Edge detection with reaction-diffusion equations having a local average threshold

Abstract

The present paper proposes an edge detection algorithm with the FitzHugh-Nagumo reaction-diffusion equations. The authors previously found that the discretized version of the reaction-diffusion equations organizes a static pulse at an edge position for a binary image or for a binarized image with a fixed threshold level. By finding static pulses from the result of the discretized version, we can detect edges. The algorithm proposed here furthermore detects edges from a gray-scale image. In order to handle the gray-scale image, the proposed algorithm computes a local average level of image brightness distribution with a simple diffusion equation and simultaneously utilizes the average level as the threshold level of the reaction-diffusion equations. That is, the local average level obtained by the simple diffusion equation modulates the threshold level of the reaction-diffusion equations. The proposed set of the reaction-diffusion equations coupled with the simple diffusion equation causes a pulse at a true edge position and also a pseudopulse at a pseudoposition. Thus, we additionally propose an algorithm that eliminates the pseudopulse and extracts the true one. We apply the proposed algorithm and a previous representative algorithm to well-known test images for confirming the validity of the proposed algorithm.