Perspective angle trnsform and its application to 3-D configuration recovery

A relation between apparent and real angles in perspective projection is applied to the 3-D configuration recovery from images. The relation, called a perspective angle transform (PAT) is extracted using a new type of coordinate system. The properties of the perspective angle transform are also discussed, as is 3-D configuration recovery from three arbitrary line segments in the image plane. This recovery corresponds to a generalization of the right-angled interpretation problem proposed and discussed by S. T. Barnard (1980). A geometric and algebraic solution of the problem, using the general PAT form in conjunction with the concept of virtual crossing point, is given. Algebraic solutions for the right-angled interpretation problem are obtained by solving a quadratic equation.