A symbolic approach to reconstruct polyhedral scene from single 2D line drawing

Scene reconstruction based on polyhedral solids is an important problem in computer vision. Generally speaking, an efficient representation is to use a line drawing which is regarded as a projection of the 3D object. In this paper, we consider a single line drawing whose face topology is already known and all the vertices are given in the 2D projection. To recover the possible 3D polyhedra which project to the line drawing, we present a symbolic geometric algorithm based on the Grassmann-Cayley algebra. A number of examples demonstrate its outstanding performance which can lead to an very significant simplifications in symbolic manipulation of geometric data.