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CorAl – Are the point clouds Correctly Aligned?
... However, without ground truth and user intervention, most registration methods cannot tell whether the point sets are correctly aligned solely based on the values of their metrics. Recently, several approaches [6], [15], [17] have been proposed that utilize different spatial properties of points to assess pair-wise registration qualities in the absence of ground truth and user intervention. These approaches further advance registration studies toward full automation. ...
... In addition, few of them consider registration quality assessments in the absence of ground truth and user intervention. The recently proposed pair-wise registration quality assessments [6], [15], [17] can be applied to sequentially check the alignment accu- Fig. 2. An example of using the proposed method to align four bunny scans. ...
... Recently, a few studies have devoted efforts to resolving this problem. The method called CorAl in [17] checks the pair-wise registration accuracy based on the joint and separate entropy of point sets, where a classifier needs to be pre-trained to detect misalignment. In [6], a pair-wise registration method called TEASER++ is developed that can certify the optimum of its registration metric. ...
This article studies group-wise point set registration and makes the following contributions: ``FuzzyGReg'', which is a new fuzzy cluster-based method to register multiple point sets jointly, and ``FuzzyQA'', which is the associated quality assessment to check registration accuracy automatically. Given a group of point sets, FuzzyGReg creates a model of fuzzy clusters and equally treats all the point sets as the elements of the fuzzy clusters. Then, the group-wise registration is turned into a fuzzy clustering problem. To resolve this problem, FuzzyGReg applies a fuzzy clustering algorithm to identify the parameters of the fuzzy clusters while jointly transforming all the point sets to achieve an alignment. Next, based on the identified fuzzy clusters, FuzzyQA calculates the spatial properties of the transformed point sets and then checks the alignment accuracy by comparing the similarity degrees of the spatial properties of the point sets. When a local misalignment is detected, a local re-alignment is performed to improve accuracy. The proposed method is cost-efficient and convenient to be implemented. In addition, it provides reliable quality assessments in the absence of ground truth and user intervention. In the experiments, different point sets are used to test the proposed method and make comparisons with state-of-the-art registration techniques. The experimental results demonstrate the effectiveness of our method.
The code is available at https://gitsvn-nt.oru.se/qianfang.liao/FuzzyGRegWithQA
... Some examples of methods that have been used in practice to assess the alignment quality include point-to-point or point-to-plane distances [9], [10], point-to-distribution [11], [12] or distribution-to-distribution [13], [14] likelihood estimates, mean map entropy [15] or dense radar-image comparison [16]. However, except for some notable exceptions [12], [17], few studies in the literature have specifically and methodically targeted the measurement of alignment correctness. ...
... In short, our previous contribution was an intuitive and simple measure of alignment correctness between point cloud pairs that generalizes across environments and highlights regions of misalignment. This paper extends our previous work on CorAl [17] by showing how it can be applied to FMCW (frequency-modulated continuous wave) radar data, thus pushing further towards truly robust perception, and includes quantitative evaluations on two new largescale benchmarks and four new baselines. In summarize, we present the following new contributions: ...
... In a similar vein, Liao et al. [14] propose distribution-todistribution registration based on fuzzy clusters, and estimate coarse alignment quality via the dispersion and disposition of points around fuzzy cluster centers. These methods have also been shown to generalize poorly for assessing 3D lidar scan alignment in different environments [17]. ...
