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Surface Reconstruction from LiDAR Data with Extended Snake Theory
Abstract
Surface reconstruction from implicit data of sub-randomly distributed 3D points is the key work of extracting explicit information
from LiDAR data. This paper proposes an approach of extended snake theory to surface reconstruction from LiDAR data. The proposed
algorithm approximates a surface with connected planar patches. Growing from an initial seed point, a surface is reconstructed
by attaching new adjacent planar patches based on the concept of minimizing the deformable energy. A least-squares solution
is sought to keep a local balance of the internal and external forces, which are inertial forces maintaining the flatness
of a surface and pulls of observed LiDAR points bending the growing surface toward observations. Experiments with some test
data acquired with a ground-based LiDAR demonstrate the feasibility of the proposed algorithm. The effects of parameter settings
on the delivered results are also investigated.
... When this data is studied interactively it is easy to form a mental image of the geometry of the scene. The collection of 3D points gives insight into the surfaces that were sampled, and many methods have been proposed to automatically detect these surfaces [12] [14]. ...
... When this data is studied interactively it is easy to form a mental image of the geometry of the scene. The collection of 3D points gives insight into the surfaces that were sampled, and many methods have been proposed to automatically detect these surfaces [12, 14]. One influential group of methods is the methods based on RANSAC [3] , which uses a minimal random sample to define a surface and iterates to find the surface containing most points. ...
... One influential group of methods is the methods based on RANSAC [3] , which uses a minimal random sample to define a surface and iterates to find the surface containing most points. Another group of methods is based on region growing [14], which initializes a bounded surface at a certain point and tries to expand this while maintaining some constraint like maximal deviation from the surface in location or normal. Finally , Funke, Malamatos, and Ray [4] give an approximation algorithm for finding a connected component with comparable normals in a triangulation. ...
Laser range imaging is an upcoming data source for many elds of research. Although many methods are proposed for nding surfaces and classifying points, nding the bounds of these surfaces is still a dicult problem. We propose a method for nding, in a point set of size n, a rectangle that contains a predened subset of the points and none of the other points in O(n logn) time. Further, there may not be places in the rectangle that are too far from all points in the predened subset.
... While interactive methods like SmartBoxes [14] significantly speed up manual reconstruction, their reliance on a human operator makes them less appropriate for handling massive datasets within limited time. Recent research into automatic geometry reconstruction from laser range scans has focused on smooth sur- faces [2, 11, 20] . A likely reason for using smooth surfaces is that traditionally most high-density laser range scans were made using close range measurements of natural objects in a controlled environment. ...
... In other cases, our building shapes are not limited to models determined a priori. Some earlier methods for urban reconstruction classify data points into vegetation and buildings, and cluster the data set into a point set per surface [16, 20] . However , limited effort has been invested in creating an ex-plicit geometric boundary for these clusters. ...
In urban scenes, many of the surfaces are planar and bounded by simple shapes. In a laser scan of such a scene, these simple shapes can still be identified. We present a one-parameter algorithm that can identify point sets on a plane for which a rectangle is a fitting boundary. These rectangles have a guaranteed density: no large part of the rectangle is empty of points. We prove that our algorithm identifies all angles for which a rectangle fits the point set of size n in O(nlogn) time. We evaluate our method experimentally on 13 urban data sets and we compare the rectangles found by our algorithm to the @a@?shape as a surface boundary.
... The angular difference between the two unit normal vectors ̃ and ̃ are calculated by computing the inverse cosine of the dot product of the two vectors as in Equation (1) [14], [23], [24]. The angle can be in the range from the degree of 0 o to 90 o , corresponding from the lowest dissimilarity to the highest dissimilarity between the tendencies of the two planes. ...
