Fuzzy theoretic model based analysis of image features

• Mohit Kumar
• Sromona Chatterjee
• Weiping Zhang
• Jingzhi Yang
• Lutz M. Kolbe

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 be- tween 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 mem- bership functions. The membership functions are determined analytically by solving a de- terministic constrained optimization problem using variational optimization. The member- ship 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.