgeführten Feldvermessungskampagne mit Tachymeter, dazu der verwendeten ALOS-PRISM und CORONA Stereo-Satellitendaten, sowie deren Aufbereitung mit Methoden der Digitalen Bildverarbeitung. Durch Differenzbildung multitemporaler Digitaler Geländemodelle (DGM) aus Fernerkundungs- und Felddaten konnten in dieser Kombination erstmals über einen Zeitraum von 40 Jahren volumetrisch Veränderungen im ostsibirischen Alas-Yedoma Thermokarstrelief bestimmt werden. Für einen detailliert vermessenen Alas konnten Ausdehnungsraten von bis zu 9,4 cm/a ermittelt werden. Der Vergleich zweier Uferabschnitte am Olenyokskaya Deltaarm zeigt, dass mit 2,9 m/a am Buor-Khaya Ufer (50 m Kliffhöhe) gegenüber 1,8 m/a am Olenyokskaya Ufer (35 m Kliffhöhe), der Uferrückgang in mächtigeren Eiskomplexprofilen stärker ausgeprägt ist, was sich auch im erodierten Sedimentäquivalent von 0,17 gegenüber 0,25 Mio. t/a widerspiegelt. Aus der DGM-Analyse ist hervorgegangen, dass Veränderungen auch mit Thermokarstseen verbunden sind. Die Seen wurden manuell in hochauflösenden Orthobildern kartiert. Über den Zeitraum 1964-2006 sind 122 ha Seefläche dräniert worden (-3,5 %), während sich die persistenten Seen um +2,1 % vergrößert haben. Die von Seen eingenommene Fläche hat sich, bezogen auf eine veränderliche Untersuchungsgebietsgröße, infolge dieser parallelen Prozesse, leicht von 8,7 auf 8,5% verringert und ist Ergebnis sowohl kontinuierlicher als auch abrupter Veränderungen. Die aktuelle Geomorphodynamik erlaubt im Weiteren Rückschlüsse auf die zukünftige Landschaftsentwicklung, die durch endogene und exogene Faktoren, lateral und vertikal konsequenter Einebnung folgt.
Compare to the ICP (Iterative Closet Points) registration method and its variants, the registration method based on GMM (Gaussian Mixture Models) is less sensitive to initial position, noise and outliers. For efficiency in a large-scale point sets alignment, the algorithm involved with FGT (Fast Gaussian Transformation) was proposed. However, due to its accuracy degeneration, the application of fast implementation is limited in large-scale point registration. Thus a modified GMM method is established to improve its accuracy and efficiency in point sets registration. To improve the precision and robustness of point density, noise and outliers, the corresponding weight matrix consisted of bidirectional gauss distance is proposed in this study. Instead of FGT (Fast Gaussian Transformation), the IFGT (Improved Fast Gaussian Transformation) and an adaptive adjustment based on axis-angle is proposed to further improve its efficiency and robustness about initial position simultaneously. We test capabilities of methods in classical model and symmetric and featureless manufacture parts. Compared to state-of-the-art methods in experiment, the result demonstrated applicability of proposed method in real life.
Photogrammetry based on high-resolution satellite image can acquire geospatial information within a large area rapidly and timely, but its geopositioning accuracy is highly dependent on ground control points. Under the background of global mapping, a public digital elevation model (DEM) assisted Chinese satellite image geopositioning scheme was proposed to realize satellite photogrammetry without ground control points. To make full use of public DEM advantages of consistent and high accuracy, public DEM was regarded as reference data and matched with the DEM extracted from image, and then the determined transformation parameters were applied to correct direct georeferencing results in object space. A fast least Z-difference method combined with least trimmed squares estimator was proposed to achieve DEM matching, which can not only automatically select corresponding point determination model, but also self-adaptively detect and eliminate difference between DEMs. Multi-groups of comparative experiments using Mapping Satellite-1 and ZiYuan-3 surveying satellite images were designed. Experimental results show that the DEM assisted geopositioning scheme exploits advantages of reference DEM, which can greatly improve the accuracy of photogrammetry without ground control points to a relatively high level. The geopositioning accuracy of image is largely determined by, but not confined to, the accuracy of reference DEM, but it is slightly affected by the resolution of reference DEM. If target DEM resolution is relatively high, the geopositioning accuracy of a single image assisted by Shuttle Radar Topography Mission (SRTM) DEM can satisfy the accuracy requirements of 1:50,000 scale mapping perfectly. This scheme also has good robustness and high computational efficiency.