Processing of 3D point cloud data is seen as a problem due to the difficulties of processing millions of unstructured points. The point cloud segmentation process is a crucial pre-classification stage such that it reduces the high processing time required to extract meaningful information from raw data and produces some distinctive features for the classification stage. Local surface inclinations of objects are the most effective features of 3D point clouds to provide meaningful information about the objects. Sampling the points into sub-volumes (voxels) is a technique commonly used in the literature to obtain the required neighboring point groups to calculate local surface directions (with normal vectors). The graph-based segmentation approaches are widely used for the surface segmentation using the attributes of the local surface orientations and continuities. In this study, only two geometrical primitives which are normal vectors and barycenters of point groups are used to weight the connections between the adjacent voxels (vertices). The defined 14 possible dissimilarity calculations of three angular values getting from the primitives are experimented and evaluated on five sample datasets that have reference data for segmentation. Finally, the results of the measures are compared in terms of accuracy and F1 score. According to the results, the weight measure W7 (seventh calculation) gives 0.8026 accuracy and 0.7305 F1 score with higher standard deviations, while the original weight measure (W8) of the segmentation method gives 0.7890 accuracy and 0.6774 F1 score with lower standard deviations.
... Apart from digital images, few methods based on active contour models have also been developed for extracting features from LiDAR data. [40] proposed an approach for surface reconstruction from LiDAR data. In their algorithm, a surface was grown from an initial seed point in the LiDAR data based on the extended snake model. ...
Active contour models present a robust segmentation approach which make efficient use of specific information about objects in the input data rather than processing all the data. They have been widely used in many applications including image segmentation, object boundary localisation, motion tracking, shape modelling, stereo matching and object reconstruction. In this paper, we investigate the potential of active contour models in extracting roads from Mobile Laser Scanning (MLS) data. The categorisation of active contours based on their mathematical representation and implementation are discussed in detail. We discuss an integrated version in which active contour models are combined to overcome their limitations. We review various active contour based methodologies which have been developed to extract roads and other features from LiDAR and digital imaging datasets. We present a small case study in which an integrated version of active contour models is applied to automatically extract road edges from MLS dataset. An accurate extraction of left and right edges from the tested road section validates the use of active contour models. The present study provides a valuable insight on the potential of active contours for extracting roads and other infrastructures from 3D LiDAR point cloud data.
... If θ is found to be greater than 90, the value of θ is replaced with the value that is supplementary of itself. The value of θ ranges from 0 to 90 ( Tseng, Tang, & Chou, 2007 ). ...
In 3D point cloud processing, the spatial continuity of points is convenient for segmenting point clouds obtained by 3D laser scanners, RGB-D cameras and LiDAR (light detection and ranging) systems in general. In real life, the surface features of both objects and structures give meaningful information enabling them to be identified and distinguished. Segmenting the points by using their local plane directions (normals), which are estimated by point neighborhoods, is a method that has been widely used in the literature. The angle difference between two nearby local normals allows for measurement of the continuity between the two planes. In real life, the surfaces of objects and structures are not simply planes. Surfaces can also be found in other forms, such as cylinders, smooth transitions and spheres. The proposed voxel-based method developed in this paper solves this problem by inspecting only the local curvatures with a new merging criteria and using a non-sequential region growing approach. The general prominent feature of the proposed method is that it mutually one-to-one pairs all of the adjoining boundary voxels between two adjacent segments to examine the curvatures of all of the pairwise connections. The proposed method uses only one parameter, except for the parameter of unit point group (voxel size), and it does not use a mid-level over-segmentation process, such as supervoxelization. The method checks the local surface curvatures using unit normals, which are close to the boundary between two growing adjacent segments. Another contribution of this paper is that some effective solutions are introduced for the noise units that do not have surface features. The method has been applied to one indoor and four outdoor datasets, and the visual and quantitative segmentation results have been presented. As quantitative measurements, the accuracy (based on the number of true segmented points over all points) and F1 score (based on the means of precision and recall values of the reference segments) are used. The results from testing over five datasets show that, according to both measurement techniques, the proposed method is the fastest and achieves the best mean scores among the methods tested.
... Second, for the growing criteria, the similarity of normal vectors and the distance between neighbor points and the current region are widely adopted [30][31][32]. Alternatively, neighboring patches can be applied to growing regions [33] based on minimizing the deformable energy. Third, as the region grows larger, the fitting error also monotonically increases, and the termination criteria are determined by the largest error. ...