Robust perception is an essential component to enable long-term operation of mobile robots. It depends on failure resilience through reliable sensor data and preprocessing, as well as failure awareness through introspection, for example the ability to self-assess localization performance. This paper presents CorAl: a principled, intuitive, and generalizable method to measure the quality of alignment between pairs of point clouds, which learns to detect alignment errors in a self-supervised manner. CorAl compares the differential entropy in the point clouds separately with the entropy in their union to account for entropy inherent to the scene. By making use of dual entropy measurements, we obtain a quality metric that is highly sensitive to small alignment errors and still generalizes well to unseen environments. In this work, we extend our previous work on lidar-only CorAl to radar data by proposing a two-stage filtering technique that produces high-quality point clouds from noisy radar scans. Thus we target robust perception in two ways: by introducing a method that introspectively assesses alignment quality, and applying it to an inherently robust sensor modality. We show that our filtering technique combined with CorAl can be applied to the problem of alignment classification, and that it detects small alignment errors in urban settings with up to 98% accuracy, and with up to 96% if trained only in a different environment. Our lidar and radar experiments demonstrate that CorAl outperforms previous methods both on the ETH lidar benchmark, which includes several indoor and outdoor environments, and the large-scale Oxford and MulRan radar data sets for urban traffic scenarios The results also demonstrate that CorAl generalizes very well across substantially different environments without the need of retraining.
... A comparative evaluation of several misaligned point cloud detection methods for point cloud registration problem, where multiple point clouds need to be aligned or merged together is presented in [106]. Similarly, in [107], researchers proposed a novel system to detect alignment errors in point cloud registration. They later extended their work to incorporate RADAR in [108]. ...
Automated driving systems (ADSs) aim to improve the safety, efficiency and comfort of future vehicles. To achieve this, ADSs use sensors to collect raw data from their environment. This data is then processed by a perception subsystem to create semantic knowledge of the world around the vehicle. State-of-the-art ADSs’ perception systems often use deep neural networks for object detection and classification, thanks to their superior performance compared to classical computer vision techniques. However, deep neural network-based perception systems are susceptible to errors, e.g., failing to correctly detect other road users such as pedestrians. For a safety-critical system such as ADS, these errors can result in accidents leading to injury or even death to occupants and road users. Introspection of perception systems in ADS refers to detecting such perception errors to avoid system failures and accidents. Such safety mechanisms are crucial for ensuring the trustworthiness of ADSs. Motivated by the growing importance of the subject in the field of autonomous and automated vehicles, this paper provides a comprehensive review of the techniques that have been proposed in the literature as potential solutions for the introspection of perception errors in ADSs. We classify such techniques based on their main focus, e.g., on object detection, classification and localisation problems. Furthermore, this paper discusses the pros and cons of existing methods while identifying the research gaps and potential future research directions.
... Similarly, [15] relies on the condition number to determine the health of the optimization process and includes partial constraints along non-degenerate direction for sensor fusion. Other methods, such as [16,17] rely on the final alignment of scans to capture the adequacy of geometric constraints provided by the environment for correct solution convergence. However, all these methods either rely on the point cloud registration process or its result to determine the performance of the pose estimation process, and do not exploit the information provided by the point cloud data directly to facilitate the estimation process itself. ...
LiDAR-based localization and mapping is one of the core components in many modern robotic systems due to the direct integration of range and geometry, allowing for precise motion estimation and generation of high quality maps in real-time. Yet, as a consequence of insufficient environmental constraints present in the scene, this dependence on geometry can result in localization failure, happening in self-symmetric surroundings such as tunnels. This work addresses precisely this issue by proposing a neural network-based estimation approach for detecting (non-)localizability during robot operation. Special attention is given to the localizability of scan-to-scan registration, as it is a crucial component in many LiDAR odometry estimation pipelines. In contrast to previous, mostly traditional detection approaches, the proposed method enables early detection of failure by estimating the localizability on raw sensor measurements without evaluating the underlying registration optimization. Moreover, previous approaches remain limited in their ability to generalize across environments and sensor types, as heuristic-tuning of degeneracy detection thresholds is required. The proposed approach avoids this problem by learning from a collection of different environments, allowing the network to function over various scenarios. Furthermore, the network is trained exclusively on simulated data, avoiding arduous data collection in challenging and degenerate, often hard-to-access, environments. The presented method is tested during field experiments conducted across challenging environments and on two different sensor types without any modifications. The observed detection performance is on par with state-of-the-art methods after environment-specific threshold tuning 1.
