Graph matching using position coordinates and local features for image analysis

Abstract

Finding the correspondences between two images is a crucial problem in the computer vision & pattern recognition field. It is relevant to a broad range of purposes going from object recognition applications in the areas of biometry, document analysis and shape analysis to applications involving multiple view geometry such as pose recovery, structure from motion and localization & mapping. Many existing techniques approach this problem either using local image features or point-set registration methods (or a mixture of both). In the former ones, a sparse set of features is first extracted from the images and then characterized in the form of descriptor-vectors using the local image evidence. Features are associated according to the similarity between their descriptors. In the second ones, feature-sets are regarded as point-sets which are associated using non-linear optimization techniques. These are iterative procedures that estimate correspondence and alignment parameters in alternate steps. Graphs are representations that allow for binary relations between the features. Accounting for binary relations in the correspondence problem often leads to the so-called graph matching problem. There exists a number of methods in the literature aimed at finding approximate solutions to different instances of the graph matching problem, which in most cases is known to be NP-hard. Regardless of the type of representation used, part of our work is devoted to the comparison of local image features. Specifically, we investigate the benefits of using cross-bin measurements such as the Earth Movers’ Distance to that end. The rest of our work is dedicated to formulating both the image features association and point-set registration problems as instances of the graph matching problem. In all the cases, we propose approximate algorithms to solve these problems and compare to a number of existing methods from different areas, namely, outlier rejectors, point-set registration methods and other graph matching methods. Experiments show that in most cases the proposed methods outperform the rest. Occasionally the proposed methods either share the best performances with some competing method or they get slightly worse results. In these cases, the proposed methods usually present lower computational times.