Perspective angle transform—shape from angle

This paper derives the perspective angle transform as a relation between the angle in the three‐dimensional space and its perspective projection. The properties of the transform are discussed, together with its application to the scene interpretation. As the initial step, the first perspective moving coordinate is defined anew, and based on that coordinate, the primary form of the perspective angle transform is derived as a relation composed of three variables. Then the relation is arranged in the coordinate, which is determined only by the apparent angle, and the general form of the perspective angle transform is derived. It is shown that the transform is equivalent to determining the fourth‐order curve on the image. Finally, a problem is considered in which the gradient information should be recovered for three segments separated in the three‐dimensional space. An algebraic solution is shown. The solution is determined using the concept of virtual intersection and the perspective angle transform, based on the perspective moving coordinate .