Final Technical Report 133 8 Pose Estimation of Multi-Part Curved Objects Mourad Zerroug and Ramakant Nevatia 8.1 Introduction Recognizing 3-D objects from a 2-D image is important for many visual tasks. Part of this problem is the estimation of the 3-D pose of the viewed objects. Alignment, introduced by [134], is a very attractive method since it is simple and efficient. Most objects demonstrated under the alignment technique are those for which low-level im- age features can be identified and matched with model features. These include polyhedra and objects with sharp corners or distinguished lines. Dealing with com- plex, curved, objects is more difficult because no such low-level features may be iden- tifiable. This is due to the possible view-dependency of the outlines which may vary wildly with changes in viewpoint and thus are hard to match with object models. Few efforts have addressed the pose estimation of curved objects. Kriegman and Ponce [136] use a complex method based on elimination theory which finds the pose by minimizing an objective function which is the distance between the viewed silhou- ettes and the projection of an algebraic surface representation of object models. The method of [131] addresses surfaces of revolution, a somewhat restriced class. A recent method of [139] uses invariants based on the cross-ratio along surfaces of revolution having bi-tangents. The above methods have been demonstrated on relatively simple, though curved, objects. In this paper, we show that alignment-like techniques can still be used for a large class of complex, curved, multi-part objects provided adequate features and rep- resentations are used. More specifically, we demonstrate that high-level descriptions, based on a part-based formalism using generalized cylinders, provide means to estab- lish quasi-invariant correspondences (meaning that they are almost exact over al- most all viewpoints) between image and model shapes. These correspondences are in terms of powerful intrinsic quantitative shape attributes such as the axis, the scaling function and the cross-section of a part. The idea is that although the outlines may be viewpoint dependent, or may not have distinguished points, the derived shape de- scriptions in terms of the above powerful attributes (and their combinations) provide viewpoint independent entities which can be put into correspondence with models so represented. We believe this to be an important demonstration of the usefulness of high-level, part-based, descriptions in extending the classes of shapes which can be handled. The classes of shapes demonstrated here currently include arrangements of SHGCs (straight homogeneous generalized cylinders), a straight-axis primitive, and