This paper presents how to estimate two parameters: slope and roughness representing lunar terrain quality for HDA (Hazard Detection and Avoidance) of lunar lander. Robust plane fitting technique based on LMS (Least Median Square) is applied to standardized DEM (Digital Elevation Model) from LIDAR (Light Detection and Ranging) sensor measurement in order to estimate the parameters. Since a number of hazards exist on the lunar surface such as craters, rocks and cliff, which are able to damage lunar lander, it is important for HDA system to precisely detect hazards and select safe landing site by meticulously characterizing terrain condition. For this reason, out research has been conducted using various sensors such as camera, infrared sensor, LIDAR sensors for HDA algorithm. Because sensor measurement can be processed in high speed relative to optical image and obtained at any light condition, it is an effective way to perform hazard detection and avoidance landing based on the LIDAR measurement. Therefore, it is confirmed that safe landing site can be extracted based on the parameters through simulation in this paper.
Digital elevation model (DEM) matching is a necessary task that must be conducted in many applications of remote sensing, especially for purposes of disaster surveillance (e.g., landslide, debris flow). In this paper, we propose a robust matching method based on contour lines and least squares surface matching. Challenges involve detecting stable and invariant control points (CPs) in un-deformed areas in varying situations and complex topographies. We utilize a shape context descriptor to compare contour lines and detect invariant peaks for CPs based on contour line shapes, which can generate good initial values of transformation parameters. Finally, the least squares surface matching technique is used for optimal matching. The proposed methodology is tested for DEM matching between a new InSAR DEM and ASTER DEM. The experimental results show that the proposed method shows considerable noise resistance and can alleviate deformation and nonlinear distortion effects of different systems.
The Hudson Bay Railway (HBR) is a 510 mile railway completed in 1929 in northern Manitoba, Canada. It connects domestic locations in North America with international destinations through the Port of Churchill.
Permafrost was encountered during construction at milepost 136 in isolated peat bogs which continued in a gradual northward transition from discontinuous to continuous permafrost. Over the past 80 years, warming climate combined with poor engineering properties of the railway embankment material has resulted in further thawing of the discontinuous permafrost leading to differential settlement, termed ‘sinkholes’, along the rail embankment and high annual maintenance costs.
This study incorporated geophysical investigations, track geometry data and remote sensing techniques to investigate the current condition of the underlying permafrost. Without employing the use of boreholes, two geophysical methods, electrical resistivity tomography (ERT) and ground penetrating radar (GPR) have proved to be effective in validating each other’s results. These were used to establish a baseline for future work in delineating the permafrost conditions along the entire 510-mile HBR route.
A predictive model has been developed that shows a correlation between vegetation and surface water raster data and track geometry exceptions. A three-level severity rating scheme was also developed that classified the susceptibility of sections to permafrost degradation as low, moderate or high. A rating of 1 represents a low degradation susceptibility region in the lowest 10th percentile which is likely to develop a maximum of four track exceptions per year and hence can be inferred that they are less susceptible to permafrost degradation. A rating of 2 represents the section of track with a moderate susceptibility to permafrost degradation likely to develop at most eight exceptions per year. Finally, a rating of 3 represents the very critical sections of track whose values are above the highest 50th percentile are likely to develop more than eight exceptions every year.
Digital elevation model (DEM) matching is a necessary task in many remote-sensing applications, especially in geohazard detection (e.g., landslides, debris flows, etc.). However, DEM matching presents two challenges: determining the alignment between the surface features of the two DEMs and estimating the matching transformation parameters. In this article, we present a two-step robust DEM-matching method in variable mountainous areas based on contour-based point matching and least squares surface matching. During the first step, point features were used to generate accurate initial values for the transformation parameters, which were used in the second step of surface matching. To overcome the shortage of point features, which are difficult to detect with the stable and invariant properties in complex terrains, we utilize a shape context descriptor to compare contour lines and detect invariant terrain peaks as control points based on contour line shapes. Then, in the second step, a least squares surface-matching method was used for optimization. The experimental results indicate that the proposed method exhibits robustness to noise and artefacts caused by terrain changes and nonlinear distortion from DEMs that are derived from different systems.
