further applications of the principles of the invention as illustrated therein are contemplated as would normally occur to one skilled in the art to which the invention relates one embodiment of this system transforms at least one orthographic image of a symmetric polyhedron into a three dimensional representation using method 100 as illustrated in fig1 this system assumes that it is known which points in the image correspond to symmetric points in the 3 d object and also knows which points form contours of faces on the object because the objects in images are usually opaque not all vertices of an object are usually visible this system uses three pairs of symmetric points that are visible to perform a first step which establishes a relation between the real image and a virtual image of the object according to the pseudocode below a virtual image of the 3 d object is created assuming that the object has at least one plane of symmetry in a first step 110 3 d coordinates of visible pairs of symmetric vertices are reconstructed using a method similar to that found in huang amp lee huang t amp lee c 1989 ieee trans pami2 536 540 the teachings of which are incorporated herein by reference to the extent they do not contradict the teachings herein where up to one free parameter a represents the stretch along the depth direction once these points are reconstructed the system applies a planarity constraint in step 120 to reconstruct the pairs of points for which one point is invisible that is occluded in the image the 3 d coordinates of all of these points both visible and occluded are determined in up to that one free parameter u03c3 the value of the.