Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.
There are many heuristic or stochastic methods for global alignment that are not guaranteed to converge. One class utilises stochastic optimisation techniques, such as particle filtering @cite_37 , genetic algorithms @cite_45 @cite_62 and simulated annealing @cite_43 @cite_31 . Another class is feature-based alignment, which exploits the transformation invariance of a local descriptor to build sparse feature correspondences, such as fast point feature histograms @cite_42 . The transformation can be found from the correspondences using random sampling @cite_42 , greedy algorithms @cite_39 , Hough transforms @cite_4 or branch-and-bound @cite_17 @cite_40 . @cite_58 is a recent example of a method that uses random sampling without features. It is a four-points congruent sets method that exploits a clever data structure to achieve linear-time performance, extending the original 4PCS algorithm @cite_7 .
@cite_37 @cite_62 @cite_4 @cite_7 @cite_42 @cite_39 @cite_43 @cite_40 @cite_45 @cite_31 @cite_58 @cite_17
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In this paper, we propose a new algorithm for pairwise rigid point set registration with unknown point correspondences. The main properties of our method are noise robustness, outlier resistance and global optimal alignment. The problem of registering two point clouds is converted to a minimization of a nonlinear cost function. We propose a new cost function based on an inverse distance kernel that significantly reduces the impact of noise and outliers. In order to achieve a global optimal registration without the need of any initial alignment, we develop a new stochastic approach for global minimization. It is an adaptive sampling method which uses a generalized BSP tree and allows for minimizing nonlinear scalar fields over complex shaped search spaces like, e.g., the space of rotations. We introduce a new technique for a hierarchical decomposition of the rotation space in disjoint equally sized parts called spherical boxes. Furthermore, a procedure for uniform point sampling from spherical boxes is presented. Tests on a variety of point sets show that the proposed registration method performs very well on noisy, outlier corrupted and incomplete data. For comparison, we report how two state-of-the-art registration algorithms perform on the same data sets. Most range data registration techniques are variants on the iterative closest point (ICP) algorithm, proposed by Y. Chen and G. Medioni (1991, Proceedings of the IEEE Conference on Robotics and Automation) and P. J. Besl and N. D. McKay ( 1992, IEEE Trans. Pattern Anal. Mach. Intell. 14, 239-256). That algorithm, though, is only one approach to optimizing a least-squares point correspondence sum proposed by K. S. Arun. T. Huang, and S. D. Blostein (1987, IEEE Trans. Pattern Anal. Mach. Intell, 9, 698-700). In its basic form ICP has many problems, for example, its reliance on preregistration by hand close to the global minimum and its tendency to converge to suboptimal or incorrect solutions. This paper reports on an evolutionary registration algorithm which does not require initial prealignment and has a very broad basin of convergence. It searches many areas of a registration parameter space in parallel and has available to it a selection of evolutionary techniques to avoid local minima which plague both ICP and its variants. In applying the Hough transform to the problem of 3D shape recognition and registration, we develop two new and powerful improvements to this popular inference method. The first, intrinsic Hough, solves the problem of exponential memory requirements of the standard Hough transform by exploiting the sparsity of the Hough space. The second, minimum-entropy Hough, explains away incorrect votes, substantially reducing the number of modes in the posterior distribution of class and pose, and improving precision. Our experiments demonstrate that these contributions make the Hough transform not only tractable but also highly accurate for our example application. Both contributions can be applied to other tasks that already use the standard Hough transform. We introduce 4PCS, a fast and robust alignment scheme for 3D point sets that uses wide bases, which are known to be resilient to noise and outliers. The algorithm allows registering raw noisy data, possibly contaminated with outliers, without pre-filtering or denoising the data. Further, the method significantly reduces the number of trials required to establish a reliable registration between the underlying surfaces in the presence of noise, without any assumptions about starting alignment. Our method is based on a novel technique to extract all coplanar 4-points sets from a 3D point set that are approximately congruent, under rigid transformation, to a given set of coplanar 4-points. This extraction procedure runs in roughly O(n2 + k) time, where n is the number of candidate points and k is the number of reported 4-points sets. In practice, when noise level is low and there is sufficient overlap, using local descriptors the time complexity reduces to O(n + k). We also propose an extension to handle similarity and affine transforms. Our technique achieves an order of magnitude asymptotic acceleration compared to common randomized alignment techniques. We demonstrate the robustness of our algorithm on several sets of multiple range scans with varying degree of noise, outliers, and extent of overlap. In our recent work [1], [2], we proposed Point Feature Histograms (PFH) as robust multi-dimensional features which describe the local geometry around a point p for 3D point cloud datasets. In this paper, we modify their mathematical expressions and perform a rigorous analysis on their robustness and complexity for the problem of 3D registration for overlapping point cloud views. More concretely, we present several optimizations that reduce their computation times drastically by either caching