To improve the performance of the existing deformation detecting algorithms, a novel method based on the differential model was proposed for DEM (digital elevation model) deformation detecting without control points. In addition, it has been successfully used to the deformation detecting of Puwaigou, a debris region with a deformation proportion of over 50%. This method is based on the LZD (least Z-difference) algorithm, as a result, both the magnitude and the relationship of observations can be taken into account by introducing the differential model to greatly improve the ability of deformation detecting. The research result shows that its matching accuracy is higher than that of the M-LZD (LZD using M-estimator) and LMS-LZD (LZD using least-median-of-squares estimator) algorithms.
Inspection of a manufactured freeform surface can be conducted by sampling measurement points on the manufactured surface and comparing the measurement points with the ideal design geometry and its tolerance. Since measurement coordinate system and design coordinate system are usually different, these measured points should be first aligned with the design surface through localization. In this research, robust localization methods are developed for both rough localization and fine localization processes. For rough localization, some target measurement points are selected and their corresponding points on the design surface are obtained based on similarities in curvatures and distances of these points. Compared with curvatures that are often used in localization, the distances are less sensitive to the errors introduced in manufacturing and measurement processes. In fine localization, uncertainties in the measurement and localization processes are considered to predict the uncertainties of the localized measurement points. The optimal design coordinate system is also selected such that the uncertainties of the localized measurement points can be minimized. Two case studies are provided to demonstrate the effectiveness of the developed methods for freeform surface inspection.
The comparison of multitemporal Digital Elevation Models (DEMs) of the same area is a powerful tool in an integrated approach for studying Earth surface features and their evolution. At the same time, the differences in the techniques used to generate different datasets and the presence of artefacts constitute an important problem that must be solved in order to allow a meaningful study of the geomorphologic evolution of the area. Geographic Information Systems (GIS) tools can b e of great help in this approach, allowing users to obtain significant morphometric parameters from co-registered DEMs and giving at the same time the possibility to estimate artefacts in the datasets, to evaluate differences between ground surfaces in the different years and to validate results through geostatistical processes. In this study photogrammetry has been applied to extract multitemporal DEMs datasets of a hydrographic basin affected by landslides (Bologna, Italy) and GIS techniques have been used for morphologic enquiry on the test site. A time series of stereo digital images, derived from aerial photogrammetric surveys (1976, 1986, 1988 and 1993), was analysed and processed for obtaining high spatial resolution DEMs through softcopy photogrammetric techniques. DEMs accuracies, strictly related to the quality of images, to the adopted systems and strategies and to the morphologic features of the test area, were estimated. The analysis of the derived data in a GIS environment allowed the generation of correction maps and shaded relief maps for each dataset, evidencing various types of 3-Dimensional (3-D) artefacts in the models. After appropriate filtering of data, in order to make datasets comparable, geomorphologic features of the site were studied by means of 3-D raster analysis techniques. GIS functions were applied to the DEMs in order to display morphometric parameters for each dataset (elevation, slope, aspect, curvature) and to compare the ground surfaces, generating differential elevation maps for the whole of basin. Generally, differen tial movements inside the landslide areas in the basin appear to be comparable to the movements of the whole of basin in the considered time span: these differences must otherwise be weighted and validated, considering the accuracy of the different datasets and the limits of these comparison techniques.
