Projective alignment with regions

We consider a recent approach to recognition that uses regions to determine the pose of objects while allowing for partial occlusion of the regions. We further analyze properties of the method for planar objects undergoing projective transformations. We prove that three visible regions are sufficient to determine the transformation uniquely, and that for a large class of objects two regions are insufficient. However, we show that when several regions are available, the pose of the object can generally be recovered even when all but two regions are significantly occluded. Our analysis is based on investigating the flow patterns of points under projective transformations in the presence of fixed points.