Fuzzy theoretic model based analysis of image features

Abstract

Recently, membership functions based image descriptors were introduced as competing alternative to the classical histograms based image descriptors. The design of a suitable mathematical criterion for matching image descriptors to detect the correspondences between the images remains as one of the basic problems of image matching and computer vision. This study derives analytically a fuzzy theoretic model of local image features to facilitate a mathematical analysis of the correspondences between descriptors of multiple images. The analytical model of the local image features defines a membership function on the descriptors as a finite mixture of the descriptor’s memberships to different descriptor-prototypes. The so-defined membership function involves parameter vectors with a special structure such that all elements of the vector are non-negatives and sum to unity. These parameter vectors are considered as uncertain and are modeled by Dirichlet type membership functions. The membership functions are determined analytically by solving a deterministic constrained optimization problem using variational optimization. The membership functions based analysis leads to significantly more accurate and reliable multi-image matching algorithm that can be applied under different scenarios including that of Collage creation and fully automated image clustering.