Variable-resolution Compression of Vector Data

The compression of spatial data is a promising solution to reduce the space of data storage and to decrease the transmission time of spatial data over the Internet. This paper proposes a new method for variable-resolution compression of vector data. Three key steps are encompassed in the proposed method, namely, the simplification of vector data via the elimination of vertices, the compression of removed vertices, and the decoding of the compressed vector data. The proposed compression method was implemented and applied to compress vector data to investigate its performance in terms of the compression ratio, distortions of geometric shapes. The results show that the proposed method provides a feasible and efficient solution for the compression of vector data, is able to achieve good compression ratios and maintains the main shape characteristics of the spatial objects within the compressed vector dat

Information Analysis for Steganography and Steganalysis in 3D Polygonal Meshes

Information hiding, which embeds a watermark/message over a cover signal, has recently found extensive applications in, for example, copyright protection, content authentication and covert communication. It has been widely considered as an appealing technology to complement conventional cryptographic processes in the field of multimedia security by embedding information into the signal being protected. Generally, information hiding can be classified into two categories: steganography and watermarking. While steganography attempts to embed as much information as possible into a cover signal, watermarking tries to emphasize the robustness of the embedded information at the expense of embedding capacity. In contrast to information hiding, steganalysis aims at detecting whether a given medium has hidden message in it, and, if possible, recover that hidden message. It can be used to measure the security performance of information hiding techniques, meaning a steganalysis resistant steganographic/watermarking method should be imperceptible not only to Human Vision Systems (HVS), but also to intelligent analysis. As yet, 3D information hiding and steganalysis has received relatively less attention compared to image information hiding, despite the proliferation of 3D computer graphics models which are fairly promising information carriers. This thesis focuses on this relatively neglected research area and has the following primary objectives: 1) to investigate the trade-off between embedding capacity and distortion by considering the correlation between spatial and normal/curvature noise in triangle meshes; 2) to design satisfactory 3D steganographic algorithms, taking into account this trade-off; 3) to design robust 3D watermarking algorithms; 4) to propose a steganalysis framework for detecting the existence of the hidden information in 3D models and introduce a universal 3D steganalytic method under this framework. %and demonstrate the performance of the proposed steganalysis by testing it against six well-known 3D steganographic/watermarking methods. The thesis is organized as follows. Chapter 1 describes in detail the background relating to information hiding and steganalysis, as well as the research problems this thesis will be studying. Chapter 2 conducts a survey on the previous information hiding techniques for digital images, 3D models and other medium and also on image steganalysis algorithms. Motivated by the observation that the knowledge of the spatial accuracy of the mesh vertices does not easily translate into information related to the accuracy of other visually important mesh attributes such as normals, Chapters 3 and 4 investigate the impact of modifying vertex coordinates of 3D triangle models on the mesh normals. Chapter 3 presents the results of an empirical investigation, whereas Chapter 4 presents the results of a theoretical study. Based on these results, a high-capacity 3D steganographic algorithm capable of controlling embedding distortion is also presented in Chapter 4. In addition to normal information, several mesh interrogation, processing and rendering algorithms make direct or indirect use of curvature information. Motivated by this, Chapter 5 studies the relation between Discrete Gaussian Curvature (DGC) degradation and vertex coordinate modifications. Chapter 6 proposes a robust watermarking algorithm for 3D polygonal models, based on modifying the histogram of the distances from the model vertices to a point in 3D space. That point is determined by applying Principal Component Analysis (PCA) to the cover model. The use of PCA makes the watermarking method robust against common 3D operations, such as rotation, translation and vertex reordering. In addition, Chapter 6 develops a 3D specific steganalytic algorithm to detect the existence of the hidden messages embedded by one well-known watermarking method. By contrast, the focus of Chapter 7 will be on developing a 3D watermarking algorithm that is resistant to mesh editing or deformation attacks that change the global shape of the mesh. By adopting a framework which has been successfully developed for image steganalysis, Chapter 8 designs a 3D steganalysis method to detect the existence of messages hidden in 3D models with existing steganographic and watermarking algorithms. The efficiency of this steganalytic algorithm has been evaluated on five state-of-the-art 3D watermarking/steganographic methods. Moreover, being a universal steganalytic algorithm can be used as a benchmark for measuring the anti-steganalysis performance of other existing and most importantly future watermarking/steganographic algorithms. Chapter 9 concludes this thesis and also suggests some potential directions for future work

