3-D to 2-D Recognition with Regions

We present new methods for determining the pose of a known 3-D object in a single 2-D image, extending our previous work ((7]) which focused on the case of planar models. In our method we represent the parts of objects directly as volumes, and make use of correspondences between these volumes and regions in the image, without requiring knowledge of the correspondence between speciic points in the model and image. We then consider several methods for using these correspondences to determine pose. The forward constraints allow for self-occlusion of parts. We show that we can nd model poses satisfying these constraints using linear programming. Moreover, typically given a correspondence between three model volumes and image regions, we can use these constraints to correctly determine the model pose. The backward constraints also allow for occlusion by other objects. We show, however, that it is computationally diicult to nd poses that satisfy these constraints. We therefore introduce an approximation to these constraints that can also be eeciently solved using linear programming. We show theoretically that in cases of interest this approximation can also be used to determine the correct model pose, and present experiments to illustrate the performance of both methods.