Understanding of ridge-valley lines on image-intensity surfaces in scale-space

Abstract

When a grey-scale image is regarded as a surface, the considerable topographic primal structures are stationary points, ridge and valley lines. The ridge and valley lines are rich in information because they pass through all stationary points, and are invariant with respect to monotonic image transformations. As images can be interpreted at multiresolutions by using scale-space filtering, this paper presents an analysis of the local topology of ridge-valley lines and its change in the scale-space. The result shows that the topology of ridge-valley lines along a stationary path will change when the path reaches a singular stationary point or an umbilicus; whereas the change at any non-stationary point occurs when a ridge-valley line gets contact with another or vanishes.