A ZERO-CROSSING-BASED OPTIMAL 3-DIMENSIONAL EDGE DETECTOR

Three-dimensional (3D) image processing and interpretation is very imp ortant in many medical and industrial applications. Detection of 3D bo undaries is an essential step in most of the 3D image analysis tasks. In this paper a new computational approach to 3D edge detection is pro posed. Optimality criteria such as signal-to-noise ratio, localization , and spurious response for zero-crossing-based, rotationally invarian t 3D step edge detectors are derived. An optimal 3D step edge detector is obtained by optimizing a penalty function which combines all the t hree criteria. The closed form solution to the optimization problem yi elds the optimal detector. The detector is the Laplacian of a rotation ally invariant function, which has a finite spatial support. The behav ior of the proposed detector is theoretically analyzed and compared to that of the 3D Laplacian of Gaussian detector. Experimental results w ith some synthetic and real images are presented. (C) 1994 Academic Pr ess, Inc.