The Complexity and Enumerative Geometry of Aspect Graphs of Smooth Surfaces

Aspect graphs have been the object of very active research by the computer vision community in recent years, but most of it has concentrated on the design of algorithms to compute the representation. In this paper, we work on a more theoretical level to give enumerative properties of the di erent entities entering in the construction of aspect graphs of objects bounded by smooth surfaces, namely the loci of singular points and visual event surfaces. We show how tools from algebraic geometry allow to compute their elementary projective characters and other numerical invariants. The mathematics needed for our computations use results from three overlapping subject areas, i.e. multiple-point theory, enumerative geometry, and intersection theory.