Recovering a 3D shape of a generalized cone from a single 2D image

Recovering veridical 3D shape of an object from a single 2D image is an ill-posed problem. a priori constraints are required to produce a unique and veridical solution. Previous studies showed that mirror symmetry is used by human visual system as an a priori constraint. In this study we explored the role of another type of symmetry, translational symmetry in human 3D shape recovery. Objects characterized by translational symmetry are called Generalized Cones (GCs). Since natural and man-made objects are composed of parts which can be characterized by translational symmetry, it is reasonable to assume that translational symmetry is also used as an a priori constraint in human 3D shape recovery. To verify this hypothesis, we tested subject\u27s perception of the 3D shape of GCs using a shape recovery experiment. The experimental result suggests that subjects can perceive the 3D shape of a GC accurately. The result further suggests that translational symmetry is used as an a priori constraint in human 3D shape recovery. To explore the computational mechanism of this recovery process, we proposed a computational model which can recover the 3D shape of a GC from a single 2D orthographic image. The model assumes that all cross sections of a GC are planar shapes, the axis is a planar curve and all cross sections are perpendicular to the axis. These assumptions are used as implicit constraints. The model also assumes that all cross sections have the same shape. This assumption is used as an explicit constraint and it is one of two terms in the cost function. The second term in the cost function biases the recovered 3D shape towards maximum 3D compactness. The model produced similar adjustment errors compared to the errors produced by the subjects. The correlation between the performance of each subject and the performance of the model is similar to the correlation between the performance of the two subjects