A new progressive lossy-to-lossless coding framework for 2.5-dimensional (2.5-D) triangle meshes with arbitrary connectivity is proposed by combining ideas from the previously proposed average-difference image-tree (ADIT) method and the Peng-Kuo (PK) method with several modifications. The proposed method represents the 2.5-D triangle mesh with a binary tree data structure, and codes the tree by a top-down traversal. The proposed framework contains several parameters. Many variations are tried in order to find a good choice for each parameter considering both the lossless and progressive coding performance. Based on extensive experimentation, we recommend a particular set of best choices to be used for these parameters, leading to the mesh-coding method proposed herein / Graduate

The need to compactly represent 3D data is motivated by the ever-increasing size of these data. Furthermore, for large data sets it is useful to randomly access and process a small part of the data. In this thesis we propose two methods of compactly representing 3D data while allowing random access. The first is the multiresolution sphere-packing tree (MSP-tree). The MSP-tree is a multiresolution 3D hierarchy on regular grids based on sphere-packing arrangements. The grids of the MSP-tree compactly represent underlying point-sampled data by using more efficient grids than existing methods while maintaining high granularity and a hierarchical structure that allows random access. The second is distance-ranked random-accessible mesh compression (DR-RAMC). DR-RAMC is a lossless simplicial mesh compressor that allows random access and decompression of the mesh data based on a spatial region-of-interest. DR-RAMC encodes connectivity based on relative proximity of vertices to each other and organizes both this proximity data and vertex coordinates using a k-d tree. DR-RAMC is insensitive to a variety of topological mesh problems (e.g. holes, handles, non-orientability) and can compress simplicial meshes of any dimension embedded in spaces of any dimension. Testing of DR-RAMC shows competitive compression rates for triangle meshes and first-ever random accessible compression rates for tetrahedral meshes. / Thesis (Ph.D, Computing) -- Queen's University, 2012-07-17 15:28:39.406

A compressão de dados é uma área de muito interesse em termos computacionais devido à necessidade de armazená-los e transmiti-los. Em particular, a compressão de malhas possui grande interesse em função do crescimento de sua utilização em jogos tridimensionais e modelagens diversas. Nos últimos anos, uma nova teoria de aquisição e reconstrução de sinais foi desenvolvida, baseada no conceito de esparsidade na minimização da norma L1 e na incoerência do sinal, chamada Compressive Sensing (CS). Essa teoria possui algumas características marcantes, como a aleatoriedade de amostragem e a reconstrução via minimização, de modo que a própria aquisição do sinal é feita considerando somente os coeficientes significativos. Qualquer objeto que possa ser interpretado como um sinal esparso permite sua utilização. Assim, ao se representar esparsamente um objeto (sons, imagens) é possível aplicar a técnica de CS. Este trabalho verifica a viabilidade da aplicação da teoria de CS na compressão de malhas, de modo que seja possível um sensoreamento e representação compressivos na geometria de uma malha. Nos experimentos realizados, foram utilizadas variações dos parâmetros de entrada e técnicas de minimização da Norma L1. Os resultados obtidos mostram que a técnica de CS pode ser utilizada como estratégia de compressão da geometria das malhas. / Data compression is an area of a major interest in computational terms due to the issues on storage and transmission. Particularly, mesh compression has wide usage due to the increase of its application in games and three-dimensional modeling. In recent years, a new theory of acquisition and reconstruction of signals was developed, based on the concept of sparsity and in the minimization of the L1 norm and the incoherency of the signal, called Compressive Sensing (CS). This theory has some remarkable features, such as random sampling and reconstruction by minimization, in a way that the signal acquisition is done by considering only its significant coefficients. Any object that can be interpreted as a sparse sign allows its use. Thus, representing an object sparsely (sounds, images), you can apply the technique of CS. This work explores the viability of CS theory on mesh compression, so that it is possible a representative and compressive sensing on the mesh geometry. In the performed experiments, different parameters and L1 Norm minimization strategies were used. The results show that CS can be used as a mesh geometry compression strategy.

A compressão de dados é uma área de muito interesse em termos computacionais devido à necessidade de armazená-los e transmiti-los. Em particular, a compressão de malhas possui grande interesse em função do crescimento de sua utilização em jogos tridimensionais e modelagens diversas. Nos últimos anos, uma nova teoria de aquisição e reconstrução de sinais foi desenvolvida, baseada no conceito de esparsidade na minimização da norma L1 e na incoerência do sinal, chamada Compressive Sensing (CS). Essa teoria possui algumas características marcantes, como a aleatoriedade de amostragem e a reconstrução via minimização, de modo que a própria aquisição do sinal é feita considerando somente os coeficientes significativos. Qualquer objeto que possa ser interpretado como um sinal esparso permite sua utilização. Assim, ao se representar esparsamente um objeto (sons, imagens) é possível aplicar a técnica de CS. Este trabalho verifica a viabilidade da aplicação da teoria de CS na compressão de malhas, de modo que seja possível um sensoreamento e representação compressivos na geometria de uma malha. Nos experimentos realizados, foram utilizadas variações dos parâmetros de entrada e técnicas de minimização da Norma L1. Os resultados obtidos mostram que a técnica de CS pode ser utilizada como estratégia de compressão da geometria das malhas. / Data compression is an area of a major interest in computational terms due to the issues on storage and transmission. Particularly, mesh compression has wide usage due to the increase of its application in games and three-dimensional modeling. In recent years, a new theory of acquisition and reconstruction of signals was developed, based on the concept of sparsity and in the minimization of the L1 norm and the incoherency of the signal, called Compressive Sensing (CS). This theory has some remarkable features, such as random sampling and reconstruction by minimization, in a way that the signal acquisition is done by considering only its significant coefficients. Any object that can be interpreted as a sparse sign allows its use. Thus, representing an object sparsely (sounds, images), you can apply the technique of CS. This work explores the viability of CS theory on mesh compression, so that it is possible a representative and compressive sensing on the mesh geometry. In the performed experiments, different parameters and L1 Norm minimization strategies were used. The results show that CS can be used as a mesh geometry compression strategy.

Yes / The development of the patchwise Partial Di erential Equation (PDE) framework a few years a- go has paved the way for the PDE method to be used in mesh signal processing. In this paper we, for the rst time, extend the use of the PDE method to progressive mesh compression and mesh denoising. We, meanwhile, upgrade the existing patchwise PDE method in patch merging, mesh partitioning, and boundary extraction to accommodate mesh signal processing. In our new method an arbitrary mesh model is partitioned into patches, each of which can be represented by a small set of coe cients of its PDE spectral solution. Since low- frequency components contribute more to the recon- structed mesh than high-frequency ones, we can achieve progressive mesh compression and mesh denoising by manipulating the frequency terms of the PDE solution. Experimental results demonstrate the feasibility of our method in both progressive mesh compression and mesh denoising.

This thesis introduces a representation of graphical data, progressive meshes, and its fields of usage. The main part of this work is mathematical representation of progressive meshes and the simplification algorithm, which leads to this representation. Examples of changes in progressive mesh representation are also part of this thesis, along with few examples. The result is an application that implements the calculation of the Progressive Meshes model representation

The document describes developing graphical application with limited size. It describes suitable techniques for a polygonal mesh's compression. The second part is focused on practical usage of this techniques for developing scene in 3D modeling environment and also describes how to transfer this model to the executable file. The work attends to optimalizations of source code compilation and executables compression at the final chapters.