Feature-based methods for non-rigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, feature-based non-rigid matching requires us to automatically solve for correspondences between two sets of features. In addition, there could be many features in either set that have no counterparts in the other. This outlier rejection problem further complicates an already di#cult correspondence problem. We formulate feature-based non-rigid registration as a non-rigid point matching problem. After a careful review of the problem and an in-depth examination of two types of methods previously designed for rigid robust point matching (RPM), we propose a new general framework for non-rigid point matching. We consider it a general framework because it does not depend on any particular form of spatial mapping. We have also developed an algorithm---the TPS-RPM algorithm---with the thin-plate spline (TPS) as the parameterization of the non-rigid spatial mapping and the softassign for the correspondence. The performance of the TPS-RPM algorithm is demonstrated and validated in a series of carefully designed synthetic experiments. In each of these experiments, an empirical comparison with the popular iterated closest point (ICP) algorithm is also provided. Finally, we apply the algorithm to the problem of non-rigid registration of cortical anatomical structures which is required in brain mapping. While these results are somewhat preliminary, they clearly demonstrate the applicability of our approach to real world tasks involving feature-based non-rigid registration.

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A new algorithm has been developed in this thesis for the non-rigid point matching problem. Designed as an integrated framework, the algorithm jointly estimates a one-to-one correspondence and a non-rigid transformation between two sets of points. The resulting algorithm is called “robust point matching (RPM) algorithm ” because of its capability to tolerate noise and to reject possible outliers existed within the data points. The algorithm is built upon the heuristic of “fuzzy correspondence”, which allows for multiple partial cor-respondences between points. With the help of the deterministic annealing technique, this new heuristic enables the algorithm to overcome many local minima that can be encountered in the matching process. Devised as a general point matching framework, the algorithm can be easily extended to accommodate differ-ent speci£c requirements in many registration applications. Firstly, the modular design of the transformation module enables convenient incorporation of different non-rigid splines. Secondly, the point matching algorithm can be easily extended into a symmetric joint clustering-matching framework. It will be shown that by introducing a super point-set, the joint cluster-matching extension can be applied to estimate an average shape point-set from multiple point shape sets. The algorithm is applied to the registration of 3D brain anatomical structures. We proposed in this work a joint feature registration framework, which is mainly based on the joint clustering-matching extension of the robust

We present a new superquadrics based object representation strategy for automotive parts in this paper. Starting from a 3D watertight surface model, a part decomposition step is first performed to segment the original multi-part objects into their constituent single parts. Each single part is then represented by a superquadric. The originalities of this approach include first, our approach can represent complicated shapes, e.g., multi-part objects, by utilizing part decomposition as a preprocessing step. Second, superquadrics recovered using our approach have the highest confidence and accuracy due to the 3D watertight surfaces utilized. A novel, generic 3D part decomposition algorithm based on curvature analysis is also proposed in this paper. The proposed part decomposition algorithm is generic and flexible due to the popularity of triangle meshes in the 3D computer community. The proposed algorithms were tested on a large set of 3D data and experimental results are presented. The experimental results demonstrate that our proposed part decomposition algorithm can segment complicated shapes, in our case automotive parts, efficiently into meaningful single parts. And our proposed superquadric representation strategy can then represent each part (if possible) of the complicated objects successfully.

. We construct probabilistic generative models for the nonrigid matching of point-sets. Our formulation is explicitly Platonist. Beginning with a Platonist super point-set, we derive real-world point-sets through the application of four operations: i) spline-based warping, ii) addition of noise, iii) point removal and iii) amnesia regarding the pointto -point correspondences between the real-world point-sets and the Platonist source. Given this generative model, we are able to derive new non-quadratic distance measures w.r.t. the "forgotten" correspondences by a) eliminating the spline parameters from the generative model and by b) integrating out the Platonist super point-set. The result is a new non-quadratic distance measure which has the interpretation of weighted graph matching. The graphs are related in a straightfoward manner to the spline kernel used for non-rigid warping. Experimentally, we show that the new distance measure outperforms the conventional quadratic assignment di...

Deformable models are central to non-rigid motion analysis, shape matching and non-rigid medical image registration. Spline-based deformations are a very popular class of parameterizations of deformable models and have been heavily used in multiple domains. In a somewhat separate sub-field, weighted graphs are a frequently used object parameterization. Graph matching using weighted graph object parameterizations finds application in a spectrum ranging from rigid pose estimation to deformable object recognition. Here, we demonstrate a hitherto unsuspected relationship between spline-based deformable models and weighted graphs. It turns out that spline parameterizations in the kernel representation can be used to construct equivalent weighted graphs. With this connection established, we envision a cross-fertilization between these two seemingly disparate sub-fields of computer vision.

We present a new robust point matching algorithm (RPM) that can jointly estimate the correspondence and non-rigid transformations between two point-sets that may be of dierent sizes. The algorithm utilizes the softassign for the correspondence and the thinplate spline for the non-rigid mapping. Embedded within a deterministic annealing framework, the algorithm can automatically reject a fraction of the points as outliers. Experiments on both 2D synthetic pointsets with varying degrees of deformation, noise and outliers, and on real 3D sulcal point-sets (extracted from brain MRI) demonstrate the robustness of the algorithm. 1 Introduction It is a fundamental yet still open problem in computer vision to match two point-sets, i.e, to nd the geometric mapping and correspondence between two sets of points in 2D or in 3D [11]. There are various factors that make the point matching problem dicult. One such factor is the existence of outliersmany point features may exist in one point-set ...

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