Error analysis of localization and positioning using linear combination of model views

The method of localization and positioning using linear combinations of model views can accurately approximate the appearance of scenes and handles changes in viewpoint assuming the images are obtained under weak perspective projection. However, the method is invalid when perspective distortions get very large. This paper proposes an algorithm that can improve matching between the model and the image using an iterative scheme for reducing these perspective distortions when they are too large to be handled by a weak perspective approximation, analyzes errors resulting from the projection assumption, and impose contraints on the motion to reduce the computation complexity of the method presented. The suggested iterative process is based on Taylor expansion of the perspective coordinates. This expansion results in a polynomial consisting of terms each of which can be approximated by linear combinations of views. Error analysis and experimental results demonstrate that in many practical cases the method is valid