New exact and approximate solutions of the three-point perspective problem

An exact method for computing the position of a triangle in space from its image is presented. Also presented is an approximate method based on orthoperspective, an approximation of perspective which produces lower errors for off-center triangle images than scaled orthographic projection. A comparison is made of exact and approximate solutions for the triangle pose. This comparison gives the relative combinations of image and triangle characteristics which are likely to generate the largest errors. Model-based pose estimation techniques which match image and model triangles require large numbers of matching operations in real-world applications. It is shown that the approximate model can be used to build lookup tables for each of the triangles of a model and that they speed up the estimation of an object pose