Shape representation and coding of visual objets in multimedia applications — An overview

Emerging multimedia applications have created the need for new functionalities in digital communications. Whereas existing compression standards only deal with the audio-visual scene at a frame level, it is now necessary to handle individual objects separately, thus allowing scalable transmission as well as interactive scene recomposition by the receiver. The future MPEG-4 standard aims at providing compression tools addressing these functionalities. Unlike existing frame-based standards, the corresponding coding schemes need to encode shape information explicitly. This paper reviews existing solutions to the problem of shape representation and coding. Region and contour coding techniques are presented and their performance is discussed, considering coding efficiency and rate-distortion control capability, as well as flexibility to application requirements such as progressive transmission, low-delay coding, and error robustnes

Compression of 3D models with NURBS

With recent progress in computing, algorithmics and telecommunications, 3D models are increasingly used in various multimedia applications. Examples include visualization, gaming, entertainment and virtual reality. In the multimedia domain 3D models have been traditionally represented as polygonal meshes. This piecewise planar representation can be thought of as the analogy of bitmap images for 3D surfaces. As bitmap images, they enjoy great flexibility and are particularly well suited to describing information captured from the real world, through, for instance, scanning processes. They suffer, however, from the same shortcomings, namely limited resolution and large storage size. The compression of polygonal meshes has been a very active field of research in the last decade and rather efficient compression algorithms have been proposed in the literature that greatly mitigate the high storage costs. However, such a low level description of a 3D shape has a bounded performance. More efficient compression should be reachable through the use of higher level primitives. This idea has been explored to a great extent in the context of model based coding of visual information. In such an approach, when compressing the visual information a higher level representation (e.g., 3D model of a talking head) is obtained through analysis methods. This can be seen as an inverse projection problem. Once this task is fullled, the resulting parameters of the model are coded instead of the original information. It is believed that if the analysis module is efficient enough, the total cost of coding (in a rate distortion sense) will be greatly reduced. The relatively poor performance and high complexity of currently available analysis methods (except for specific cases where a priori knowledge about the nature of the objects is available), has refrained a large deployment of coding techniques based on such an approach. Progress in computer graphics has however changed this situation. In fact, nowadays, an increasing number of pictures, video and 3D content are generated by synthesis processing rather than coming from a capture device such as a camera or a scanner. This means that the underlying model in the synthesis stage can be used for their efficient coding without the need for a complex analysis module. In other words it would be a mistake to attempt to compress a low level description (e.g., a polygonal mesh) when a higher level one is available from the synthesis process (e.g., a parametric surface). This is, however, what is usually done in the multimedia domain, where higher level 3D model descriptions are converted to polygonal meshes, if anything by the lack of standard coded formats for the former. On a parallel but related path, the way we consume audio-visual information is changing. As opposed to recent past and a large part of today's applications, interactivity is becoming a key element in the way we consume information. In the context of interest in this dissertation, this means that when coding visual information (an image or a video for instance), previously obvious considerations such as decision on sampling parameters are not so obvious anymore. In fact, as in an interactive environment the effective display resolution can be controlled by the user through zooming, there is no clear optimal setting for the sampling period. This means that because of interactivity, the representation used to code the scene should allow the display of objects in a variety of resolutions, and ideally up to infinity. One way to resolve this problem would be by extensive over-sampling. But this approach is unrealistic and too expensive to implement in many situations. The alternative would be to use a resolution independent representation. In the realm of 3D modeling, such representations are usually available when the models are created by an artist on a computer. The scope of this dissertation is precisely the compression of 3D models in higher level forms. The direct coding in such a form should yield improved rate-distortion performance while providing a large degree of resolution independence. There has not been, so far, any major attempt to efficiently compress these representations, such as parametric surfaces. This thesis proposes a solution to overcome this gap. A variety of higher level 3D representations exist, of which parametric surfaces are a popular choice among designers. Within parametric surfaces, Non-Uniform Rational B-Splines (NURBS) enjoy great popularity as a wide range of NURBS based modeling tools are readily available. Recently, NURBS has been included in the Virtual Reality Modeling Language (VRML) and its next generation descendant eXtensible 3D (X3D). The nice properties of NURBS and their widespread use has lead us to choose them as the form we use for the coded representation. The primary goal of this dissertation is the definition of a system for coding 3D NURBS models with guaranteed distortion. The basis of the system is entropy coded differential pulse coded modulation (DPCM). In the case of NURBS, guaranteeing the distortion is not trivial, as some of its parameters (e.g., knots) have a complicated influence on the overall surface distortion. To this end, a detailed distortion analysis is performed. In particular, previously unknown relations between the distortion of knots and the resulting surface distortion are demonstrated. Compression efficiency is pursued at every stage and simple yet efficient entropy coder realizations are defined. The special case of degenerate and closed surfaces with duplicate control points is addressed and an efficient yet simple coding is proposed to compress the duplicate relationships. Encoder aspects are also analyzed. Optimal predictors are found that perform well across a wide class of models. Simplification techniques are also considered for improved compression efficiency at negligible distortion cost. Transmission over error prone channels is also considered and an error resilient extension defined. The data stream is partitioned by independently coding small groups of surfaces and inserting the necessary resynchronization markers. Simple strategies for achieving the desired level of protection are proposed. The same extension also serves the purpose of random access and on-the-fly reordering of the data stream

