A Computational Approach to Zero-Crossing-Based Two-Dimensional Edge Detection

Abstract A commonly employed computational approach to the design of an edge detector is to formulate the edge detection problem as an optimization problem by defining a penalty function and constraints in terms of performance measures such as signal-to-noise ratio (SNR), spurious response, and edge localization. Unfortunately, this approach generally results in highly complex optimization problems for two-dimensional (2D) and higher dimensional edge detection. Therefore, most of the previously reported efforts have either proposed 1D optimal detectors or their approximations to higher dimensions. This paper presents a computational approach to optimal edge detector design, which utilizes some desirable properties of detector functions to simplify the optimization problems. Specifically, a zero-crossing-based 2D edge detector, which is the Laplacian of a rotationally invariant finite support function with a smooth boundary and yields optimal performance with respect to a penalty function defined in terms of a simplified SNR measure and Canny's edge localization, and spurious response measures. The performance of the proposed 2D step edge detector is theoretically and empirically analyzed and compared to that of the Laplacian of Gaussian detector. Experimental results with some synthetic and real images are presented