3-D Mesh Geometry Compression With Set Partitioning in the Spectral Domain

Abstract

This paper explains the development of a highly efficient progressive 3-D mesh geometry coder based on the region adaptive transform in the spectral mesh compression method. A hierarchical set partitioning technique, originally proposed for the efficient compression of wavelet transform coefficients in high performance wavelet based image coding methods, is proposed for the efficient compression of the coefficients of this transform. Experiments confirm that the proposed coder employing such a region adaptive transform has a high compression performance rarely achieved by other state of the art 3-D mesh geometry compression algorithms. A new, high performance fixed spectral basis method is also proposed for reducing the computational complexity of the transform. Many-to-one mappings are employed to relate the coded irregular mesh region to a regular mesh whose basis is used. To prevent loss of compression performance due to the low-pass nature of such mappings, transitions are made from transform based coding to spatial coding on a per region basis at high coding rates. Experimental results show the performance advantage of the newly proposed fixed spectral basis method over the original fixed spectral basis method in the literature that employs one-to-one mappings.

3D Mesh Compression

“…The compression becomes less efficient but the decompression is accelerated since the eigenvector decomposition is not computed anymore. Bayazit et al [2010] reduced the computational complexity of the mapping method. They also used a bit plane encoder for the spectral coefficients.…”

Optimization techniques of static 3D triangular mesh compression: A survey

“…That has improved the visual quality in the cost of low rate-distortion trade-off. After that, in 2010, Bayazit et al [25] solved the problem of complexity by proposing a new fixed-spectral bases scheme that employs many-to-one mappings. Geometry image introduced by GU et al [26] to represent an arbitrary mesh onto a regular mesh in 2D space.…”

Novel methods of image compression for 3D reconstruction

“…The GPUs (Graphic Processor unit) can be usedto process a 3D mesh in parallel [64]. An optimized method to transfer mesh data can significantly decrease processing time such as the use of triangle strips.These strips are transferred from main memory to GPU memory.…”

“…The prediction uses correlation between adjacent coordinates, and the most important aspect of prediction is to reduce the amount of geometry, and then encoding with one of entropy coding methods (Huffman or Arithmetic coding).There are different prediction methods that have been proposed in theliterature: delta prediction [78], linear prediction [64,65], and parallelogramprediction [101]. Overall, the predictions schema is considered as linear prediction and their coefficients are chosen carefully.…”

“…Chow [64]proposed a mesh compression method for real-time rendering as showed in Figure 2.3. The methods start with finding the boundary edges, next step searching for triangle fans around a vertex fallen on two successive boundary edges.…”