We focus on the positive K-relation model for annotated relations in which U-tuples are annotated with elements of a commutative semiring K. We propose a new operation into K, called negation, which allows to define difference of K-relations, the only basic relational operation not modeled by the positive K-relational algebra. The existence of negation is guaranteed in special lattices called De Morgan frames. Requiring of K to be a De Morgan frame has another positive consequence ̶ in the obtained L-relational algebra, all the (positive) relational identities known from classical relational algebra hold, including those that fail to hold in the K-relational algebra.
Face recognition technology has come a long way since its beginnings in the previous century. Due to its countless application possibilities in both the private as well as the public sector, it has attracted the interest of research groups from universities and companies around the world. Thanks to this enormous research effort, the recognition rates achievable with the state-of-the-art face recognition technology are steadily growing, even though some issues still pose major challenges to the technology. Amongst these challenges, coping with illumination induced appearance variations is one of the biggest and still not satisfactorily solved. A number of techniques have been proposed in the literature to cope with the illumination induced appearance variations ranging from simple image enhancement techniques, such as histogram equalization or gamma intensity correction, to more elaborate methods, such as homomorphic filtering, anisotropic smoothing or the logarithmic total variation model. This chapter presents an overview of the most popular and efficient normalization techniques which try to solve the illumination variation problem at the preprocessing level. It assesses the techniques on the publicly available YaleB face database and explores their strengths and weaknesses from the theoretical and implementational point of view.
The alignment of the facial region with a predefined canonical form is one of the most crucial steps in a face recognition system. Most of the existing alignment techniques rely on the position of the eyes and, hence, require an efficient and reliable eye localization procedure. In this paper we propose a novel technique for this purpose, which exploits a new class of correlation filters called Prinicpal directions of Synthetic Exact Filters (PSEFs). The proposed filters represent a generalization of the recently proposed Average of Synthetic Exact Filters (ASEFs) and exhibit desirable properties, such as relatively short training times, computational simplicity, high localization rates and real time capabilities. We present the theory of PSEF filter construction, elaborate on their characteristics and finally develop an efficient procedure for eye localization using several PSEF filters. We demonstrate the effectiveness of the proposed class of correlation filters for the task of eye localization on facial images from the FERET database and show that for the tested task they outperform the established Haar cascade object detector as well as the ASEF correlation filters.