11 August 1995 Ridges, ravines, and related point features on a surface
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Abstract
Analyzing the 3D images of a given surface as viewed from different positions naturally leads to investigation of coordinate-independent geometric surface features reflecting its essential properties. In the present paper we study surface point features related to ridge and ravine lines on a surface. These lines introduced in our previous works are defined as curves corresponding to the boundary points of the skeleton of the distance transform of the surface. We show that the ridges and ravines can be extracted via the directional derivatives of the principal curvatures along the associated principal directions. However, even after this local description the direct extraction of the ridges and ravines is a time-consuming procedure. It turns out that the ridge and ravine lines contain some remarkable points (end points and others) that can be extracted relatively easily. After finding such points the procedure of ridge and ravine extraction becomes much simpler. Moreover, these points are closely connected with some singularities of caustics and wavefronts, and have an independent interest in image analysis as visual invariants. The paper is devoted to the investigation of such points and the accompanying geometry of singularities of wavefronts and caustics. We also demonstrate applicability of the ridges and ravines defined as above and related point features in image understanding.
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Alexander G. Belyaev, Alexander G. Belyaev, Elena V. Anoshkina, Elena V. Anoshkina, Tosiyasu L. Kunii, Tosiyasu L. Kunii, "Ridges, ravines, and related point features on a surface", Proc. SPIE 2573, Vision Geometry IV, (11 August 1995); doi: 10.1117/12.216443; https://doi.org/10.1117/12.216443
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