The inverse perspective problem from a single view for polyhedra location

Abstract

A method to find the analytical solutions of the inverse perspective problem for the determination of the 3-D object attitude in space from a single perspective image is presented. Its principle is based on the interpretation of a triplet of any image lines as the perspective projection of triplet of linear ridges of the object model. The geometrical transformations to apply to the model to bring it into the corresponding location are obtained by the resolution of an eighth-degree equation. The number of admissible solutions can still be reduced, using simple pruning rules. This approach leads to very strong results useful for both location and recognition of 3D objects. Because few admissible hypotheses are retained, the line-matching procedure by prediction-verification is less complex.