We propose connectivity-preserving geometry images (CGIMs), which map a three-dimensional mesh onto a rectangular regular array of an image, such that the reconstructed mesh produces no sampling errors, but merely round-off errors. We obtain a V-matrix with respect to the original mesh, whose elements are vertices of the mesh, which intrinsically preserves the vertex-set and the connectivity of the original mesh in the sense of allowing round-off errors. We generate a CGIM array by using the Cartesian coordinates of corresponding vertices of the V-matrix. To reconstruct a mesh, we obtain a vertex-set and an edge-set by collecting all the elements with different pixels, and all different pairwise adjacent elements from the CGIM array respectively. Compared with traditional geometry images, CGIMs achieve minimum reconstruction errors with an efficient parametrization-free algorithm via elementary permutation techniques. We apply CGIMs to lossy compression of meshes, and the experimental results show that CGIMs perform well in reconstruction precision and detail preservation.
Research work on applications of GIMs includes mesh compression @cite_7 , smooth surface representation @cite_0 , face recognition @cite_14 , texture synthesis @cite_15 , and facial expression modeling @cite_4 . We do not list detailed work in order to focus in priority on our work.
@cite_14 @cite_4 @cite_7 @cite_0 @cite_15
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As the size of the available collections of 3D objects grows, database transactions become essential for their management with the key operation being retrieval (query). Large collections are also precategorized into classes so that a single class contains objects of the same type (e.g., human faces, cars, four-legged animals). It is shown that general object retrieval methods are inadequate for intraclass retrieval tasks. We advocate that such intraclass problems require a specialized method that can exploit the basic class characteristics in order to achieve higher accuracy. A novel 3D object retrieval method is presented which uses a parameterized annotated model of the shape of the class objects, incorporating its main characteristics. The annotated subdivision-based model is fitted onto objects of the class using a deformable model framework, converted to a geometry image and transformed into the wavelet domain. Object retrieval takes place in the wavelet domain. The method does not require user interaction, achieves high accuracy, is efficient for use with large databases, and is suitable for nonrigid object classes. We apply our method to the face recognition domain, one of the most challenging intraclass retrieval tasks. We used the Face Recognition Grand Challenge v2 database, yielding an average verification rate of 95.2 percent at to 10-3 false accept rate. The latest results of our work can be found at http: www.cbl.uh.edu UR8D In this paper, we present a novel geometry video (GV) framework to model and compress 3-D facial expressions. GV bridges the gap of 3-D motion data and 2-D video, and provides a natural way to apply the well-studied video processing techniques to motion data processing. Our framework includes a set of algorithms to construct GVs, such as hole filling, geodesic-based face segmentation, expression-invariant parameterization (EIP), and GV compression. Our EIP algorithm can guarantee the exact correspondence of the salient features (eyes, mouth, and nose) in different frames, which leads to GVs with better spatial and temporal coherence than that of the conventional parameterization methods. By taking advantage of this feature, we also propose a new H.264 AVC-based progressive directional prediction scheme, which can provide further 10 -16 bitrate reductions compared to the original H.264 AVC applied for GV compression while maintaining good video quality. Our experimental results on real-world datasets demonstrate that GV is very effective for modeling the high-resolution 3-D expression data, thus providing an attractive way in expression information processing for gaming and movie industry. We recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genus-zero surface onto a regular 2D grid, a spherical geometry image. These geometry images offer several advantages for shape compression. First, simple extension rules extend the square image domain to cover the infinite plane, thereby providing a globally smooth surface parametrization. The 2D grid structure permits use of ordinary image wavelets, including higher-order wavelets with polynomial precision. The coarsest wavelets span the entire surface and thus encode the lowest frequencies of the shape. Finally, the compression and decompression algorithms operate on ordinary 2D arrays, and are thus ideally suited for hardware acceleration. In this paper, we detail two wavelet-based approaches for shape compression using spherical geometry images, and provide comparisons with previous compression schemes. In this paper, we present an automatic method which can transfer geometric textures from one object to another, and can apply a manually designed geometric texture to a model. Our method is based on geometry images as introduced by The key ideas in this method involve geometric texture extraction, boundary consistent texture synthesis, discretized orientation and scaling, and reconstruction of synthesized geometry. Compared to other methods, our approach is efficient and easy-to-implement, and produces results of high quality.