Symmetry Feature Extraction Based on Quaternionic Local Phase

Abstract

It has been shown that lines and edges are important for biological visual systems and this information can be described in terms of symmetric relations (even and odd) which permits a compact data representation. In order to define symmetry, we need two basic concepts, an object definition and transforms definitions. The main aim of this work is the feature symmetry extraction for computer vision applications using the local phase. In order to compute the local phase, we use the quaternion analytical signal and the monogenic with the atomic function up(x) a novel window which is easy to derivate and has compact support in space domain. In addition, we use the up(x) and Plop(x, y) to compute the Hilbert and the Riesz transform in terms of them first derivative. As an illustration, we apply the atomic function based Riesz transform using a multiscale approach to obtain characteristics of symmetry of object shapes in images to build feature signature vectors which in turn can be used for object classification.