... Similarly, [15] relies on the condition number to determine the health of the optimization process and includes partial constraints along non-degenerate direction for sensor fusion. Other methods, such as [16,17] rely on the final alignment of scans to capture the adequacy of geometric constraints provided by the environment for correct solution convergence. However, all these methods either rely on the point cloud registration process or its result to determine the performance of the pose estimation process, and do not exploit the information provided by the point cloud data directly to facilitate the estimation process itself. ...
LiDAR-based localization and mapping is one of the core components in many modern robotic systems due to the direct integration of range and geometry, allowing for precise motion estimation and generation of high quality maps in real-time. Yet, as a consequence of insufficient environmental constraints present in the scene, this dependence on geometry can result in localization failure, happening in self-symmetric surroundings such as tunnels. This work addresses precisely this issue by proposing a neural network-based estimation approach for detecting (non-)localizability during robot operation. Special attention is given to the localizability of scan-to-scan registration, as it is a crucial component in many LiDAR odometry estimation pipelines. In contrast to previous, mostly traditional detection approaches, the proposed method enables early detection of failure by estimating the localizability on raw sensor measurements without evaluating the underlying registration optimization. Moreover, previous approaches remain limited in their ability to generalize across environments and sensor types, as heuristic-tuning of degeneracy detection thresholds is required. The proposed approach avoids this problem by learning from a corpus of different environments, allowing the network to function over various scenarios. Furthermore, the network is trained exclusively on simulated data, avoiding arduous data collection in challenging and degenerate, often hard-to-access, environments. The presented method is tested during field experiments conducted across challenging environments and on two different sensor types without any modifications. The observed detection performance is on par with state-of-the-art methods after environment-specific threshold tuning.
Odometry is crucial for robot navigation, particularly in situations where global positioning methods like global positioning system are unavailable. The main goal of odometry is to predict the robot’s motion and accurately determine its current location. Various sensors, such as wheel encoder, inertial measurement unit (IMU), camera, radar, and Light Detection and Ranging (LiDAR), are used for odometry in robotics. LiDAR, in particular, has gained attention for its ability to provide rich three-dimensional (3D) data and immunity to light variations. This survey aims to examine advancements in LiDAR odometry thoroughly. We start by exploring LiDAR technology and then scrutinize LiDAR odometry works, categorizing them based on their sensor integration approaches. These approaches include methods relying solely on LiDAR, those combining LiDAR with IMU, strategies involving multiple LiDARs, and methods fusing LiDAR with other sensor modalities. In conclusion, we address existing challenges and outline potential future directions in LiDAR odometry. Additionally, we analyze public datasets and evaluation methods for LiDAR odometry. To our knowledge, this survey is the first comprehensive exploration of LiDAR odometry.
This paper presents CorAl: a principled, intuitive, and generalizable method to measure the quality of alignment between pairs of point clouds, which learns to detect alignment errors in a self-supervised manner. CorAl compares the differential entropy in the point clouds separately with the entropy in their union to account for entropy inherent to the scene. By making use of dual entropy measurements, we obtain a quality metric that is highly sensitive to small alignment errors and still generalizes well to unseen environments. In this work, we extend our previous work on lidar-only CorAl to radar data by proposing a two-step filtering technique that produces highquality point clouds from noisy radar scans. Thus we target robust perception in two ways: by introducing a method that introspectively assesses alignment quality, and applying it to inherently robust sensor modalities. We show that our filtering technique combined with CorAl can be applied to the problem of alignment classification, and detect small alignment errors in urban settings with up to 98% accuracy, and with up to 96% if trained only in a different environment. Our lidar and radar experiments demonstrate that CorAl outperforms previous methods both on the ETH lidar benchmark, which includes several indoor and outdoor environments, and the large-scale Oxford and MulRan radar data sets for urban traffic scenarios, and also enables a high degree of generalization across substantially different environments without the need of retraining.
