Direct construction of the perspective projection aspect graph of convex polyhedra

The aspect graph concept was first described by Koenderink and van Doorn as a possible mechanism in human vision and has subsequently become an active research topic in computer vision. This paper describes an algorithm for constructing the perspective projection aspect graph of convex polyhedra. In the perspective projection aspect graph, viewpoint space is modeled as all of 3D space surrounding the object. This makes the perspective projection aspect graph a more realistic representation than the orthographic projection aspect graph, in which viewpoint space is modeled by the Gaussian sphere. The algorithm uses an intermediate data structure which represents a complete parcellation of 3D space derived from the geometric definition of the object. All information necessary for identifying object aspects and corresponding viewing cells is obtained as a result of this parcellation. The resulting aspect graph structure has a node for each distinct aspect/viewing cell. The upper bounds on the time complexity of the algorithm and the space complexity of the resulting data structure are Θ(N⁴), where N is the number of faces of the polyhedron. The algorithm has been implemented in C, runs on a SUN workstation, and can use PADL-2 files for its input description of objects.