decision support system is applied to provide the decision A spatial dynamic model (SDM) in a ~Is-based urban planning support for location seeking i irk in, 1996; Sui, 1998). popular decision support system has been developed for the city of approaches, such as location-seeking models and location-allo- ~~ih~i in southern china. ~h~ sDM was used to the cation models, have been developed. A location-seeking model dynamic change of the urban spatial structure by considering searches for the most optimal spatial location or spatial pattern urban spatial growth as the result of spatial interaction between from a set of predefined ~~hemes by considering the spatial demand and supply of urban resources. ~h~ sDM acts as an choice behavior of individuals as an objective function. A loca- analog sDM modeling provides information for de- tion-allocation model searches for spatial patterns or location cision support in urban planning and land use management. schemes based on multiple criteria analysis. In urban plan- The utility function of spatial choice and a methodology for ning, an ultimate goal is to seek the most optimal urban spatial the construction of the utility function were developed to Structure. andmodels havebeendevelO~edtomatch incorporate socioeconomic factors into the modeling process. or optimize the decision needs on spatial locations (Parrot and Multiple scenarios of urban planning and the consequences Stutz, 1991;Densham~ lggl; Harris and lgg3). of urban spatial growth, as well as the impacts of planning Because of the complexities of an urban system, it would schemes on traffic pow and on the environment, were sim- be extremely difficult to construct a mathematical expression ulated. Comparisons of simulation results allowed planners to to optimize s~cioeconomic spatial structure for a city of any
In automotive industry there is an interest of controlling the shape of a large number of identical components on-line in the manufacturing process. We propose a method to do this by capturing a digital hologram of the object and then using information from its computer aided design (CAD) model to calculate the shape and determine the agreement between the manufactured object and the CAD-model. The holographic recording of the object is done using dual wavelengths with a synthetic wavelength of approximately 400 mum. The optical measurement results in a wrapped phase map with the phase values in the interval [ - pi, pi]. Each phase interval represents a depth distance on the object of about 0.2 mm. The phase unwrapping is done iteratively using information from the CAD-model. This implies that it is possible to measure large discontinuities on the surface of the measured object. The method also gives a point-to-point correspondence between the measurement and the CAD-model which is vital for tolerance control.
At the dynamic coastal fringe, numerous processes interact with local morphology. In soft-cliff environments, this can often lead to the occurrence of coastal geohazards. These can pose a major threat to property and cultural heritage, and an effective monitoring strategy is therefore essential. While contemporary monitoring techniques have been applied, these are often unsuitable in isolation. This paper presents an integrated approach, with the development of weighted surface matching software enabling reliable dataset fusion and multi-temporal change detection, even where significant surface differences exist. Evaluation of this approach is presented and discussed.
We describe a method to verify the shape of manufactured objects by using their design model. A non-contact measuring method that consists of a stereo-camera system and a single projected fringe pattern is used. The method acquires one image from each camera. Additional shape information from the design model is also used. This surface-measurement method gives an accuracy of about 45μm. Deviations from the design model within ±1.6mm can be correctly detected. The measured surface representation is matched to the design model using the ICP-method. Fast performance has been considered adapting the method for on-line use.
We consider the problem of matching sets of 3D points from a measured surface to the surface of a corresponding computer-aided
design (CAD) object. The problem arises in the production line where the shape of the produced items is to be compared on-line
with its pre-described shape. The involved registration problem is solved using the iterative closest point (ICP) method.
In order to make it suitable for on-line use, i.e., make it fast, we pre-process the surface representation of the CAD object.
A data structure for this purpose is proposed and named Distance Varying Grid tree. It is based on a regular grid that encloses
points sampled from the CAD surfaces. Additional finer grids are added to the vertices in the grid that are close to the sampled
points. The structure is efficient since it utilizes that the sampled points are distributed on surfaces, and it provides
fast identification of the sampled point that is closest to a measured point. A local linear approximation of the surface
is used for improving the accuracy. Experiments are done on items produced for the body of a car. The experiments show that
it is possible to reach good accuracy in the registration and decreasing the computational time by a factor 700 compared with
using the common kd-tree structure.
KeywordsICP–Inspection–Registration–Surface matching
Digital elevation models (DEMs) produced from photogrammetric
data sources have long relied on the use of ground
control points to give them scale and orientation. However,
in areas such as coastlines, landslides, or glaciers, where
identification of suitable natural features and pre-marking is
difficult, the use of conventional ground control may be
unfeasible. This paper reports on research that uses independently
collected DEMs derived from kinematic GPS to orient
surfaces produced by aerial photogrammetric methods, using
a least-squares surface matching algorithm. During algorithm
development, three stages of testing were carried out, using
increasingly more complex datasets. Initially, simulated surfaces
were used to validate the matching theory and program.
Then, a DEM derived from conventional aerial photography
was matched with a GPS model, highlighting the effectiveness
of surface matching to recover systematic errors in datasets.
Finally, surfaces derived from small format digital imagery
were successfully fused with wireframe GPS surfaces, the high
redundancy and automation potential creating an elegant and
cheaper alternative to photocontrol.