This study presents a new point set registration method to align 3D range scans. Fuzzy clusters are utilized to represent a scan, and the registration of two given scans is realized by minimizing a fuzzy weighted sum of the distances between their fuzzy cluster centers. This metric has a broad basin of convergence and is robust to noise. Moreover, it provides analytic gradients, allowing standard gradient-based algorithms to be applied for optimization. For the first time in rigid point set registration, a registration quality assessment in the absence of ground truth is provided. Given specified rotation and translation spaces, we derive the upper and lower bounds of the fuzzy cluster-based metric and develop a branch-and-bound (BnB)-based optimization scheme, which can globally minimize the metric regardless of the initialization. This optimization scheme is performed in an efficient coarse-to-fine fashion: First, fuzzy clustering is applied to describe each of the two given scans by a small number of fuzzy clusters. Then, a global search, which integrates BnB and gradient-based algorithms, is implemented to achieve a coarse alignment for the two scans. During the global search, the registration quality assessment offers a beneficial stop criterion to detect whether a good result is obtained.
Modern 3D laser-range scanners have a high data rate, making online simultaneous localization and mapping (SLAM) computationally challenging. Recursive state estimation techniques are efficient but commit to a state estimate immediately after a new scan is made, which may lead to misalignments of measurements. We present a 3D SLAM approach that allows for refining alignments during online mapping. Our method is based on efficient local mapping and a hierarchical optimization back-end. Measurements of a 3D laser scanner are aggregated in local multiresolution maps by means of surfel-based registration. The local maps are used in a multi-level graph for allocentric mapping and localization. In order to incorporate corrections when refining the alignment, the individual 3D scans in the local map are modeled as a sub-graph and graph optimization is performed to account for drift and misalignments in the local maps. Furthermore, in each sub-graph, a continuous-time representation of the sensor trajectory allows to correct measurements between scan poses. We evaluate our approach in multiple experiments by showing qualitative results. Furthermore, we quantify the map quality by an entropy-based measure.
Local scan registration approaches commonly
only utilize ego-motion estimates (e.g. odometry) as an
initial pose guess in an iterative alignment procedure. This
paper describes a new method to incorporate ego-motion
estimates, including uncertainty, into the objective function of a
registration algorithm. The proposed approach is particularly
suited for feature-poor and self-similar environments,
which typically present challenges to current state of the
art registration algorithms. Experimental evaluation shows
significant improvements in accuracy when using data acquired
by Automatic Guided Vehicles (AGVs) in industrial production
and warehouse environments.
3D laser scanners are frequently used sensors for mobile robots or autonomous cars and they are often used to perceive the static as well as dynamic aspects in the scene. In this context, matching 3D point clouds of objects is a crucial capability. Most matching methods such as numerous flavors of ICP provide little information about the quality of the match, i.e. how well do the matched objects correspond to each other, which goes beyond point-to-point or point-to-plane distances. In this paper, we propose a projective method that yields a probabilistic measure for the quality of matched scans. It not only considers the differences in the point locations but can also take free-space information into account. Our approach provides a probabilistic measure that is meaningful enough to evaluate scans and to cluster real-world data such as scans taken with Velodyne scanner in urban scenes in an unsupervised manner.
Matching and merging overlapping point clouds is a common procedure in many applications, including mobile robotics, three-dimensional mapping, and object visualization. However, fully automatic point-cloud matching, without manual verification, is still not possible because no matching algorithms exist today that can provide any certain methods for detecting misaligned point clouds. In this article, we make a comparative evaluation of geometric consistency methods for classifying aligned and nonaligned point-cloud pairs. We also propose a method that combines the results of the evaluated methods to further improve the classification of the point clouds. We compare a range of methods on two data sets from different environments related to mobile robotics and mapping. The results show that methods based on a Normal Distributions Transform representation of the point clouds perform best under the circumstances presented herein.
