Finding correspondences between two surfaces is a fundamental operation in various applications in computer graphics and related fields. Candidate correspondences can be found by matching local signatures, but as they only consider local geometry, many are globally inconsistent. We provide a novel algorithm to prune a set of candidate correspondences to those most likely to be globally consistent. Our approach can handle articulated surfaces, and ones related by a deformation which is globally non-isometric, provided that the deformation is locally approximately isometric. Our approach uses an efficient diffusion framework, and only requires geodesic distance calculations in small neighbourhoods, unlike many existing techniques which require computation of global geodesic distances. We demonstrate that, for typical examples, our approach provides significant improvements in accuracy, yet also reduces time and memory costs by a factor of several hundred compared to existing pruning techniques. Our method is furthermore insensitive to holes, unlike many other methods.

This paper presents a skeleton-based method for deforming meshes (the skeleton need not be the medial axis). The significant difference from previous skeleton-based methods is that the latter use the skeleton to control movement of vertices, whereas we use it to control the simplices defining the model. By doing so, errors that occur near joints in other methods can be spread over the whole mesh, via an optimization process, resulting in smooth transitions near joints of the skeleton. By controlling simplices, our method has the additional advantage that no vertex weights need be defined on the bones, which is a tedious requirement in previous skeleton-based methods. Furthermore, by incorporating the translation vector in our optimization, unlike other methods, we do not need to fix an arbitrary vertex, and the deformed mesh moves with the deformed skeleton. Our method can also easily be used to control deformation by moving a few chosen line segments, rather than a skeleton.

In this report, we propose a new semi-fragile watermarking algorithm for the authentication of 3D models based on integral invariants. To do so, we embed a watermark image by modifying the integral invariants of some of the vertices. Basically, we shift a vertex and its neighbors in order to change the integral invariants. To extract the watermark, test all the vertices for the embedded information, and combine them to recover the watermark image. How many parts can the watermark image be recovered would help us to make the authentication decision. Experimental test shows that this method is robust against rigid transform and noise attack, and useful to test purposely attack besides transferring noise and geometrical transforming noise. An additional contribution of this paper is a new algorithm for computing two kinds of integral invariants.

Remeshing aims to produce a more regular mesh from a given input mesh, while representing the original geometry as accurately as possible. Many existing remeshing methods focus on where to place new mesh vertices; these samples are placed exactly on the input mesh. However, considering the output mesh as a piecewise linear approximation of some geometry, this simple scheme leads to significant systematic error in non-planar regions. Here, we use parameterised meshes and the recent mathematical development of orthogonal approximation using Sobolev-type inner products to develop a novel sampling scheme which allows vertices to lie in space near the input surface, rather than exactly on it. The algorithm requires little extra computational effort and can be readily incorporated into many remeshing approaches. Experimental results show that on average, approximation error can be reduced by 40% with the same number of vertices.

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