Algebraic Geometry and Object Representation in Computer Vision

The goal of algebraic geometry is to gain an understanding of the behaviour of functions related by polynomial relationships. Algebraic curves and surfaces having considerable advantages as objects of study in computer vision, the relevance of algebraic geometry when dealing with the representation of polynomial objects seems only natuever, due to its high level of abstraction, this mathematical eld has seen only few applications in computer vision in comparison to its huge achievements, by contrast with di erential geometry for instance. In this paper, we examine several methods that we think could see some developments in object representation. An example of their use is presented for the construction of aspect graphs of smooth surfaces and for the understanding of the complexity of this representation.

• Type: Conference
• Year: 1994
• Where: NSF
• Authors: Sylvain Petitjean
• Keywords: Algebraic Curves, Algebraic Geometry, Computer Vision, NSF 1994, Polynomial Relationships