The number of registration solutions in the literature has bloomed recently. The iterative closest point, for example, could be considered as the backbone of many laser-based localization and mapping systems. Although they are widely used, it is a common challenge to compare registration solutions on a fair base. The main limitation is to overcome the lack of accurate ground truth in current data sets, which usually cover environments only over a small range of organization levels. In computer vision, the Stanford 3D Scanning Repository pushed forward point cloud registration algorithms and object modeling fields by providing high-quality scanned objects with precise localization. We aim to provide similar high-caliber working material to the robotic and computer vision communities but with sceneries instead of objects. We propose eight point cloud sequences acquired in locations covering the environment diversity that modern robots are susceptible to encounter, ranging from inside an apartment to a woodland area. The core of the data sets consists of 3D laser point clouds for which supporting data (Gravity, Magnetic North and GPS) are given for each pose. A special effort has been made to ensure global positioning of the scanner within mm-range precision, independent of environmental conditions. This will allow for the development of improved registration algorithms when mapping challenging environments, such as those found in real-world situations.
Existing methods for estimating the covariance of the ICP (iterative closest/corresponding point) algorithm are either inaccurate or are computationally too expensive to be used online. This paper proposes a new method, based on the analysis of the error function being minimized. It considers that the correspondences are not independent (the same measurement being used in more than one correspondence), and explicitly utilizes the covariance matrix of the measurements, which are not assumed to be independent either. The validity of the approach is verified through extensive simulations: it is more accurate than previous methods and its computational load is negligible. The ill-posedness of the surface matching problem is explicitly tackled for under-constrained situations by performing an observability analysis; in the analyzed cases the method still provides a good estimate of the error projected on the observable manifold.
This paper presents a new generalisation of simultaneous localisation and mapping (SLAM). SLAM implementations based on extended Kalman filter (EKF) data fusion have traditionally relied on simple geometric models for defining landmarks. This limits EKF-SLAM to environments
suited to such models and tends to discard much potentially useful data. The approach presented in this paper is a marriage
of EKF-SLAM with scan correlation. Instead of geometric models, landmarks are defined by templates composed of raw sensed
data, and scan correlation is shown to produce landmark observations compatible with the standard EKF-SLAM framework. The
resulting Scan-SLAM combines the general applicability of scan correlation with the established advantages of an EKF implementation: recursive
data fusion that produces a convergent map of landmarks and maintains an estimate of uncertainties and correlations. Experimental
results are presented which validate the algorithm.
Scan registration is an essential subtask when building maps based on range finder data from mobile robots. The problem is to deduce how the robot has moved between con- secutive scans, based on the shape of overlapping portions of the scans. This paper pre- sents a new algorithm for registration of 3D data. The algorithm is a generalization and improvement of the normal distributions transform NDT for 2D data developed by Biber and Strasser, which allows for accurate registration using a memory-efficient rep- resentation of the scan surface. A detailed quantitative and qualitative comparison of the new algorithm with the 3D version of the popular ICP iterative closest point algorithm is presented. Results with actual mine data, some of which were collected with a new prototype 3D laser scanner, show that the presented algorithm is faster and slightly more reliable than the standard ICP algorithm for 3D registration, while using a more memory- efficient scan surface representation. © 2007 Wiley Periodicals, Inc.
We introduce a labeled point set registration algorithm based on a family of novel information-theoretic measures derived as a generalization of the well-known Shannon entropy. This generalization, known as the Havrda-Charvat-Tsallis entropy, permits a fine-tuning between solution types of varying degrees of robustness of the divergence measure between multiple point sets. A variant of the traditional free-form deformation approach, known as directly manipulated free-form deformation, is used to model the transformation of the registration solution. We provide an overview of its open source implementation based on the Insight Toolkit of the National Institutes of Health. Characterization of the proposed framework includes comparison with other state of the art kernel-based methods and demonstration of its utility for lung registration via labeled point set representation of lung anatomy.
