Detection of ridges and ravines on range images and triangular meshes

Surface creases, ridges and ravines, provide us with important information about the shapes of 3D objects and can be intuitively defined as curves on a surface along which the surface bends sharply. Our mathematical description of the ridges and ravines is based on the study of sharp variation points of the surface normals or equivalently, extrema of the principal curvatures along their curvature lines. We explore similarity between image intensity edges (sharp variation points of an image intensity) and curvature extrema of a 3D surface. It allows us to adopt a basic edge detection technique for detection of the ridges and ravines on range images and smooth surfaces approximated by polygonal meshes. Because the ridges and ravines are of high-order differential nature, careful smoothing is required in order to achieve stable detection of perceptually salient ridges and ravines. To detect the ridges and ravines on a range image we use a nonlinear diffusion process acting on the image intensity surface normals. To detect the ridges and ravines on a triangular mesh we use a coupled nonlinear diffusion of mesh normals and vertices. We demonstrate feasibility of the ridges and ravines for segmentation and shape recognition purposes.