Differential Geometry from the Frenet Point of View: Boundary Detection, Stereo, Texture and Color

Abstract

Frenet frames are a central construction in modern differential geometry, in which structure is described with respect to an object of interest rather than with respect to external coordinate systems. The Cartan moving frame model specifies how these frames adapt when they are transported along the object. We consider this as a model for integrating local information with information in a neighborhood for curve detection, stereo, texture, and color. These different objects results in a series of geometric compatibility constructions useful within a number of different optimization and probabilistic inference techniques.