We propose a novel technique for the registration of 3D point clouds which makes very few assumptions: we avoid any manual rough alignment or the use of landmarks, displacement can be arbitrarily large, and the two point sets can have very little overlap. Crude alignment is achieved by estimation of the 3D-rotation from two Extended Gaussian Images even when the data sets inducing them have partial overlap. The technique is based on the correlation of the two EGIs in the Fourier domain and makes use of the spherical and rotational harmonic transforms. For pairs with low overlap which fail a critical verification step, the rotational alignment can be obtained by the alignment of constellation images generated from the EGIs. Rotationally aligned sets are matched by correlation using the Fourier transform of volumetric functions. A fine alignment is acquired in the final step by running Iterative Closest Points with just few iterations.
This paper addresses the range image registration problem for views having low overlap and which may include substantial noise. The current state of the art in range image registration is best represented by the well-known iterative closest point (ICP) algorithm and numerous variations on it. Although this method is effective in many domains, it nevertheless suffers from two key limitations: It requires prealignment of the range surfaces to a reasonable starting point and it is not robust to outliers arising either from noise or low surface overlap. This paper proposes a new approach that avoids these problems. To that end, there are two key, novel contributions in this work: a new, hybrid genetic algorithm (GA) technique, including hillclimbing and parallel-migration, combined with a new, robust evaluation metric based on surface interpenetration. Up to now, interpenetration has been evaluated only qualitatively; we define the first quantitative measure for it. Because they search in a space of transformations, GAs are capable of registering surfaces even when there is low overlap between them and without need for prealignment. The novel GA search algorithm we present offers much faster convergence than prior GA methods, while the new robust evaluation metric ensures more precise alignments, even in the presence of significant noise, than mean squared error or other well-known robust cost functions. The paper presents thorough experimental results to show the improvements realized by these two contributions.
Matching 2D range scans is a basic component of many localization and mapping algorithms. Most scan match algorithms require finding correspondences between the used features, i.e. points or lines. We propose an alternative representation for a range scan, the normal distributions transform. Similar to an occupancy grid, we subdivide the 2D plane into cells. To each cell, we assign a normal distribution, which locally models the probability of measuring a point. The result of the transform is a piecewise continuous and differentiable probability density, that can be used to match another scan using Newton's algorithm. Thereby, no explicit correspondences have to be established. We present the algorithm in detail and show the application to relative position tracking and simultaneous localization and map building (SLAM). First results on real data demonstrate, that the algorithm is capable to map unmodified indoor environments reliable and in real time, even without using odometry data.
The authors describe 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 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. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces
This letter introduces a framework for evaluation of the losses used in point set registration. In order for a loss to be useful with a local optimizer, such as e.g. Levenberg-Marquardt, or expectation maximization (EM), it must be monotonic with respect to the sought transformation. This motivates us to introduce
monotonicity violation probability
(MVP) curves, and use these to assess monotonicity empirically for many different local distances, such as point-to-point, point-to-plane, and plane-to-plane. We also introduce a local shape-to-shape distance, based on the Wasserstein distance of the local normal distributions. Evaluation is done on a comprehensive benchmark of terrestrial lidar scans from two publicly available datasets. It demonstrates that matching robustness can be improved significantly, by using kernel versions of local distances together with inverse density based sample weighting.
The ability to maintain and continuously update geometric calibration parameters of a mobile platform is a key functionality for every robotic system. These parameters include the intrinsic kinematic parameters of the platform, the extrinsic parameters of the sensors mounted on it, and their time delays. In this letter, we present a unified pipeline for motion-based calibration of mobile platforms equipped with multiple heterogeneous sensors. We formulate a unified optimization problem to concurrently estimate the platform kinematic parameters, the sensors extrinsic parameters, and their time delays. We analyze the influence of the trajectory followed by the robot on the accuracy of the estimate. Our framework automatically selects appropriate trajectories to maximize the information gathered and to obtain a more accurate parameters estimate. In combination with that, our pipeline observes the parameters evolution in long-term operation to detect possible values change in the parameters set. The experiments conducted on real data show a smooth convergence along with the ability to detect changes in parameters value. We release an open-source version of our framework to the community.
