Dynamic Mesh Compression

The interdisciplinary research area of geometry processing combines concepts from informatics, applied mathematics, and engineering for the efficient acquisition, reconstruction, optimization, editing, and simulation of geometric objects. Applications of geometry processing algorithms can be found in a wide range of areas, including computer graphics, computer aided design, geography, and scientific computing. Moreover, this research field enjoys a significant economic impact as it delivers essential ingredients for the production of cars, airplanes, movies, and computer games, for example.

Over the last years, a novel trend has emerged within this field, which concentrates on time-varying geometry. As opposed to classical processing of static 3D surfaces, the new goal is to develop algorithms for efficiently handling dynamic 3D surfaces, which frequently occur in applications like character animation or physical simulations. These kind of 4D objects are most commonly represented as a discrete sequence of frames, each of which is given as a mesh with a common graph structure. Such sequences have the flexibility to represent a wide range of mesh deformations used in practice, but they are also highly redundant and expensive to store. Hence, there is a great need for dynamic mesh compression algorithms.

While common methods for compressing mesh sequences rely on the meshes being stored in terms of vertex coordinates, the aim of this project is to develop lossy compression algorithms based on an alternative mesh representation in an edge-based shape space, that is, by storing lengths and dihedral angles for all edges. This approach is motivated by the observation that these quantities vary comparatively little over time, in particular for the rigid parts of an animated character. We plan to further investigate this behaviour, to provide a better understanding of the underlying principles, and to turn our findings into efficient algorithms for encoding and decoding sequences of meshes. We expect our results to considerably advance the state of the art in this field and to have an impact on related geometry processing algorithms which may benefit from an edge-based mesh representation.

In particular, we will address the following problems: First, we will explore the setting of single-rate compression, where each frame of the sequence must be fully decoded before decoding the next one. Second, we will consider a progressive approach, where the sequence is considered at different levels of detail and the compression algorithm takes advantage of this multi-resolution representation. Third, we plan to develop a technique that is based on a segmentation of the dynamic mesh into rigid and non-rigid parts and is therefore particularly tailored for compressing character animations. A key ingredient to all these approaches is to have an efficient method at hand for converting meshes from the edge-based representation back into usual vertex coordinates. Currently, two methods exist for performing this operation, both with advantages and disadvantages, and we want to design a hybrid approach that combines the positive aspects of the two methods. Finally, we will also focus on the problem of measuring the distance between a given mesh sequence and its reconstructed counterpart, so as to be able to properly evaluate the results of lossy compression algorithms, as well as to optimize their performance. Recent results reveal that edge-based error measures capture visually perceived artefacts better than vertex-based variants, and we want to further explore the use of such error measures which naturally fit our approach of working with edge-based mesh representations.