Based On The Figure 3 D Shape Matching

Shape matching is a fundamental problem in computer graphics, computer vision and pattern recognition. In computer graphics, it is the basis for critical problems like registration, attribute transferring, object reconstruction and retrieval. There are massive researches in shape matching in recent years, partly due to the fast developments and large amount of applications in shape analysis in these years. In shape matching, matching isometric objects are now the central objec-tive, while isometric-invariants, such as geodesic, diffusion distance or Mobius transform are used. Thus topics in which people is interested include:proposing new isometric-invariants, matching partial objects, matching different elements, obtaining dense correspondences and matching non-isometric objects. Matching non-isometric objects is a new topic appears in recent a couple of years. As opposed to matching isometric objects having theoretical foundations, it has not and it is very challenging.Shape descriptors of elements and relations between elements are used in shape matching. According to this criterion, researches in shape matching include developing new shape descriptors or new relations or both. In computer vision, the pixels in an image contain full information and gradient-based shape descriptors are highly discriminative, thus in practice many results are achieved with only shape descriptors. In computer graphics, similar ideas are adopted into3D to develop new shape descriptors. However without the full information as pixels, shape descriptors in3D are often not discriminative enough and element relations are always required.We focus on matching non-isometric objects mainly depending on element relations. As elements and their relations form a graph, we are using graph matching to do the shape matching. The works include:1. We propose a new skeleton matching technique, as the nodes in skeleton are elements and the links in skeleton are naturally element’s relations which are used to constrain matching the nodes. Since the skeleton describe the structural information of the objects but ignore geometrical details, it is suitable for matching non-isometric objects of structurally similar but geometrically different. Based on the fact that skeleton better describing the topology of objects, we use the matched skeletons to repair the topology of object sequences. This technique is aiming at reducing the interaction in topology repairing for object sequence, while former techniques focus on repairing single object. The biggest challenge in this work is matching efficiency, and we use temporal coherence to dramatically improve the matching time.2. We propose an isometric-invariant element relations based on Morse-Smale complex. It is also not sensitive to non-isometric deformation as geodesic or diffusion distance do. By using this relation in place of former relations, techniques can obtain the ability to matching objects away from isometric deformation. In our experiments, even objects of large geometrical differences can be matched. Another advantage of this new relation is its discrimination power, which can greatly relieve the deficiency problem of shape descriptors in3D. As the geodesic and Mobius transform are bounded by topology, our technique has no limit in object type or topology and is much faster than state-of-the-art techniques in orders of magnitude. We apply our matching results in cross-parametrization and texture transfer.