previously computed values or by revising their theoretical formulations. The latter results in a new type of local features, called Fast Point Feature Histograms (FPFH), which retain most of the discriminative power of the PFH. Moreover, we propose an algorithm for the online computation of FPFH features for realtime applications. To validate our results we demonstrate their efficiency for 3D registration and propose a new sample consensus based method for bringing two datasets into the convergence basin of a local non-linear optimizer: SAC-IA (SAmple Consensus Initial Alignment). We present a 3D shape-based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion. Recognition is based on matching surfaces by matching points using the spin image representation. The spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes. We present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models. Furthermore, we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes. Concerns the problem of range image registration for the purpose of building surface models of 3D objects. The registration task involves finding the translation and rotation parameters which properly align overlapping views of the object so as to reconstruct from these partial surfaces, an integrated surface representation of the object. The registration task is expressed as an optimization problem. We define a function which measures the quality of the alignment between the partial surfaces contained in two range images as produced by a set of motion parameters. This function computes a sum of Euclidean distances from control points on one surfaces to corresponding points on the other. The strength of this approach is in the method used to determine point correspondences. It reverses the rangefinder calibration process, resulting in equations which can be used to directly compute the location of a point in a range image corresponding to an arbitrary point in 3D space. A stochastic optimization technique, very fast simulated reannealing (VFSR), is used to minimize the cost function. Dual-view registration experiments yielded excellent results in very reasonable time. A multiview registration experiment took a long time. A complete surface model was then constructed from the integration of multiple partial views. The effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3D objects must be constructed. > A popular approach to detect outliers in a data set is to find the largest consensus set, that is to say maximizing the number of inliers and estimating the underlying model. RANSAC is the most widely used method for this aim but is non-deterministic and does not guarantee to return the optimal solution. In this paper, we consider a rotation model and we present a new approach that performs consensus set maximization in a mathematically guaranteed globally optimal way. We solve the problem by a branch-and-bound framework associated with a rotation space search. Our mathematical formulation can be applied for various computer vision tasks such as panoramic image stitching, 3D registration with a rotating range sensor and line clustering and vanishing point estimation. Experimental results with synthetic and real data sets have successfully confirmed the validity of our approach. 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 hill climbing 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, GA 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. Data acquisition in large-scale scenes regularly involves accumulating information across multiple scans. A common approach is to locally align scan pairs using Iterative Closest Point (ICP) algorithm (or its variants), but requires static scenes and small motion between scan pairs. This prevents accumulating data across multiple scan sessions and or different acquisition modalities (e.g., stereo, depth scans). Alternatively, one can use a global registration algorithm allowing scans to be in arbitrary initial poses. The state-of-the-art global registration algorithm, 4PCS, however has a quadratic time complexity in the number of data points. This vastly limits its applicability to acquisition of large environments. We present Super 4PCS for global pointcloud registration that is optimal, i.e., runs in linear time (in the number of data points) and is also output sensitive in the complexity of the alignment problem based on the (unknown) overlap across scan pairs. Technically, we map the algorithm as an 'instance problem' and solve it efficiently using a smart indexing data organization. The algorithm is simple, memory-efficient, and fast. We demonstrate that Super 4PCS results in significant speedup over alternative approaches and allows unstructured efficient acquisition of scenes at scales previously not possible. Complete source code and datasets are available for research use at http: geometry.cs.ucl.ac.uk projects 2014 super4PCS . We present an algorithm for the automatic alignment of two 3D shapes (data and model), without any assumptions about their initial positions. The algorithm computes for each surface point a descriptor based on local geometry that is robust to noise. A small number of feature points are automatically picked from the data shape according to the uniqueness of the descriptor value at the point. For each feature point on the data, we use the descriptor values of the model to find potential corresponding points. We then develop a fast branch-and-bound algorithm based on distance matrix comparisons to select the optimal correspondence set and bring the two shapes into a coarse alignment. The result of our alignment algorithm is used as the initialization to ICP (iterative closest point) and its variants for fine registration of the data to the model. Our algorithm can be used for matching shapes that overlap only over parts of their extent, for building models from partial range scans, as well as for simple symmetry detection, and for matching shapes undergoing articulated motion.