This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationship between quantization, modelling, and encoding in a compression scheme is examined. Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed. A coder with explicit separation of the modelling and encoding roles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees. Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW, coders are discussed. A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder. Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video).

In digital watermarking, one embeds a watermark into a covertext, in such a way that the resulting watermarked signal is robust to a certain distortion caused by either standard data processing in a friendly environment or malicious attacks in an unfriendly environment. In addition to the robustness, there are two other conflicting requirements a good watermarking system should meet: one is referred as perceptual quality, that is, the distortion incurred to the original signal should be small; and the other is payload, the amount of information embedded (embedding rate) should be as high as possible. To a large extent, digital watermarking is a science and/or art aiming to design watermarking systems meeting these three conflicting requirements. As watermarked signals are highly desired to be compressed in real world applications, we have looked into the design and analysis of joint watermarking and compression (JWC) systems to achieve efficient tradeoffs among the embedding rate, compression rate, distortion and robustness. Using variable-rate scalar quantization, an optimum encoding and decoding scheme for JWC systems is designed and analyzed to maximize the robustness in the presence of additive Gaussian attacks under constraints on both compression distortion and composite rate. Simulation results show that in comparison with the previous work of designing JWC systems using fixed-rate scalar quantization, optimum JWC systems using variable-rate scalar quantization can achieve better performance in the distortion-to-noise ratio region of practical interest. Inspired by the good performance of JWC systems, we then investigate its applications in image compression. We look into the design of a joint image compression and blind watermarking system to maximize the compression rate-distortion performance while maintaining baseline JPEG decoder compatibility and satisfying the additional constraints imposed by watermarking. Two watermarking embedding schemes, odd-even watermarking (OEW) and zero-nonzero watermarking (ZNW), have been proposed for the robustness to a class of standard JPEG recompression attacks. To maximize the compression performance, two corresponding alternating algorithms have been developed to jointly optimize run-length coding, Huffman coding and quantization table selection subject to the additional constraints imposed by OEW and ZNW respectively. Both of two algorithms have been demonstrated to have better compression performance than the DQW and DEW algorithms developed in the recent literature. Compared with OEW scheme, the ZNW embedding method sacrifices some payload but earns more robustness against other types of attacks. In particular, the zero-nonzero watermarking scheme can survive a class of valumetric distortion attacks including additive noise, amplitude changes and recompression for everyday usage.

This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationship between quantization, modelling, and encoding in a compression scheme is examined. Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed. A coder with explicit separation of the modelling and encoding roles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees. Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW, coders are discussed. A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder. Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video).

In digital watermarking, one embeds a watermark into a covertext, in such a way that the resulting watermarked signal is robust to a certain distortion caused by either standard data processing in a friendly environment or malicious attacks in an unfriendly environment. In addition to the robustness, there are two other conflicting requirements a good watermarking system should meet: one is referred as perceptual quality, that is, the distortion incurred to the original signal should be small; and the other is payload, the amount of information embedded (embedding rate) should be as high as possible. To a large extent, digital watermarking is a science and/or art aiming to design watermarking systems meeting these three conflicting requirements. As watermarked signals are highly desired to be compressed in real world applications, we have looked into the design and analysis of joint watermarking and compression (JWC) systems to achieve efficient tradeoffs among the embedding rate, compression rate, distortion and robustness. Using variable-rate scalar quantization, an optimum encoding and decoding scheme for JWC systems is designed and analyzed to maximize the robustness in the presence of additive Gaussian attacks under constraints on both compression distortion and composite rate. Simulation results show that in comparison with the previous work of designing JWC systems using fixed-rate scalar quantization, optimum JWC systems using variable-rate scalar quantization can achieve better performance in the distortion-to-noise ratio region of practical interest. Inspired by the good performance of JWC systems, we then investigate its applications in image compression. We look into the design of a joint image compression and blind watermarking system to maximize the compression rate-distortion performance while maintaining baseline JPEG decoder compatibility and satisfying the additional constraints imposed by watermarking. Two watermarking embedding schemes, odd-even watermarking (OEW) and zero-nonzero watermarking (ZNW), have been proposed for the robustness to a class of standard JPEG recompression attacks. To maximize the compression performance, two corresponding alternating algorithms have been developed to jointly optimize run-length coding, Huffman coding and quantization table selection subject to the additional constraints imposed by OEW and ZNW respectively. Both of two algorithms have been demonstrated to have better compression performance than the DQW and DEW algorithms developed in the recent literature. Compared with OEW scheme, the ZNW embedding method sacrifices some payload but earns more robustness against other types of attacks. In particular, the zero-nonzero watermarking scheme can survive a class of valumetric distortion attacks including additive noise, amplitude changes and recompression for everyday usage.