This paper addresses the problem of registering multiple point sets. Solutions to this problem are often approximated by repeatedly solving for pairwise registration, which results in an uneven treatment of the sets forming a pair: a model set and a data set. The main drawback of this strategy is that the model set may contain noise and outliers, which negatively affects the estimation of the registration parameters. In contrast, the proposed formulation treats all the point sets on an equal footing. Indeed, all the points are drawn from a central Gaussian mixture, hence the registration is cast into a clustering problem. We formally derive batch and incremental EM algorithms that robustly estimate both the GMM parameters and the rotations and translations that optimally align the sets. Moreover, the mixture's means play the role of the registered set of points while the variances provide rich information about the contribution of each component to the alignment. We thoroughly test the proposed algorithms on simulated data and on challenging real data collected with range sensors. We compare them with several state-of-the-art algorithms, and we show their potential for surface reconstruction from depth data.
Registration of Point Cloud Data (PCD) forms a core component of many 3D vision algorithms such as object matching and environment reconstruction. In this paper, we introduce a PCD registration algorithm that utilizes Gaussian Mixture Models (GMM) and a novel dual-mode parameter optimization technique which we call mixture decoupling. We show how this decoupling technique facilitates both faster and more robust registration by first optimizing over the mixture parameters (decoupling the mixture weights, means, and co variances from the points) before optimizing over the 6 DOF registration parameters. Furthermore, we frame both the decoupling and registration process inside a unified, dual-mode Expectation Maximization (EM) framework, for which we derive a Maximum Likelihood Estimation (MLE) solution along with a parallel implementation on the GPU. We evaluate our MLE-based mixture decoupling (MLMD) registration method over both synthetic and real data, showing better convergence for a wider range of initial conditions and higher speeds than previous state of the art methods.
The need to align multiple representations of anatomy is a problem frequently encountered in clinical applications. A new algorithm for feature-based registration is presented that solves this problem by aligning both position and orientation information of the shapes being registered.
The iterative most likely oriented-point (IMLOP) algorithm and its generalization (G-IMLOP) to the anisotropic noise case are described. These algorithms may be understood as probabilistic variants of the popular iterative closest point (ICP) algorithm. A probabilistic model provides the framework, wherein both position information and orientation information are simultaneously optimized. Like ICP, the proposed algorithms iterate between correspondence and registration subphases. Efficient and optimal solutions are presented for implementing each subphase of the proposed methods.
Experiments based on human femur data demonstrate that the IMLOP and G-IMLOP algorithms provide a strong accuracy advantage over ICP, with G-IMLOP providing additional accuracy improvement over IMLOP for registering data characterized by anisotropic noise. Furthermore, the proposed algorithms have increased ability to robustly identify an accurate versus inaccurate registration result.
The IMLOP and G-IMLOP algorithms provide a cohesive framework for incorporating orientation data into the registration problem, thereby enabling improvement in accuracy as well as increased confidence in the quality of registration outcomes. For shape data having anisotropic uncertainty in position and/or orientation, the anisotropic noise model of G-IMLOP enables further gains in registration accuracy to be achieved.
Rigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. These methods alternate between closest point computations to establish correspondences between two data sets, and solving for the optimal transformation that brings these correspondences into alignment. A major difficulty for this approach is the sensitivity to outliers and missing data often observed in 3D scans. Most practical implementations of the ICP algorithm address this issue with a number of heuristics to prune or reweight correspondences. However, these heuristics can be unreliable and difficult to tune, which often requires substantial manual assistance. We propose a new formulation of the ICP algorithm that avoids these difficulties by formulating the registration optimization using sparsity inducing norms. Our new algorithm retains the simple structure of the ICP algorithm, while achieving superior registration results when dealing with outliers and incomplete data. The complete source code of our implementation is provided at http://lgg.epfl.ch/sparseicp.
