Static 3D Triangle Mesh Compression Overview

3D triangle meshes are extremely used to model discrete surfaces, and almost always represented with two tables: one for geometry and another for connectivity. While the raw size of a triangle mesh is of around 200 bits per vertex, by coding cleverly (and separately) those two distinct kinds of information it is possible to achieve compression ratios of 15:1 or more. Different techniques must be used depending on whether single-rate vs. progressive bitstreams are sought; and, in the latter case, on whether or not hierarchically nested meshes are desirable during reconstructio

Connectivity Compression for Irregular Quadrilateral Meshes

Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and VRML models, however, are represented as quadrilateral meshes or mixed triangle/quadrilateral meshes, and these models may also require compression. We present an algorithm for encoding the connectivity of such quadrilateral meshes, and we demonstrate that by preserving and exploiting the original quad structure, our approach achieves encodings 30 - 80% smaller than an approach based on randomly splitting quads into triangles. We present both a code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per vertex for meshes without valence-two vertices) and entropy-coding results for typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the regularity of the mesh. Our method may be implemented by a rule for a particular splitting of quads into triangles and by using the compression and decompression algorithms introduced in [Rossignac99] and [Rossignac&Szymczak99]. We also present extensions to the algorithm to compress meshes with holes and handles and meshes containing triangles and other polygons as well as quads

Row Compression and Nested Product Decomposition of a Hierarchical Representation of a Quasiseparable Matrix

This research introduces a row compression and nested product decomposition of an nxn hierarchical representation of a rank structured matrix A, which extends the compression and nested product decomposition of a quasiseparable matrix. The hierarchical parameter extraction algorithm of a quasiseparable matrix is efficient, requiring only O(nlog(n))operations, and is proven backward stable. The row compression is comprised of a sequence of small Householder transformations that are formed from the low-rank, lower triangular, off-diagonal blocks of the hierarchical representation. The row compression forms a factorization of matrix A, where A = QC, Q is the product of the Householder transformations, and C preserves the low-rank structure in both the lower and upper triangular parts of matrix A. The nested product decomposition is accomplished by applying a sequence of orthogonal transformations to the low-rank, upper triangular, off-diagonal blocks of the compressed matrix C. Both the compression and decomposition algorithms are stable, and require O(nlog(n)) operations. At this point, the matrix-vector product and solver algorithms are the only ones fully proven to be backward stable for quasiseparable matrices. By combining the fast matrix-vector product and system solver, linear systems involving the hierarchical representation to nested product decomposition are directly solved with linear complexity and unconditional stability. Applications in image deblurring and compression, that capitalize on the concepts from the row compression and nested product decomposition algorithms, will be shown

Morphological operators for very low bit rate video coding

This paper deals with the use of some morphological tools for video coding at very low bit rates. Rather than describing a complete coding algorithm, the purpose of this paper is to focus on morphological connected operators and segmentation tools that have proved to be attractive for compression.Peer ReviewedPostprint (published version

Image compression with anisotropic diffusion

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec

Artificial Sequences and Complexity Measures

In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We introduce in particular a class of methods which use in a crucial way data compression techniques in order to define a measure of remoteness and distance between pairs of sequences of characters (e.g. texts) based on their relative information content. We also discuss in detail how specific features of data compression techniques could be used to introduce the notion of dictionary of a given sequence and of Artificial Text and we show how these new tools can be used for information extraction purposes. We point out the versatility and generality of our method that applies to any kind of corpora of character strings independently of the type of coding behind them. We consider as a case study linguistic motivated problems and we present results for automatic language recognition, authorship attribution and self consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression approach to Information Extraction and Classification" by A. Baronchelli and V. Loreto. 15 pages; 5 figure

Parallel data compression

Data compression schemes remove data redundancy in communicated and stored data and increase the effective capacities of communication and storage devices. Parallel algorithms and implementations for textual data compression are surveyed. Related concepts from parallel computation and information theory are briefly discussed. Static and dynamic methods for codeword construction and transmission on various models of parallel computation are described. Included are parallel methods which boost system speed by coding data concurrently, and approaches which employ multiple compression techniques to improve compression ratios. Theoretical and empirical comparisons are reported and areas for future research are suggested

Language Trees and Zipping

In this letter we present a very general method to extract information from a generic string of characters, e.g. a text, a DNA sequence or a time series. Based on data-compression techniques, its key point is the computation of a suitable measure of the remoteness of two bodies of knowledge. We present the implementation of the method to linguistic motivated problems, featuring highly accurate results for language recognition, authorship attribution and language classification.Comment: 5 pages, RevTeX4, 1 eps figure. In press in Phys. Rev. Lett. (January 2002