Oblique photogrammetric point clouds are currently one of the major data sources for the three-dimensional level-of-detail reconstruction of buildings. However, they are severely noise-laden and pose serious problems for the effective and automatic surface extraction of buildings. In addition, conventional methods generally use normal vectors estimated in a local neighborhood, which are liable to be affected by noise, leading to inferior results in successive building reconstruction. In this paper, we propose an intact planar abstraction method for buildings, which explicitly handles noise by integrating information in a larger context through global optimization. The information propagates hierarchically from a local to global scale through the following steps: first, based on voxel cloud connectivity segmentation, single points are clustered into supervoxels that are enforced to not cross the surface boundary; second, each supervoxel is expanded to nearby supervoxels through the maximal support region, which strictly enforces planarity; third, the relationships established by the maximal support regions are injected into a global optimization, which reorients the local normal vectors to be more consistent in a larger context; finally, the intact planar surfaces are obtained by region growing using robust normal and point connectivity in the established spatial relations. Experiments on the photogrammetric point clouds obtained from oblique images showed that the proposed method is effective in reducing the influence of noise and retrieving almost all of the major planar structures of the examined buildings.
... Straight lines were fitted to the linearly clustered data using slope information for extracting the road surface area. Tseng et al. (2007) developed an approach for surface reconstruction from terrestrial LiDAR data. In their approach, a surface was grown from an initial seed point in the LiDAR data based on the extended snake model. ...
The applicability of Mobile Laser Scanning (MLS) systems continue to prove their worth in route corridor mapping due to the rapid, continuous and cost effective 3D data acquisition capability. LiDAR data provides a number of attributes which can be useful for extracting various road features. Road edge is a fundamental feature and its accurate knowledge increases the reliability and precision of extracting other road features. We developed an automated algorithm for extracting left and right edges from MLS data. The algorithm involved several input parameters which are required to be analysed in order to find their optimal values. In this paper, we present a detailed analysis of the dimension parameters of input data and raster cell in our algorithm. These parameters were analysed based on temporal, completeness and accuracy performance of our algorithm for their different sets of values. This analysis provided the estimation of an optimal values of parameters which were used to automate the process of extracting road edges from MLS data.
We introduce the concept of -sleeves as a variation on the well-known -shapes. The concept is used to develop a simple algorithm for constructing a rectilinear polygon inside a plane; such an algorithm can be used to delineate a building facet inside a single plane in 3D from a set of points obtained from LiDAR scanning. We explain the algorithm, analyse different parameter settings on artificial data, and show some results on LiDAR data.
The demand for large geometric models is increasing, especially of urban environments. This has resulted in production of massive point cloud data from images or LiDAR. Visualization and further processing generally require a detailed, yet concise representation of the scene's surfaces. Related work generally either approximates the data with the risk of over‐smoothing, or interpolates the data with excessive detail. Many surfaces in urban scenes can be modeled more concisely by planar approximations. We present a method that combines these polygons into a watertight model. The polygon‐based shape is closed with free‐form meshes based on visibility information. To achieve this, we divide 3‐space into inside and outside volumes by combining a constrained Delaunay tetrahedralization with a graph‐cut. We compare our method with related work on several large urban LiDAR data sets. We construct similar shapes with a third fewer triangles to model the scenes. Additionally, our results are more visually pleasing and closer to a human modeler's description of urban scenes using simple boxes.
Lidar (light detection and ranging) data implicitly contains abundant three-dimensional spatial information. The segmentation of lidar point clouds is the key procedure for transforming implicit spatial information into explicit spatial information. Common criteria used for point cloud segmentation are proximity and coherence of point distribution. An effective segmentation algorithm may apply various steps or combinations of criteria depending on the application. This paper proposes a four-step segmentation method for lidar point clouds to deliver incremental segmentation results. Segmentation results of each step can provide the fundamental data for the next step. In the first step, the input point cloud is organised into an octree-structured voxel space, in which the point neighbourhood is established. In the second step, connected voxels which are not empty are grouped to obtain grouped points based on proximity. The third step is a coplanar point segmentation based on both coherence and proximity, which was performed on each point group obtained in the second step. Finally, neighbouring coplanar point groups are merged into "co-surface" point groups based on the criteria of plane connection and intersection. This scheme enables an incremental retrieval and analysis of a large lidar data-set. Experimental results demonstrate the effectiveness of the segmentation algorithm in handling both airborne and terrestrial lidar data. It is anticipated that the incremental segmentation results will be useful for object modelling using lidar data.
Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct urban models. In urban scenes, the individual surfaces can be reconstructed and connected to form the scene geometry. There are various methods for reconstructing the free-form shape of a point sample on a single surface. However, these methods do not take the context of the surface into account. We present the guided α-shape: an extension of the well known α-shape that uses lines (guides) to indicate preferred locations for the boundary of the shape. The guided α-shape uses (parts of) these lines as boundary where the points suggest that this is appropriate. We prove that the guided α-shape can be constructed in O((n + m) log (n + m)) time, from an input of n points and m guides. We apply guided α-shapes to urban reconstruction from LiDAR, where neighboring surfaces can be connected conveniently along their intersection lines into adjacent surfaces of a 3D model. We analyze guided α-shapes of both synthetic and real data and show they are consistently better than α-shapes for this application.
Terrestrial laser scanners produce point clouds with a huge number of points within a very limited surrounding. In built-up areas, many of the man-made objects are dominated by planar surfaces. We introduce a RANSAC based preprocessing technique that transforms the irregular point cloud into a set of locally delimited surface patches in order to reduce the amount of data and to achieve a higher level of abstraction. In a second step, the resulting patches are grouped to large planes while ignoring small and irrelevant structures. The approach is tested with a dataset of a built-up area which is described very well needing only a small number of geometric primitives. The grouping emphasizes man-made structures and could be used as a preclassification
In this paper, we introduce a semi-automated topology generator for 3-D objects, CC-Modeler (CyberCity Modeler). Given the data as point clouds measured on Analytical Plotters or Digital Stations, we present a new method for fitting planar structures to the measured sets of point clouds. While this topology generator has been originally designed to model buildings, it can also be used for other objects, which may be approximated by polyhedron surfaces. We have used it so far for roads, rivers, parking lots, ships, etc. The CC-Modeler is a generic topology generator. The problem of fitting planar faces to point clouds is treated as a Consistent Labelling problem, which is solved by probabilistic relaxation. Once the faces are defined and the related points are determined, we apply a simultaneous least-squares adjustment in order to fit the faces jointly to the given measurements in an optimal way. We first present the processing flow of the CC-Modeler. Then, the algorithm of structuring the 3-D point data is outlined. Finally, we show the results of several data sets that have been produced with the CC-Modeler.
The authors present a physically based approach to fitting complex three-dimensional shapes using a novel class of dynamic models that can deform both locally and globally. The authors formulate deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The model's six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. The local deformation parameters reconstruct the details of complex shapes that the global abstraction misses. The equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces. The authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational, rotational, and deformational degrees of freedom of the models. The authors present model fitting experiments involving 2-D monocular image data and 3-D range data.
A physically-based approach is presented to fitting complex 3D
shapes using a novel class of dynamic models. These models can deform
both locally and globally. The authors formulate deformable
superquadrics which incorporate the global shape parameters of a
conventional superellipsoid with the local degrees of freedom of a
spline. The local/global representational power of a deformable
superquadric simultaneously satisfies the conflicting requirements of
shape reconstruction and shape recognition. The model's six global
deformational degrees of freedom capture gross shape features from
visual data and provide salient part descriptors for efficient indexing
into a database of stored models. Model fitting experiments involving 2D
monocular image data and 3D range data are reported
Light detection and ranging (LIDAR) techniques represent a new and fruitful approach in the determination of digital surface models. One of the goals in processing this data is to set up filtering methods which automatically allows to extract the ground and the features (buildings, vegetation, etc.) superimposed on the terrain itself. In our work the emphasis is focused on the first topic. The implemented method takes advantage of the use of spline functions regularised by means of Tychonov functional in a least-squares approach. Firstly, the DSM pixels have been classified in order to previously detect any edges of the non-terrain feature. Then all the pixels corresponding to the ground, by means of a region growing algorithm, has been identified through a correction procedure. Finally, by a new interpolation on the classified ground pixel only, we can derive the digital terrain model. In the paper the processing methodology is discussed; and a first extensive example is presented.
