Forma, Vol. 10 (No. 2), pp. 119-131, 1995
Original Paper

Original PaperRidge-Valley Lines of Images in Scale-Space

Supoj Chinveeraphan, Ryo Takamatsu and Makoto Sato

Precision and Intelligence Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226, Japan

(Received May 19, 1995; Accepted July 31, 1995)

Keywords: Ridge-Valley Line, Scale-Space Filtering, Singular Stationary Points

Abstract. This paper presents a mathematical analysis of the topology of ridge-valley lines of image-intensity surfaces and its changes in the Gaussian scale-space. The analysis is proceeded by considering the Taylor's series of the topology of ridge-valley lines at the location of stationary and non-stationary points. The result shows that there are in general two ridge-valley lines crossing along a stationary path. This topology of the lines will change when the path reaches a singular stationary point or an umbilicus. The change at any non-stationary point occurs when a ridge-valley line gets contact with another or vanishes.