Point Matching Based On Non-Parametric Model

Point matching, which aims to establish correspondence between two given point sets, is a fundamental and critical problem in the areas of computer vision and pattern recogni-tion. It has recently received a lot of attentions in a wide range of applications including stereo matching, object recognition and tracking, medical image analysis, remote sensing image processing, etc. Point matching is essentially an NPC complicate combinatorial opti-mization problem with large computation; and due to the existence of noise, outliers, as well as unknown deformations, the performances of point matching algorithms are often badly degraded, which limits theirs applicabilities in practical engineering problems. Therefore, researching universal, efficient and robust point matching methods has high theoretic signif-icance and practical values.In order to efficiently handle the effects of noise, outliers and non-rigid deformations in point matching, this dissertation aims to research robust point matching methods for general tasks. To this end, in the dissertation, several novel algorithms are proposed based on non-parametric model, and are applied to image feature point matching, non-rigid point set registration, as well as non-rigid image registration. The experimental results on various2D and3D cases show that the proposed methods outperforms many state-of-the-art methods. The main works and contributions of this dissertation are as follows.First, the problem of vector field interpolation is carefully studied in the framework of regularization and the representer theorem. A robust vector field interpolation algorithm VFC is proposed, which is able to handle a very large number of outliers. To improve the efficiency of kernel-based methods, the dissertation introduces a sparse approximation, which significantly reduces the time and space complexities (from O(N3) and O(N2) to both O(N)) without much performance degradation. A statistical learning bound on the speed of the convergence is also derived for the sparse approximation.Second, as an application, the dissertation demonstrates the effectiveness of VFC in solving the problem of image feature matching, and gives some theoretical and empirical evidences to justify the reasonability of VFC for point matching. Moreover, the dissertation generalizes VFC to parametric models and a multi-layer motion model, and hence compen-sates for its weaknesses in some special cases. The qualitative and quantitative comparisons with other state-of-the-art methods demonstrate the advantages of VFC in solving various point matching problems, including image pairs of homography, wide baseline image pairs, image pairs of non-rigid objects, image pairs with severe outliers,3D image pairs, etc.Third, a robust L2E estimator is introduced for the point matching problem. A robust point matching method RPM-L2E is proposed and applied to non-rigid sparse correspon-dence such as point set registration and sparse image feature correspondence, as well as non-rigid dense correspondence such as image registration. Experiments on public datasets demonstrate that the proposed approach yields results superior to those of state-of-the-art methods when there is significant noise, occlusions, outliers, rotations, and/or scale changes in the data.Fourth, the dissertation studies a traditional problem in the areas of computer graphics and image processing-non-rigid image deformation, and proposes a deformation method MRLS based on moving regularized least squares. It is able to generate detail-preserving and intuitive deformations, and is extremely computationally efficient which can be per-formed in real-time. Therefore, MRLS can not only provide experimental data for quantita-tively evaluation of image registration methods, but also has potential values in some other applications such as animation, reshaping human body, medical image analysis, etc.At last, a non-rigid point set registration method PR-GLS is proposed based on preserving global and local structures. It formulates point registration as the estimation of a mixture of densities, combines with soft-assignment under a uniform framework to estimate the correspondence and transformation between two points, and hence improves the match-ing performance. Comparing to RPM-L2E and other state-of-the-art methods, PR-GLS is able to produce much better performance when there is very serious degeneration in the data.