A method for matching pairs of digital elevation models (DEMs), based on surface shape and without control points, has been evaluated in close-range photogrammetry. Results presented for 30 DEM pairs of the human body trunk and of varying relief indicate that the influence of orientation errors has been effectively removed from the transformed models. The final RMS differences in relief are close to the RMS errors of the elevations themselves. Introduction of gross error detection techniques, such as 'data-snooping,' simultaneously allows orientation based on similar model regions and localization of deformations. The magnitude of the latter is adequately estimated using the weight cofactor matrix of residuals. Experiments with simulated and actual deformations illuminate the potential of the approach for close-range photogrammetry.
We study the problem of creating a complete model of a physical object. Although this may be possible using intensity images, we here use images which directly provide access to three dimensional information. The first problem that we need to solve is to find the transformation between the different views. Previous approaches either assume this transformation to be known (which is extremely difficult for a complete model), or compute it with feature matching (which is not accurate enough for integration). In this paper, we propose a new approach which works on range data directly, and registers successive views with enough overlapping area to get an accurate transformation between views. This is performed by minimizing a functional which does not require point-to-point matches. We give the details of the registration method and modelling procedure, and illustrate them on real range images of complex objects.
This paper mathematically analyzes and proposes new solutions for the problem of estimating the camera 3D location and orientation (pose determination) from a matched set of 3D model and 2D image landmark features. Least-squares techniques for line tokens, which minimize both rotation and translation simultaneously, are developed and shown to be far superior to the earlier techniques which solved for rotation first and then translation. However, least-squares techniques fail catastrophically when outliers (or gross errors) are present in the match data. Outliers arise frequently due to incorrect correspondences or gross errors in the 3D model. Robust techniques for pose determination are developed to handle data contaminated by fewer than 50.0% outliers. Finally, the sensitivity of pose determination to incorrect estimates of camera parameters is analyzed. It is shown that for small field of view systems, offsets in the image center do not significantly affect the location of the camera in a world coordinate system. Errors in the focal length significantly affect only the component of translation along the optical axis in the pose computation.
Blunder detection is a topic of great interest to surveyors and mappers because undetected blunders significantly distort the solution. Therefore a robust testing procedure has been developed for the detection and identification of multiple blunders in survey data. In the method, the theories of robust estimation and statistical hypothesis testing are successfully integrated to provide a reliable and unified testing process, The method can be applied to the case of multiple blunders and can greatly improve the detection and isolation of blunders as compared to thc statistical testing of estimated residuals from a conventional least-squares process. The conventional least-squares procedure tends to smooth the blunder into good observations, whereas the proposed method does not. Two numerical examples are given to test and illustrate the performance of the proposed method for cases of single and multiple blunders.
There are many procedures for adjusting data and detecting the presence of blunders in a set of observations. Most such procedures involve examining the adjustment results for residuals whose magnitude is in some sense "large." In data snooping, each residual is divided by its own standard deviation, resulting in a statistic whose distribution is known. Thus blunder detection becomes a statistical hypothesis testing problem. In iterated data snooping, only the observation with the largest normalized residual is deleted at each iteration. The residuals may be either from a conventional least-squares LS adjustment or from an "L1 norm" adjustment that seeks to minimize the sum of absolute values of residuals. Iterated data snooping with the LS residuals is at least as effective as any other method of detecting blunders. We show by example that it can produce much better results than the L1 norm adjustment. Both forms of data snooping are superior to the many empirical or approximate methods that are still widely used.
