We show how spectral methods may be applied to 3D mesh data to obtain compact representations. This is achieved by projecting the mesh geometry onto an orthonormal basis derived from the mesh topology. To reduce complexity, the mesh is partitioned into a number of balanced submeshes with minimal interaction, each of which are compressed independently. Our methods may be used for compression and progressive transmission of 3D content, and are shown to be vastly superior to existing methods using spatial techniques, if slight loss can be tolerated.

We present an interactive method for applying deformations to a surface mesh while preserving its global shape and local properties. Two surface editing scenarios are discussed, which conceptually differ in the specification of deformations: Either interpolation constraints are imposed explicitly, e.g., by dragging a subset of vertices, or, deformation of a reference surface is mimicked. The contribution of this paper is a novel approach for interpolation of local deformations over the manifold and for efficiently establishing correspondence to a reference surface from only few pairs of markers. As a general tool for both scenarios, a harmonic field is constructed to guide the interpolation of constraints and to find correspondence required for deformation transfer. We show that our approach fits nicely in a unified mathematical framework, where the same type of linear operator is applied in all phases, and how this approach can be used to create an intuitive and interactive editing tool. Figure 1: A simple edit: The visualized harmonic field is used as guidance for bending the cactus (left). Here, the field is defined by one source (red) at the tip of the left arm and one sink (blue) below the middle of the trunk. The result is shown in the center image. Notice the different propagation of the rotation compared to the edit on the right, where three sources on all arms were chosen (without picture).

We describe a compression scheme for the geometry component of 3D animation sequences. This scheme is based on the principle component analysis (PCA) method, which represents the animation sequence using a small number of basis functions. Second-order linear prediction coding (LPC) is applied to the PCA coefficients in order to further reduce the code size by exploiting the temporal coherence present in the sequence. Our results show that applying LPC to the PCA scheme results in significant performance improvements relative to other coding methods. The use of these codes will make animated 3D data more accessible for graphics and visualization applications. r

We present a general approach to shape deformation based on energy minimization, and applications of this approach to the problems of image resizing and 2D shape deformation. Our deformation energy generalizes that found in the prior art, while still admitting an efficient algorithm for its optimization. The key advantage of our energy function is the flexibility with which the set of "legal transformations" may be expressed; these transformations are the ones which are not considered to be distorting. This flexibility allows us to pose the problems of image resizing and 2D shape deformation in a natural way and generate minimally distorted results. It also allows us to strongly reduce undesirable foldovers or self-intersections. Results of both algorithms demonstrate the effectiveness of our approach.

An approach to automatically select stable and salient representative views of a given 3D object is proposed. Initially, a set of viewpoints are uniformly sampled along the surface of a bounding sphere. The sampled viewpoints are connected to their closest points to form a spherical graph in which each edge is weighted by a similarity measure between the two views from its incident vertices. Partitions of similar views are obtained using a graph partitioning procedure and their "centroids" are considered to be their representative views. Finally, the views are ranked based on a saliency measure to form the object's representative views. This leads to a compact, human-oriented 2D description of a 3D object, and as such, is useful both for traditional applications like presentation and analysis of 3D shapes, and for emerging ones like indexing and retrieval in large shape repositories.