Initial Conditions of Reaction-Diffusion Algorithm Designed for Image Edge Detection

Abstract

Image edges refer to steep brightness changes and provide fruitful information on image structures. This paper proposes initial conditions of a reaction-diffusion algorithm designed for image edge detection. The algorithm utilizes a network in which FitzHugh-Nagumo neurons are placed at grid points and connected to their neighboring ones. Each FitzHugh-Nagumo neuron simulates a process of excitation and inhibition observed in biological nerve axon, and is described with a pair of time-evolving ordinary differential equations (ODEs) stated by activator and inhibitor variables. The network is originally derived from discretization of FitzHugh-Nagumo type reaction-diffusion equations described by partial differential equations (PDEs). It is known that the network creates stationary pulses at edge positions of image brightness distribution provided as initial conditions. Steep brightness changes initiate processes of excitation and inhibition, and pulses having excited states at edge positions remain at their original positions, as time proceeds. However, the network is insensitive to relatively weak edges having gradual brightness changes. The novel initial conditions proposed here are composed of absolute gradients of multi-scale images. The algorithm with the initial conditions is applied to test images of BSDS300 dataset, and its performance is quantitatively confirmed by F-measure, in comparison with other edge detection algorithms.