Four Applications of Differential Geometry to Computer Vision

An unbiased implementation of regularization mechanisms

“…This powerful methodology is also very general in the sense that a large variety of computational problems are solvable within this framework (see e.g. [9,8] for a review).…”

“…[26] for a recent review) and a natural (and in fact general) requirement for such approaches [1,9] is to: (α) obtain isotropic diffusion for small gradient magnitude because we want to maximize the propagation of information in uniform (thus information less) parts of the parametric space and (β) cancel the propagation of information for high gradient magnitudes in the direction of the gradient in order to preserve large (thus significant) variations of the input function.…”

The Local Structure of Space-variant Images

“…Many other examples of the use of differential image structure by both machine and biological vision researchers can be found in the literature (e.g. Koenderink, 1984;Koenderink andvan Doorn, 1990, Koenderink andvan Doorn, 1994;Deriche et al, 1992;Deriche and Giraudon, 1993;Florack et al, 1992;Malik, 1987, Perona andMalik, 1990;Beaudet, 1978, Kitchen andRosenfeld, 1982;Krueger and Phillips, 1989).…”