In this paper, we introduce a semi-automated topology generator for 3-D objects, CC-Modeler (CyberCity Modeler). Given the data as point clouds measured on Analytical Plotters or Digital Stations, we present a new method for fitting planar structures to the measured sets of point clouds. While this topology generator has been originally designed to model buildings, it can also be used for other objects, which may be approximated by polyhedron surfaces. We have used it so far for roads, rivers, parking lots, ships, etc. The CC-Modeler is a generic topology generator. The problem of fitting planar faces to point clouds is treated as a Consistent Labelling problem, which is solved by probabilistic relaxation. Once the faces are defined and the related points are determined, we apply a simultaneous least-squares adjustment in order to fit the faces jointly to the given measurements in an optimal way. We first present the processing flow of the CC-Modeler. Then, the algorithm of structuring the 3-D point data is outlined. Finally, we show the results of several data sets that have been produced with the CC-Modeler.
Airborne laser scanning represents a new and independent technology for the highly automated generation of digital terrain models (DTM) and surface models. The described technical features of airborne laser scanning outline the present fields of application. The primary application concerns the generation of high quality topographic DTMs, described by mostly regular grid patterns. It is the unique advantage of airborne laser scanning that is equally applicable to open terrain as well as to areas which are partly or completely by forest or other vegetation. Naturally, the interactive editing efforts in the latter case are higher. Another important application of laser scanning also concerns the generation of DTMs in coastal areas or wetlands.
We present an investigation on the use of Tensor Voting for categorizing LIDAR data into outliers, line elements (e.g. high-voltage power lines), surface patches (e.g. roofs) and volumetric elements (e.g. vegetation). The Reconstruction of man-made objects is a main task of photogrammetry. With the increasing quality and availability of LIDAR sensors, range data is becoming more and more important. With LIDAR sensors it is possible to quickly aquire huge amounts of data. But in contrast to classical systems, where the measurement points are chosen by an operator, the data points do not explicitly correspond to meaningful points of the object, i.e. edges, corners, junctions. To extract these features it is necessary to segment the data into homogeneous regions wich can be processed afterwards. Our approach consists of a two step segmentation. The first one uses the Tensor Voting algorithm. It encodes every data point as a particle which sends out a vector field. This can be used to categorize the pointness, edgeness and surfaceness of the data points. After the categorization of the given LIDAR data points also the regions between the data points are rated. Meaningful regions like edges and junctions, given by the inherent structure of the data, are extracted. In a second step the so labeled points are merged due to a similarity constraint. This similarity constraint is based on a minimum description length principle, encoding and comparing different geometrical models. The output of this segmentation consists of non overlapping geometric objects in three dimensional space. The aproach is evaluated with some examples of Lidar data.
Lidar (or laser scanning) has become a viable technique for the collection of a large amount of accurate 3D point data densely distributed on the scanned object surface. The inherent 3D nature of the sub-randomly distributed point cloud provides abundant spatial information. To explore valuable spatial information from laser scanned data becomes an active research topic. The sub-randomly distributed point cloud should be segmented and classified before the extraction of spatial information and the first step in the processing of the spatial data extraction is an organization of the lidar data. This paper proposes a new algorithm to split and merge the lidar data based on the octree structure. After the process a lidar data set can be segmented to 3D plane clusters and classified by the plane attributes derived from each 3D plane, such as area, gradient, intensity etc. Some example and analysis of practical data set will be performed for segmentation and classification using the proposed methods here. The test result shows the potential of applying this method to extracting spatial information from lidar data.
