Eigen transformation based edge detector for gray images

Abstract

In this paper, a simple and a robust algorithm to detect edges in a gray image is proposed. The statistical property of the small eigenvalue of the covariance matrix of a set of connected pixels over a small region of support is explored for the purpose of edge detection. The gray image is scanned from the top left corner to the bottom right corner with a moving mask of size k x k, for some integer k. At every stage, the small eigenvalue of the covariance matrix of the connected pixels that are having approximately same intensity as that of the center pixel of the mask is computed. This small eigenvalue is used to decide if a pixel is a potential edge pixel based on a pre-defined threshold value. The set of all identified potential edge pixels are then subjected to a pruning process where true edge pixels are selected. Experiments have been conducted on benchmark gray images to establish the performance of the proposed model. Comparative analysis with the Canny edge detector [1] and Sun et al. [15] is made to demonstrate the implementation simplicity and suitability of the proposed method in vision applications. © Springer-Verlag Berlin Heidelberg 2005.