Patent ID: 8630446

Claim:
A method for determining a three-dimensional (3D) location of a reflection point of a ray between a point in a scene (PS) and a center of projection (COP) of a camera of a catadioptric system, wherein the catadioptric system is non-central and includes the camera and a reflector, wherein a surface of the reflector is a quadric surface rotationally symmetric around an axis of symmetry, wherein the reflection point is a point of reflection of the ray on the surface, and wherein a configuration of the catadioptric system includes the PS and the COP identified by 3D locations, comprising the steps of: determining a first equation describing a reflection plane defined by the COP, the PS, and a point of intersection of a normal of a reflection point with the axis of symmetry; determining a second equation based on a law of reflection at the reflection point; determining a third equation as an equation of the reflector; and solving the first, the second, and the third equations to determine 3D location of the reflection point, wherein the 3D location of the reflection point includes a first coordinate, a second coordinate, and a third coordinate, and further comprising: constructing a forward projection equation (FPE) in one unknown from the first, the second, and the third equations, wherein the unknown is the first coordinate; solving the FPE to determine the first coordinate; and determining the second coordinate and the third coordinate based on the first coordinate and the first, the second, and the third equations, wherein the steps of the method are performed by a processor.