|Abstract||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 natural. However, due to its high level of abstraction, this mathematical field has seen only few applications in computer vision in comparison to its huge achievements, by contrast with differential 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.