We investigate in this article the rigid registration of large sets of points, generally sampled from surfaces. We formulate this problem as a general Maximum-Likelihood (ML) estimation of the transformation and the matches. We show that, in the specific case of a Gaussian noise, it corresponds to the Iterative Closest Point algorithm (ICP) with the Mahalanobis distance.

We describe a linear-time algorithm that recovers absolute camera orientations and positions, along with uncertainty estimates, for networks of terrestrial image nodes spanning hundreds of meters in outdoor urban scenes. The algorithm produces pose estimates globally consistent to roughly 0.1 # (2 milliradians) and 5 centimeters on average, or about four pixels of epipolar alignment.

We introduce Coherent Point Drift (CPD), a novel probabilistic method for non-rigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coher-ence constraint over the velocity field such that one point set moves coherently to align with the second set. We formulate the motion coherence constraint and derive a solution of regularized ML estimation through the variational approach, which leads to an elegant kernel form. We also derive the EM algorithm for the penalized ML optimization with deterministic annealing. The CPD method simultaneously finds both the non-rigid transformation and the correspondence between two point sets without making any prior assumption of the transformation model except that of motion coherence. This method can estimate complex non-linear non-rigid transformations, and is shown to be accurate on 2D and 3D examples and robust in the presence of outliers and missing points.

We describe a linear-time algorithm that recovers absolute camera positions for networks of thousands of terrestrial images spanning hundreds of meters, in outdoor urban scenes, under varying lighting conditions. The algorithm requires no human input or interaction. It is robust to up to 80% outliers for synthetic data. For real data, it recovers camera pose which is globally consistent on average to roughly 0.1 # and five centimeters, or about four pixels of epipolar alignment, expending a few CPUhours of computation on a 250MHz processor. This paper's principal contributions include an extension of Monte Carlo Markov Chain estimation techniques to the case of unknown numbers of feature points, unknown occlusion and deocclusion, and large scale (thousands of images, and hundreds of thousands of point features) and dimensional extent (tens of meters of inter-camera baseline, and hundreds of meters of baseline overall). Also, a principled method is given to manage uncertainty on the sphere of directions; a new use of the Hough Transform is proposed; and a method for aggregating local baseline constraints into a globally consistent constraint set is described. The algorithm takes intrinsic calibration information, and a connected, rotationally registered image network as input. It then assembles local, purely translational motion estimates into a global constraint set, and determines camera positions with respect to a single scene-wide coordinate system. The algorithm's output is an assignment of metric, accurate 6-DOF camera pose, along with its uncertainty, to every image. We assume that the scene exhibits local point features for probabilistic matching, and that adjacent cameras observe overlapping portions of the scene; no further assumptions are made about scene str...

Automatic localisation of correspondences for the construction of Statistical Shape Models from examples has been the focus of intense research during the last decade. Several algorithms are available and benchmarking is needed to rank the different algorithms. Prior work has focused on evaluating the quality of the models produced by the algorithms by measuring compactness, generality and specificity. In this paper problems with these standard measures are discussed. We propose that a ground truth correspondence measure (gcm) is used for benchmarking and in this paper benchmarking is performed on several state of the art algorithms. Minimum Description Length (MDL) with a curvature cost comes out as the winner of the automatic methods. Hand marked models turn out to be best but a semi-automatic method is shown to lie in between the best automatic method and the hand built models in performance.

Abstract. We propose the use of a particle filter as a solution to the rigid shapebased registration problem commonly found in computer-assisted surgery. This approach is especially useful where there are only a few registration points corresponding to only a fraction of the surface model. Tests performed on patient models, with registration points collected during surgery, suggest that particle filters perform well and also provide novel quality measures to the surgeon. 1

In this report, we first propose a new classification of non-rigid registration algorithms into three main categories: in one hand, the geometric algorithms, and in the other hand, intensity based methods that we split here into standard intensity-based (SIB) and pair-and-smooth (P&S) algorithms. We then focus on the subset of SIB and P&S...

We investigate in this research report the rigid registration of a set of points with a surface for computer-guided oral implants surgery. We first formulate the Iterative Closest Point (ICP) algorithm as a Maximum Likelihood (ML) estimation of the transformation and the matches. Then, considering matches as a hidden random variable, we show that the ML estimation of the transformation alone leads to a criterion efficiently solved using an Expectation-Maximisation (EM) algorithm. This algorithm implies a new parameter, based on the standard-deviation of the noise on points position. We demonstrate that, for small values, the algorithm behaves like the accurate ICP, while, for high values, the algorithm robustly aligns the barycenter and inertia moments. Finaly, this parameter is decreased using an annealing scheme, which can be seen as a kind of multi-scale scheme. We present besides an efficient way to use oriented points - like surface points with their normals - instead of points with ICP and EM algorithms. The experimental section provides evidences that the EM algorithm is far more robust and more accurate than ICP and reaches a global accuracy of 0.2 mm with computation times compatible with a per-operative system. Another important property is that the criterion analysis enables an easy distinction between correct results and false postives.

Abstract. This paper presents a new segmentation algorithm which combines active shape model and robust point matching techniques. It can use any simple feature detector to extract a large number of feature points in the image. Robust point matching is then used to search for the correspondences between feature and model points while the model is being deformed along the modes of variation of the active shape model. Although the algorithm is generic, it is particularly suited for medical imaging applications where prior knowledge is available. The value of the proposed method is examined with two different medical imaging modalities (Ultrasound, MRI) and in both 2D and 3D. The experiments have shown that the proposed algorithm is immune to missing feature points and noise. It has demonstrated significant improvements when compared to RPM-TPS and ASM alone. 1

Shape database search is ubiquitous in the world of biometric systems, CAD systems etc. Shape data in these domains is experiencing an explosive growth and usually requires search of whole shape databases to retrieve the best matches with accuracy and efficiency for a variety of tasks. In this paper, we present a novel divergence measure between any two given points in Rn or two distribution functions. This divergence measures the orthogonal distance between the tangent to the convex function (used in the definition of the divergence) at one of its input arguments and its second argument. This is in contrast to the ordinate distance taken in the usual definition of the Bregman class of divergences [4]. We use this orthogonal distance to redefine the Bregman class of divergences and develop a new theory