A method for using digital elevation models (DEMs) as exclusive information for absolute orientation of stereo models is investigated. The discrete first derivatives of the DEMs (the slopes) are used in the observation equations. The method gave an accuracy comparable to or better than traditional absolute orientation with natural or signalized control points. Some possible areas of application are in satellite photogrammetry, in small scale topographic mapping with aerial photogrammetry, and in close-range photogrammetry in real-time, for instance, in quality control. -Authors
A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
1 Introduction.- 1.1 The Input.- 1.2 Issues in Shape Description.- 1.2.1 Criteria for shape description.- 1.2.2 Choosing segmented surface descriptions.- 1.3 Issues of Recognition.- 1.3.1 Description of models.- 1.3.2 Matching primitives and algorithms.- 1.4 Questions for the Research.- 1.5 The Contribution of the Research.- 1.6 Organization of the Book.- 2 Survey of Previous Work.- 2.1 Survey of Shape Descriptions.- 2.1.1 Volume descriptions.- 2.1.2 Curve/line descriptions.- 2.1.3 Surface descriptions.- 2.1.4 Summary.- 2.2 Survey of Recognition Systems.- 2.2.1 3DPO.- 2.2.2 Nevatia and Binford.- 2.2.3 ACRONYM.- 2.2.4 Extended Gaussian Image (EGI).- 2.2.5 Oshima and Shirai.- 2.2.6 Grimson and Lozano-Perez.- 2.2.7 Faugeras and Hebert.- 2.2.8 Bhanu.- 2.2.9 Ikeuchi.- 2.2.10 Summary.- 3 Surface Segmentation and Description.- 3.1 Curvature Properties and Surface Discontinuities.- 3.2 Detecting Surface Features.- 3.2.1 Method 1: using directional curvatures and scale-space tracking.- 3.2.2 Method 2: using principal curvatures at a single scale.- 3.2.3 Method 3: using anisotropic filtering.- 3.3 Space Grouping.- 3.4 Spatial Linking.- 3.5 Segmentation into Surface Patches.- 3.6 Surface Fitting.- 3.7 Object Inference.- 3.7.1 Labeling boundaries.- 3.7.2 Occlusion and connectivity.- 3.7.3 Inferring and describing objects.- 3.8 Representing Objects by Attributed Graphs.- 3.8.1 Node attributes.- 3.8.2 Link attributes.- 4 Object Recognition.- 4.1 Representation of Models.- 4.2 Overview of the Matching Process.- 4.3 Module 1: Screener.- 4.4 Module 2: Graph Matcher.- 4.4.1 Compatibility between nodes of the model view and scene graph.- 4.4.2 Compatibility between two pairs of matching nodes.- 4.4.3 Computing the geometric transform.- 4.4.4 Modifications based on the geometric transform.- 4.4.5 Measuring the goodness of a match.- 4.5 Module 3: Analyzer.- 4.5.1 Splitting objects.- 4.5.2 Merging objects.- 4.6 Summary.- 5 Experimental Results.- 5.1 The Models.- 5.2 A Detailed Case Study.- 5.2.1 Search nodes expanded in recognition.- 5.3 Results for Other Scenes.- 5.4 Parallel Versus Sequential Search.- 5.5 Unknown Objects.- 5.6 Occlusion.- 6 Discussion and Conclusion.- 6.1 Discussion.- 6.1.1 Problems of segmentation.- 6.1.2 Problems of approximation.- 6.2 Contribution.- 6.3 Future Research.- 6.3.1 From surface to volume.- 6.3.2 Applications.- A Directional Curvatures.- B Surface Curvature.- C Approximation by Quadric Surfaces.
If photogrammetry is to be applied to applications such as machine vision, industrial inspection, or medical analysis, more diverse three-dimensional model matching procedures need to be developed. Further, automatic surface difference detection should also be incorporated into the derived algorithms in order to accommodate the requirements of these new applications.This paper reviews a wide range of literature and presents the current status of three-dimensional model matching. A comparison is made between two-dimensional and three-dimensional matching for the purpose of delineating and similarities and differences. Finally, an algorithm developed by the author for surface matching is also discussed.
This paper describes a general purpose, representation independent
method for the accurate and computationally efficient registration of
3-D shapes including free-form curves and surfaces. The method handles
the full six-degrees of freedom and is based on the iterative closest
point (ICP) algorithm, which requires only a procedure to find the
closest point on a geometric entity to a given point. The ICP algorithm
always converges monotonically to the nearest local minimum of a
mean-square distance metric, and experience shows that the rate of
convergence is rapid during the first few iterations. Therefore, given
an adequate set of initial rotations and translations for a particular
class of objects with a certain level of 'shape complexity', one can
globally minimize the mean-square distance metric over all six degrees
of freedom by testing each initial registration. For examples, a given
'model' shape and a sensed 'data' shape that represents a major portion
of the model shape can be registered in minutes by testing one initial
translation and a relatively small set of rotations to allow for the
given level of model complexity. One important application of this
method is to register sensed data from unfixtured rigid objects with an
ideal geometric model prior to shape inspection. The described method is
also useful for deciding fundamental issues such as the congruence
(shape equivalence) of different geometric representations as well as
for estimating the motion between point sets where the correspondences
are not known. Experimental results show the capabilities of the
registration algorithm on point sets, curves, and surfaces.