Registration of range sensor measurements is an important task in mobile robotics and has received a lot of attention. Several iterative optimization schemes have been proposed in order to align three-dimensional (3D) point scans. With the more widespread use of high-frame-rate 3D sensors and increasingly more challenging application scenarios for mobile robots, there is a need for fast and accurate registration methods that current state-of-the-art algorithms cannot always meet. This work proposes a novel algorithm that achieves accurate point cloud registration an order of a magnitude faster than the current state of the art. The speedup is achieved through the use of a compact spatial representation: the Three-Dimensional Normal Distributions Transform (3D-NDT). In addition, a fast, global-descriptor based on the 3D-NDT is defined and used to achieve reliable initial poses for the iterative algorithm. Finally, a closed-form expression for the covariance of the proposed method is also derived. The proposed algorithms are evaluated on two standard point cloud data sets, resulting in stable performance on a par with or better than the state of the art. The implementation is available as an open-source package for the Robot Operating System (ROS).
This paper is about assessing the quality of maps built by a mobile robot. We extend previous work, which used solely geometric considerations, and use both temporal and spatial properties of the map to perform a binary classification of "plausible" and "suspicious". The use of the former allows the existence of low quality areas of the map to be attributed to missed loop closure events or local, online mapping errors. With an eye on our intended domain of urban operation, we adopt a Conditional Random Field as the probabilistic framework in which to model the spatial and temporal relationships between planar patches. The map quality labels are derived by using standard graph cuts optimization techniques. The approach is then illustrated with map created of an urban environment using data from a 3D laser range scanner mounted on a mobile robot.
We have previously presented a new scan-matching algorithm based on the IDC (iterative dual correspondence) algorithm, which showed a good localization performance even in environments with severe changes. The problem of the IDC algorithm is that there is no good way to estimate a covariance matrix of the position estimate, which prohibits an effective fusion with other position estimates of other sensors. This paper presents two new ways to estimate the covariance matrix. The first estimates the covariance matrix from the Hessian matrix of the error function minimized by the scan-matching algorithm. The second one, which is an off-line method, estimates the covariance matrix of a specific scan, from a specific position by simulating and matching scans around the position. Simulation results show that the covariance matrix provided by the off-line method fully corresponds with the real one. Some preliminary tests on real data indicate that the off-line method gives a good quality value of a specific scan position, which is of great value in map building.
In this paper we combine the Iterative Closest Point ('ICP') and 'point-to-plane ICP' algorithms into a single probabilistic framework. We then use this framework to model locally planar surface structure from both scans instead of just the "model" scan as is typically done with the point-to-plane method. This can be thought of as 'plane-to-plane'. The new approach is tested with both simulated and real-world data and is shown to outperform both standard ICP and point-to-plane. Furthermore, the new approach is shown to be more robust to incorrect correspondences, and thus makes it easier to tune the maximum match distance parameter present in most variants of ICP. In addition to the demonstrated performance improvement, the proposed model allows for more expressive probabilistic models to be incorporated into the ICP framework. While maintaining the speed and simplicity of ICP, the Generalized-ICP could also allow for the addition of outlier terms, measurement noise, and other probabilistic techniques to increase robustness. I. INTRODUCTION
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.
The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minimization strategy. We enumerate and classify many of these variants, and evaluate their effect on the speed with which the correct alignment is reached. In order to improve convergence for nearly-flat meshes with small features, such as inscribed surfaces, we introduce a new variant based on uniform sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to real-time 3D model acquisition and model-based tracking
A series of analytical formulas for the entropy and mutual information of multivariate continuous probability distributions is presented. For the distributions considered, the entropy and the mutual information are defined for all values of the distribution parameters. This is not always the case for the variances and the covariances or even the means. Several nonparametric estimators for the differential entropy are developed. The bias of these estimators which proved to be consistent perform on finite samples. For the formulas given, it is possible to construct parametric entropy estimators.
The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minimization strategy. We enumerate and classify many of these variants, and evaluate their effect on the speed with which the correct alignment is reached. In order to improve convergence for nearly-flat meshes with small features, such as inscribed surfaces, we introduce a new variant based on uniform sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to real-time 3D model acquisition and model-based tracking.