In this study, we implement and apply a region growing segmentation procedure based on texture to extract spatial landform objects from a light detection and ranging (LiDAR) digital surface model (DSM). The local binary pattern (LBP) operator, modeling texture, is integrated into a region growing segmentation algorithm to identify landform objects. We apply a multi-scale LBP operator to describe texture at different scales. The paper is illustrated with a case study that involves segmentation of coastal landform objects using a LiDAR DSM of a coastal area in the UK. Landform objects can be identified with the combination of a multi-scale texture measure and a region growing segmentation. We show that meaningful coastal landform objects can be extracted with this algorithm. Uncertainty values provide useful information on transition zones or fuzzy boundaries between objects.
This paper presents an algorithm for the segmentation of airborne laser scanning data. The segmentation is based on cluster analysis in a feature space. To improve the quality of the computed attributes, a recently proposed neighborhood system, called slope adaptive, is utilized. Key parameters of the laser data, e.g., point density, measurement accuracy, and horizontal and vertical point distribution, are used for defining the neighborhood among the measured points. Accounting for these parameters facilitates the computation of accurate and reliable attributes for the segmentation irrespective of point density and the 3D content of the data (step edges, layered surfaces, etc.) The segmentation with these attributes reveals more of the information that exists in the airborne laser scanning data.
This tutorial paper gives an introduction and overview of various topics related to airborne laser scanning (ALS) as used to measure range to and reflectance of objects on the earth surface. After a short introduction, the basic principles of laser, the two main classes, i.e., pulse and continuous-wave lasers, and relations with respect to time-of-flight, range, resolution, and precision are presented. The main laser components and the role of the laser wavelength, including eye safety considerations, are explained. Different scanning mechanisms and the integration of laser with GPS and INS for position and orientation determination are presented. The data processing chain for producing digital terrain and surface models is outlined. Finally, a short overview of applications is given.
A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scale-space continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest.
Deformable models have raised much interest and found various applications in the fields of computer vision and medical imaging. They provide an extensible framework to reconstruct shapes. Deformable surfaces, in particular, are used to represent 3D objects. They have been used for pattern recognition [35,2], computer animation [100], geometric modelling [59], simulation [28], boundary tracking [11], image segmentation [69,67,91,5,45], etc. In this paper we propose a survey on deformable surfaces. Many surface representation have been proposed to meet different 3D reconstruction problem requirements. We classify the main representations proposed in the literature and we study the influence of the representation on the model evolution behavior, revealing some similarities between different approaches.
Deformable models are a powerful and popular tool for image segmentation, but in 3D imaging applications the high computational cost of fitting such models can be a problem. A further drawback is the need to select the initial size and position of a model in such a way that it is close to the desired solution. This task may require particular expertise on the part of the operator, and, furthermore, may be difficult to accomplish in three dimensions without the use of sophisticated visualisation techniques. This article describes a 3D deformable model that uses an adaptive mesh to increase computational efficiency and accuracy. The model employs a distance transform in order to overcome some of the problems caused by inaccurate initialisation. The performance of the model is illustrated by its application to the task of segmentation of 3D MR images of the human head and hand. A quantitative analysis of the performance is also provided using a synthetic test image.
In this paper, a simple method for direct acquisition of a cloud of points from an object surface is presented together with a novel surface reconstruction algorithm used to obtain an explicit 3D model for the measured object. This technique is aimed at relatively accurate but simple and reliable 3D reconstruction of anatomical parts for biomedical applications. The whole system is based on acquisition of unorganized range data by laser scanning and successive image processing, by expanding and fitting a regular geometrical model within the range data, for surface reconstruction. The prototype system proved to be working finely, with an estimated resolution <10 mum, a repeatability <50mum, an acquisition noise of ~17 mum (rms value), and accuracy of ~80 mum
Surface Clustering from Airborne Laser Scanning Data. International Archives of Photogrammetry and Remote Sensing
- S Filin
- S. Filin
Dynamic 3D models with local and global deformations: deformable Superquadrics
- G Terzopoulous
- D Metaxas
- G. Terzopoulous