Clifford Algebra based Edge Detector for Color Images

Abstract

Edge detection is one of the most used methods for feature extraction in computer vision applications. Feature extraction is traditionally founded on pattern recognition methods exploiting the basic concepts of convolution and Fourier transform. For color image edge detection the traditional methods used for gray-scale images are usually extended and applied to the three color channels separately. This leads to increased computational requirements and long execution times. In this paper we propose a new, enhanced version of an edge detection algorithm that treats color value triples as vectors and exploits the geometric product of vectors defined in the Clifford algebra framework to extend the traditional concepts of convolution and Fourier transform to vector fields. Experimental results presented in the paper show that the proposed algorithm achieves detection performance comparable to the classical edge detection methods allowing at the same time for a significant reduction (about 33%) of computational times.