A Zero-Crossing-Based Optimal Three-Dimensional Edge Detector

Abstract

Three-dimensional (3D) image processing and interpretation is very important in many medical and industrial applications. Detection of 3D boundaries is an essential step in most of the 3D image analysis tasks. In this paper a new computational approach to 3D edge detection is proposed. Optimality criteria such as signal-to-noise ratio, localization, and spurious response for zero-crossing-based, rotationally invariant 3D step edge detectors are derived. An optimal 3D step edge detector is obtained by optimizing a penalty function which combines all the three criteria. The closed form solution to the optimization problem yields the optimal detector. The detector is the Laplacian of a rotationally invariant function, which has a finite spatial support. The behavior of the proposed detector is theoretically analyzed and compared to that of the 3D Laplacian of Gaussian detector. Experimental results with some synthetic and real images are presented.