The Research On Point Pattern Matching

Point Pattern Matching (PPM) is one of important and fundamental problems incomputer vision and pattern recognition, which is widely used in many applications,such as imaging registration, stereovision, image retrieval, object recognition andtracking, medical imaging analysis, image matching for navigation, etc. It is still achallenging task due to the existence of the noise, the outliers and the missing points inthe extracted point pattern from the realistic applications; moreover, the geometricdeformation between point pattern can also be from the low-dimensional rigidtransformations to the high-dimensional non-rigid transformations.Considering the difficulties of current point pattern mathing methods andaccording to the diversity of geometric distortion, the thesis lucubrates on the rigid andnon-rigid point pattern matching problems respectively, and then develops a series ofnew and robust point pattern matching methods, which can be suitable for differentgeometirc transformations.In the research on the problems of PPM which under similarity transformations,the thesis firstly propose a new point-set based invariant feature which name as RelativeShape Context (RSC). After combining the invariant feture with probabilistic relaxationlabelling and spectral matching method, the thesis presents one PPM algorithm whichbased on relative shape context and probabilistic relaxation labelling (RSC-PRL) andthe other PPM algorithm which based on relative shape context and spectral matchingmethod respectively. Compared with the other classical PPM methods under similaritytransformation, the two proposed novel methods all are more robust to noise andoutliers, and even can be applicable to some certain extant of pespective distortion.Under the same parameters setup, the RSC-PRL method is more robust to outliers thanthe RSC-SM method and inversely the RSC-SM method is more robust to noise thanthe RSC-PRL method.In the research on the problems of PPM which under affine transformations, theCoherent Point Drift (CPD) is one of popular point pattern matching algorithms becauseof its robustness. However, The CPD is local optimization and its convergent rate isslower along with the size of point-set become larger. For resolving these problems, thethesis develops a Global Optimal and Fast algorithm which based on CPD (GOF-CPD).The orthogonal normalization first reduce the general affine case to the orthogonal case,and the convex region boundary of the unoberserved data’s logarithmic likelihoodnearby the global optimal solutions are deduced by the properties of normalizedpoint-sets. Then, the Multi-start strategy based on the convex region boundary isintroduced to achieve the global optimization. Finally, a new iterative scheme, calledthe Trust Region based global convergent SQUARed iterative EM (TR-gSQUAREM) is proposed to achieve the superlinear convergence. Experiments show that the proposedalgorithm is efficient, speedy and robust.In the research on the problems of non-rigid landmark matching, the thesisproposes a novel methods which name as the Fast Large Deformation DiffeomorphicLandmarks Matching Based on Stationary Momentum (SM-FLDDLM) for the purposeof resolving the limitations of the known classical non-rigid transformation models andthe classical diffeomorphic non-rigid transformation models. The SM-FLDDLMmethod estimates the velocity vector fields by means of the Lagrangian stationarymomentum vector and time-dependent multi-scales reproducing kernels. The optimaldiffeomorphic deformation fields can be gained by the searching of optimal momentumvectors using the determinate simulative anneal based on the regularization controlsparameter. The results of comparative experiments show that the SM-FLDDLM methodis not only suitable for the large deformation diffeomorphic non-rigid transformation,but also has higher matching precision and lesser time and space consumes than thoseclassical diffeomorphic landmark mathing methods. Note that the proposed method canachieve a better balance between the accuracy of matching and the smoothness ofnon-rigid deformation.In the research on the problems of non-rigid unlabeled point pattern matching, thethesis develops a new diffeomorphic non-rigid PPM algorithm which combines theGaussian Mixture Model and Large Deformation Diffeomorphism Matching Based onStationary Momentum (GMM-SMLDDM). The GMM-SMLLDM method integratesthe soft matching technique which based on Gaussian Mixture Model with the non-rigidtransformation model which based on the above proposed SM-FLDDLM method. Theoptimal stationary momentum can be finded by the maximum likelihood estimation ofthe parameters Gaussian Mixture Model. The proposed novel method performs well inthe practical applications which under large deformation diffeomorphism and also havehigher matching accuracy and stronger robustness.