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

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. The text was submitted by the authors in English. Atsushi Nomura, born in 1966, obtained his Doctor of Engineering degree from Yamaguchi University, Japan, in 1994. Since 2001 he has been an associate professor of Faculty of Education at the university. His fields of research are image processing and computer vision. He is an author or coauthor of two book chapters and 13 research papers. He is a member of the Information Processing Society of Japan; the Physical Society of Japan; the Institute of Electronics, Information, and Communication Engineers; and the Optical Society of America. Makoto Ichikawa, born in 1965, obtained his Ph.D. degree from Osaka City University, Japan, in 1994. He was a post-doctoral fellow at Centre for Vision Research, York University, Canada. In 1998, he joined Faculty of Engineering, Yamaguchi University, Japan. Since 2006 he has been an associate professor of the Department of Psychology, Faculty of Letters, Chiba University, Japan. His fields of research are spatiotemporal aspects of perception, and integration processing in perception and cognition. He is the author or coauthor of five books and 20 research papers. He is a member of the Japan Society of KANSEI Engineering, the Japanese Psychological Association, Vision Society of Japan, and Vision Sciences Society. Rismon Hasiholan Sianipar, born in 1977, obtained his Master of Engineering degree from Mataram University, Indonesia, in 2002. In 2004, he entered Yamaguchi University as a research associate. He is currently a Ph.D. candidate in the Graduate School of Science and Engineering, Yamaguchi University, Japan. He is the coauthor of one book chapter and 2 research papers. His fields of research are signal and image processing. Hidetoshi Miike, born in 1948, obtained his Doctor of Engineering degree from Kyushu University, Japan in 1976. In 1976, he joined Faculty of Engineering, Yamaguchi University. Since 1991, he has been a professor of the university. His research interests include nonlinear sciences and fluid dynamics. He is a coauthor of 5 books and more than 100 research papers. He is a member of the Information Processing Society of Japan, the Physical Society of Japan, IEEE Computer Society, and the American Association for the Advancement of Science.