A new method for simplification and compression of 3D meshes

We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply-connected regions, called triangloids. We compute a new mesh M\u27. Each triangle of M\u27 is a close approximation of a pseudo-triangle of M. By construction, the connectivity of M\u27 is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of M\u27 are compactly encoded with our new prediction scheme, which uses a single correction parameter per vertex. For example, a variety of popular models retiled with our approach yield 10 times fewer triangles without exceeding an error of 1% of the radius of the bounding ball. Vertices of M\u27 are encoded with an average of 6 bits, which results in a total storage of 0.4 bits per triangle of the original mesh. The proposed solution may also be used to encode crude meshes for adaptive transmission and for controlling subdivision surfaces

Progressive coding of 3D objects based on overcomplete decompositions

This paper presents a progressive coding scheme for 3D objects, based on an overcomplete decomposition of the 3D model on a sphere. Due to increased freedom in the bases construction, redundant expansions have shown interesting approximation properties in the decomposition of signals with multidimensional singularities organized along embedded submanifolds. We propose to map simple 3D models on 2D spheres and then to decompose the signal over a redundant dictionary of oriented and anisotropic atoms that live on the sphere. The signal expansion is computed iteratively with a Matching Pursuit algorithm, which greedily selects the most prominent components of the 3D model. The decomposition therefore inherently represents a progressive stream of atoms, which is advantageously used in the design of scalable representations. An encoder is proposed that compresses the stream of atoms by adaptive coefficient quantization, and entropy coding of atom indexes. Experimental results show that the novel coding strategy outperforms state-of-the-art progressive coders in terms of distortion, mostly at low bit rate. Furthermore, since the dictionary is built on structured atoms, the representation simultaneously offers an increased flexibility. This enables easy stream manipulations, and we finally illustrate this advantage in the design of a view-dependent transmission scheme

Variable-resolution Compression of Vector Data

The compression of spatial data is a promising solution to reduce the space of data storage and to decrease the transmission time of spatial data over the Internet. This paper proposes a new method for variable-resolution compression of vector data. Three key steps are encompassed in the proposed method, namely, the simplification of vector data via the elimination of vertices, the compression of removed vertices, and the decoding of the compressed vector data. The proposed compression method was implemented and applied to compress vector data to investigate its performance in terms of the compression ratio, distortions of geometric shapes. The results show that the proposed method provides a feasible and efficient solution for the compression of vector data, is able to achieve good compression ratios and maintains the main shape characteristics of the spatial objects within the compressed vector data