Due to the lossy nature of image/video compression and the expensive bandwidth and computation resources in a multimedia system, one of the key design issues for image and video coding/transcoding is to optimize trade-off among distortion, rate, and/or complexity. This thesis studies the application of rate distortion (RD) optimization approaches to image and video coding/transcoding for exploring the best RD performance of a video codec compatible to the newest video coding standard H.264 and for designing computationally efficient down-sampling algorithms with high visual fidelity in the discrete Cosine transform (DCT) domain. RD optimization for video coding in this thesis considers two objectives, i.e., to achieve the best encoding efficiency in terms of minimizing the actual RD cost and to maintain decoding compatibility with the newest video coding standard H.264. By the actual RD cost, we mean a cost based on the final reconstruction error and the entire coding rate. Specifically, an operational RD method is proposed based on a soft decision quantization (SDQ) mechanism, which has its root in a fundamental RD theoretic study on fixed-slope lossy data compression. Using SDQ instead of hard decision quantization, we establish a general framework in which motion prediction, quantization, and entropy coding in a hybrid video coding scheme such as H.264 are jointly designed to minimize the actual RD cost on a frame basis. The proposed framework is applicable to optimize any hybrid video coding scheme, provided that specific algorithms are designed corresponding to coding syntaxes of a given standard codec, so as to maintain compatibility with the standard. Corresponding to the baseline profile syntaxes and the main profile syntaxes of H.264, respectively, we have proposed three RD algorithms---a graph-based algorithm for SDQ given motion prediction and quantization step sizes, an algorithm for residual coding optimization given motion prediction, and an iterative overall algorithm for jointly optimizing motion prediction, quantization, and entropy coding---with them embedded in the indicated order. Among the three algorithms, the SDQ design is the core, which is developed based on a given entropy coding method. Specifically, two SDQ algorithms have been developed based on the context adaptive variable length coding (CAVLC) in H.264 baseline profile and the context adaptive binary arithmetic coding (CABAC) in H.264 main profile, respectively. Experimental results for the H.264 baseline codec optimization show that for a set of typical testing sequences, the proposed RD method for H.264 baseline coding achieves a better trade-off between rate and distortion, i.e., 12\% rate reduction on average at the same distortion (ranging from 30dB to 38dB by PSNR) when compared with the RD optimization method implemented in H.264 baseline reference codec. Experimental results for optimizing H.264 main profile coding with CABAC show 10\% rate reduction over a main profile reference codec using CABAC, which also suggests 20\% rate reduction over the RD optimization method implemented in H.264 baseline reference codec, leading to our claim of having developed the best codec in terms of RD performance, while maintaining the compatibility with H.264. By investigating trade-off between distortion and complexity, we have also proposed a designing framework for image/video transcoding with spatial resolution reduction, i.e., to down-sample compressed images/video with an arbitrary ratio in the DCT domain. First, we derive a set of DCT-domain down-sampling methods, which can be represented by a linear transform with double-sided matrix multiplication (LTDS) in the DCT domain. Then, for a pre-selected pixel-domain down-sampling method, we formulate an optimization problem for finding an LTDS to approximate the given pixel-domain method to achieve the best trade-off between visual quality and computational complexity. The problem is then solved by modeling an LTDS with a multi-layer perceptron network and using a structural learning with forgetting algorithm for training the network. Finally, by selecting a pixel-domain reference method with the popular Butterworth lowpass filtering and cubic B-spline interpolation, the proposed framework discovers an LTDS with better visual quality and lower computational complexity when compared with state-of-the-art methods in the literature.

Due to the lossy nature of image/video compression and the expensive bandwidth and computation resources in a multimedia system, one of the key design issues for image and video coding/transcoding is to optimize trade-off among distortion, rate, and/or complexity. This thesis studies the application of rate distortion (RD) optimization approaches to image and video coding/transcoding for exploring the best RD performance of a video codec compatible to the newest video coding standard H.264 and for designing computationally efficient down-sampling algorithms with high visual fidelity in the discrete Cosine transform (DCT) domain. RD optimization for video coding in this thesis considers two objectives, i.e., to achieve the best encoding efficiency in terms of minimizing the actual RD cost and to maintain decoding compatibility with the newest video coding standard H.264. By the actual RD cost, we mean a cost based on the final reconstruction error and the entire coding rate. Specifically, an operational RD method is proposed based on a soft decision quantization (SDQ) mechanism, which has its root in a fundamental RD theoretic study on fixed-slope lossy data compression. Using SDQ instead of hard decision quantization, we establish a general framework in which motion prediction, quantization, and entropy coding in a hybrid video coding scheme such as H.264 are jointly designed to minimize the actual RD cost on a frame basis. The proposed framework is applicable to optimize any hybrid video coding scheme, provided that specific algorithms are designed corresponding to coding syntaxes of a given standard codec, so as to maintain compatibility with the standard. Corresponding to the baseline profile syntaxes and the main profile syntaxes of H.264, respectively, we have proposed three RD algorithms---a graph-based algorithm for SDQ given motion prediction and quantization step sizes, an algorithm for residual coding optimization given motion prediction, and an iterative overall algorithm for jointly optimizing motion prediction, quantization, and entropy coding---with them embedded in the indicated order. Among the three algorithms, the SDQ design is the core, which is developed based on a given entropy coding method. Specifically, two SDQ algorithms have been developed based on the context adaptive variable length coding (CAVLC) in H.264 baseline profile and the context adaptive binary arithmetic coding (CABAC) in H.264 main profile, respectively. Experimental results for the H.264 baseline codec optimization show that for a set of typical testing sequences, the proposed RD method for H.264 baseline coding achieves a better trade-off between rate and distortion, i.e., 12\% rate reduction on average at the same distortion (ranging from 30dB to 38dB by PSNR) when compared with the RD optimization method implemented in H.264 baseline reference codec. Experimental results for optimizing H.264 main profile coding with CABAC show 10\% rate reduction over a main profile reference codec using CABAC, which also suggests 20\% rate reduction over the RD optimization method implemented in H.264 baseline reference codec, leading to our claim of having developed the best codec in terms of RD performance, while maintaining the compatibility with H.264. By investigating trade-off between distortion and complexity, we have also proposed a designing framework for image/video transcoding with spatial resolution reduction, i.e., to down-sample compressed images/video with an arbitrary ratio in the DCT domain. First, we derive a set of DCT-domain down-sampling methods, which can be represented by a linear transform with double-sided matrix multiplication (LTDS) in the DCT domain. Then, for a pre-selected pixel-domain down-sampling method, we formulate an optimization problem for finding an LTDS to approximate the given pixel-domain method to achieve the best trade-off between visual quality and computational complexity. The problem is then solved by modeling an LTDS with a multi-layer perceptron network and using a structural learning with forgetting algorithm for training the network. Finally, by selecting a pixel-domain reference method with the popular Butterworth lowpass filtering and cubic B-spline interpolation, the proposed framework discovers an LTDS with better visual quality and lower computational complexity when compared with state-of-the-art methods in the literature.