The aim of this work is to learn a shape prior model for an object class and to improve shape matching with the learned shape prior. Given images of example instances, we can learn a mean shape of the object class as well as the variations of non-affine and affine transformations separately based on the thin plate spline (TPS) parameterization. Unlike previous methods, for learning, we represent shapes by vector fields instead of features which makes our learning approach general. During shape matching, we inject the shape prior knowledge and make the matching result consistent with the training examples. This is achieved by an extension of the TPS-RPM algorithm which finds a closed form solution for the TPS transformation coherent with the learned transformations. We test our approach by using it to learn shape prior models for all the five object classes in the ETHZ Shape Classes. The results show that the learning accuracy is better than previous work and the learned shape prior models are helpful for object matching in real applications such as object classification. 1.

Abstract—This paper presents a framework of layered graph matching for integrating graph partition and matching. The objective is to find an unknown number of corresponding graph structures in two images. We extract discriminative local primitives from both images and construct a candidacy graph whose vertices are matching candidates (i.e., a pair of primitives) and whose edges are either negative for mutual exclusion or positive for mutual consistence. Then we pose layered graph matching as a multicoloring problem on the candidacy graph and solve it using a composite cluster sampling algorithm. This algorithm assigns some vertices into a number of colors, each being a matched layer, and turns off all the remaining candidates. The algorithm iterates two steps: 1) Sampling the positive and negative edges probabilistically to form a composite cluster, which consists of a few mutually conflicting connected components (CCPs) in different colors and 2) assigning new colors to these CCPs with consistence and exclusion relations maintained, and the assignments are accepted by the Markov Chain Monte Carlo (MCMC) mechanism to preserve detailed balance. This framework demonstrates state-of-the-art performance on several applications, such as multi-object matching with large motion, shape matching and retrieval, and object localization in cluttered background. Index Terms—Graph matching, graph partitioning, DDMCMC, cluster sampling. Ç

This paper presents a method that enables automated morphology analysis of partially overlapping nanoparticles in electron micrographs. In the undertaking of morphology analysis, three tasks appear necessary: separate individual particles from an agglomerate of overlapping nano-objects; infer the particle’s missing contours; and ultimately, classify the particles by shape based on their complete contours. Our specific method adopts a two-stage approach: the first stage executes the task of particle separation, and the second stage conducts simultaneously the tasks of contour inference and shape classification. For the first stage, a modified ultimate erosion process is developed for decomposing a mixture of particles into markers, and an edge-to-marker association method is proposed to identify the set of evidences for the particle contours. We also provided theoretical justification regarding the separation capability of the first stage. In the second stage, the set of evidences become inputs to a Gaussian mixture model on B-splines, the solution of which leads to the joint learning of the missing contour and the particle shape. Using twelve real electron micrographs of overlapping nanoparticles, we compare the proposed method with four state-of-the-art methods. The results show the superiority of the proposed method in terms of particle recognition rate.