Recovering a 3D shape from a single 2D image is an ill-posed problem. However, our previous studies (e.g., Li et al., 2011) showed that subjects perceive shapes of mirror symmetric objects accurately even from a single 2D image. Our computational model, in which 3D mirror symmetry is the main a priori constraint, recovers 3D shapes the way human subjects do. Here we generalize these previous results to the case of "translational symmetry". 3D objects which are characterized by translational symmetry are called generalized cones (GC), and were used by Biederman in his RBC theory (1987). In this study, GCs were produced by swiping a planar closed curve (cross section) along a planar curved axis with the following constraints: all cross sections in a given GC had the same shape, but not necessarily size. Each cross section was perpendicular to the tangent of the axis. Last year we showed that the subject’s percept of such GCs is close to veridical. Specifically, the subject was able to adjust quite accurately the aspect ratio of the cross section of a GC and the slant of the plane containing the axis of the GC. This year, we describe a computational model which can solve the same recovery task from a single 2D orthographic image. The model uses the constraints listed above. The recovery is done in two steps: (i) the shape of the planar cross section and the slants of the two end cross sections are recovered from the images of these cross sections and from the estimated tilts; (ii) the normal of the plane containing the axis is computed as a cross product of the normals of the two end cross sections. The model’s recovery is strongly correlated with the subject’s recovery and both are close to the true 3D shape.
Meeting abstract presented at VSS 2012