An approach for the recognition of multiple three-dimensional
object models from three-dimensional scene data is presented. The
authors work on dense data, but neither the models nor the scene data
have to be complete. The problem is addressed in a realistic
environment: the viewpoint is arbitrary, the objects vary widely in
complexity, and no assumptions about the structure of the surface are
made. The approach is novel in that it uses two different types of
primitives for matching: small surface patches, where differential
properties can be reliably computed, and lines corresponding to depth or
orientation discontinuities. These are represented by splashes and 3-D
curves respectively. It is shown how both of these primitives can be
encoded by a set of super segments, consisting of connected linear
segments. These super segments are entered into a hash table, and
provide the essential mechanism for fast retrieval and matching
The problem of matching range images of human faces for the
purpose of establishing a correspondence between similar features of two
faces is addressed. Distinct facial features correspond to convex
regions of the range image of the face, which is obtained by a
segmentation of the range image based on the sign of the mean and
Gaussian curvature at each point. Each convex region is represented by
its extended Gaussian image, a 1-1 mapping between points of the region
and points on the unit sphere that have the same normal. Several issues
are examined that are associated with the difficult problem of
interpolation of the values of the extended Gaussian image and its
representation. A similarity measure between two regions is obtained by
correlating their extended Gaussian images. To establish the optimal
correspondence, a graph matching algorithm is applied. It uses the
correlation matrix between convex regions of the two faces and
incorporates additional relational constraints that account for the
relative spatial locations of the convex regions in the domain of the
range image
A terrain matching algorithm has been developed for use in a
passive aircraft navigation system. A sequence of aerial, optical images
is matched to a reference digital map of the three-dimensional terrain.
Stereo analysis of successive images results in the recovery of an
elevation map of the observed terrain. A `cliff map' is then used as a
novel, compact representation of the terrain surface. The position and
heading of the aircraft are determined via a terrain matching algorithm
that locates the observed cliff map within the reference cliff map.
Novel results using real terrain data and on implementation of a real
stereo algorithm provide an important extension to previous results
using simulated stereo
An algorithm is presented which uses Gaussian curvature for
extracting special points on the terrain, and then uses these points for
recognition of particular regions of the terrain. The Gaussian curvature
is chosen because it is invariant under isometry, which includes
rotation and translation. In the Gaussian curvature image, the points of
maximum and minimum curvature are extracted and used for matching. The
stability of the position of these points in the presence of noise with
resampling is investigated. The Gaussian curvature is calculated from
the 3-D digital terrain data by fitting a quadratic surface over a
square window and calculating directional derivatives of this surface. A
method of surface fitting which is invariant to coordinate system
transformation is suggested and implemented. This method involves
finding an optimal directional in which the fitting is performed
MINPRAN is a new robust estimator capable of finding good fits in
data sets containing more than 50% outliers. Unlike other techniques
that handle large outlier percentages, MINPRAN does not rely on a known
error bound for the good data. Instead, it assumes the bad data are
randomly distributed within the dynamic range of the sensor. Based on
this, MINPRAN uses random sampling to search for the fit and the inliers
to the fit that are least likely to have occurred randomly. It runs in
time O(N2+SN log N), where S is the number of random samples
and N is the number of data points. We demonstrate analytically that
MINPRAN distinguished good fits to random data and MINPRAN finds
accurate fits and nearly the correct number of inliers, regardless of
the percentage of true inliers. We confirm MINPRAN's properties
experimentally on synthetic data and show it compares favorably to least
median of squares. Finally, we apply MINPRAN to fitting planar surface
patches and eliminating outliers in range data taken from complicated
scenes
This paper mathematically analyzes and proposes new solutions for the problem of estimat- ing the camera 3D location and orientation (Pose Deter'migrations) from a matched set of 3D model and 2D image landmark features. Least-squares techniques for line tokens, which minimize both rotation and translation simultaneously, are developed and shown to be far superior to the earlier techniques which solved for rotation first and then translation. However, least-squares techniques fail catastrophically when outliers (or gross errors) are present in the match data. Outliers arise frequently due to incorrect correspondences or gross errors in the 3D model. Robust techniques for pose determination are developed to handle data contaminated by fewer than 50.0 % outliers.
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