Matching convex polygons and polyhedra, allowing for occlusion

We review our recent results on visual object recognition and reconstruction allowing for occlusion. Our scheme uses matches between convex parts of objects in the model and image to determine structure and pose, without relying on specific correspondences between local or global geometric features of the objects. We provide results determining the minimal number of regions required to uniquely determine the pose under a variety of situations, and also showing that, depending on the situation, the problem of determining pose may be a convex optimization problem that is efficiently solved, or it may be a non-convex optimization problem which has no known, efficient solution. We also relate the problem of determining pose using region matching to the problem of finding the transformation that places one polygon inside another and the problem of finding a line that intersects each of a set of 3-D volumes.