Digital image and video in their raw form require an enormous amount of storage capacity. Considering the important role played by digital imaging and video, it is necessary to develop a system that produces high degree of compression while preserving critical image/video information. There are various transformation techniques used for data compression. Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) are the most commonly used transformation. DCT has high energy compaction property and requires less computational resources. On the other hand, DWT is multiresolution transformation.<p> In this work, we propose a hybrid DWT-DCT algorithm for image compression and reconstruction taking benefit from the advantages of both algorithms. The algorithm performs the Discrete Cosine Transform (DCT) on the Discrete Wavelet Transform (DWT) coefficients. Simulations have been conducted on several natural, benchmark, medical and endoscopic images. Several QCIF, high definition, and endoscopic videos have also been used to demonstrate the advantage of the proposed scheme.<p> The simulation results show that the proposed hybrid DWT-DCT algorithm performs much better than the standalone JPEG-based DCT, DWT, and WHT algorithms in terms of peak signal to noise ratio (PSNR), as well as visual perception at higher compression ratio. The new scheme reduces false contouring and blocking artifacts significantly. The rate distortion analysis shows that for a fixed level of distortion, the number of bits required to transmit the hybrid coefficients would be less than those required for other schemes Furthermore, the proposed algorithm is also compared with the some existing hybrid algorithms. The comparison results show that, the proposed hybrid algorithm has better performance and reconstruction quality. The proposed scheme is intended to be used as the image/video compressor engine in imaging and video applications.

In this dissertation, several GA-based approaches for fractal image compression and active contour model are proposed. The main drawback of the classical fractal image compression is the long encoding time. Two methods are proposed in this dissertation to solve this problem. First, a schema genetic algorithm (SGA), in which the Schema Theorem is embedded in GA, is proposed to reduce the encoding time. In SGA, the genetic operators are adapted according to the Schema Theorem in the evolutionary process performed on the range blocks. We find that such a method can indeed speedup the encoder and also preserve the image quality. Moreover, based on the self-similarity characteristic of the natural image, a spatial correlation genetic algorithm (SC-GA) is proposed to further reduce the encoding time. There are two stages in the SC-GA method. The first stage makes use of spatial correlations in images for both the domain pool and the range pool to exploit local optima. The second stage is operated on the whole image to explore more adequate similarities if the local optima are not satisfactory. Thus not only the encoding speed is accelerated further, but also the higher compression ratio is achieved, because the search space is limited relative to the positions of the previously matched blocks, fewer bits are required to record the offset of the domain block instead of the absolute position. The experimental results of comparing the two methods with the full search, traditional GA, and other GA search methods are provided to demonstrate that they can indeed reduce the encoding time substantially. The main drawback of the traditional active contour model (ACM) for extracting the contour of a given object is that the snake cannot converge to the concave region of the object under consideration. An improved ACM algorithm is proposed in this dissertation to solve this problem. The algorithm is composed of two stages. In the first stage, the ACM with traditional energy function guides the snake to converge to the object boundary except the concave regions. In the second stage, for the control points which stay outside the concave regions, a proper energy template are chosen and are added in the external energy. The modified energy function is applied so as to move the snake toward the concave regions. Therefore, the object of interest can be completely extracted. The experimental results show that, by using this method, the snake can indeed completely extract the boundary of the given object, while the extra cost is very low. In addition, for the problem that the snake cannot precisely extract the object contour when the number of the control points on the snake is not enough, a GA-based ACM algorithm is presented to deal with such a problem. First the improved ACM algorithm is used to guide the snake to approximately extract the object boundary. By utilizing the evolutionary strategy of GA, we attempt to extract precisely the object boundary by adding a few control points into the snake. Similarly, some experimental results are provided to show the performance of the method.

In this dissertation, particle swarm optimization (PSO) is utilized for fractal image compression (FIC) and active contour model (ACM). The dissertation is divided into two parts. The first part is concerned with the FIC and the second part with ACM. FIC is promising both theoretically and practically for image compression. However, since the encoding speed of the traditional full search method is very time-consuming, FIC with full search is unsuitable for real-time applications. In this dissertation, several novel PSO-based approaches incorporating the edge property of the image blocks are proposed to speedup the encoder and preserve the image quality. Instead of the full search, a direction map is built according to the edge type of the image blocks, which directs the particles in the swarm to regions consisting of candidates of higher similarity. Therefore, the searching space is reduced and the speedup can be achieved. Also, since the strategy is performed according to the edge property, better visual effect can be preserved. Experimental results show that the visual-based particle swarm optimization speeds up the encoder 125 times faster with only 0.89 dB decay of image quality in comparison to the full search method. The second part of the dissertation is concerned with the active contour model for automatic object boundary identification. In the traditional methods for ACM, each control point searches its new position in a small nearby window. Consequently, the boundary concavities cannot be searched accurately. Some improvements have been made in the past to enlarge the searching space, yet they are still time-consuming. To overcome these drawbacks, a novel multi-population PSO technique is adopted in this dissertation to enhance the concavity searching capability and reduce the search time but in a larger searching window. In the proposed scheme, to each control point in the contour there is a corresponding swarm of particles with the best swarm particle as the new control point. The proposed optimizer not only inherits the spirit of the original PSO in each swarm but also shares information of the surrounding swarms. Experimental results demonstrate that the proposed method can improve the search of object concavities without extra computation time.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 163-178). Also available in electronic version. Access restricted to campus users.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Jayant, Nikil; Committee Member: Anderson, David; Committee Member: Lee, Chin-Hui. Part of the SMARTech Electronic Thesis and Dissertation Collection.

published_or_final_version / abstract / toc / Electrical and Electronic Engineering / Master / Master of Philosophy