This is the first book about the rapidly evolving field of operational rate distortion (ORD) based video compression. ORD is concerned with the allocation of available bits among the different sources of information in an established coding framework. Today's video compression standards leave great freedom in the selection of key parameters, such as quantizers and motion vectors. The main distinction among different vendors is in the selection of these parameters, and this book presents a mathematical foundation for this selection process. The book contains a review chapter on video compression, a background chapter on optimal bit allocation and the necessary mathematical tools, such as the Lagrangian multiplier method and Dynamic Programming. These two introductory chapters make the book self-contained and provide a fast way of entering this exciting field. Rate-Distortion Based Video Compression establishes a general theory for the optimal bit allocation among dependent quantizers. The minimum total (average) distortion and the minimum maximum distortion cases are discussed. This theory is then used to design efficient motion estimation schemes, video compression schemes and object boundary encoding schemes. For the motion estimation schemes, the theory is used to optimally trade the reduction of energy in the displaced frame difference (DFD) for the increase in the rate required to encode the displacement vector field (DVF). These optimal motion estimators are then used to formulate video compression schemes which achieve an optimal distribution of the available bit rate among DVF, DFD and segmentation. This optimal bit allocation results in very efficient video coders. In the lastpart of the book, the proposed theory is applied to the optimal encoding of object boundaries, where the bit rate needed to encode a given boundary is traded for the resulting geometrical distortion. Again, the resulting boundary encoding schemes are very efficient. Rate-Distortion Based Video Compression is ideally suited for anyone interested in this booming field of research and development, especially engineers who are concerned with the implementation and design of efficient video compression schemes. It also represents a foundation for future research, since all the key elements needed are collected and presented uniformly. Therefore, it is ideally suited for graduate students and researchers working in this field.

One of the most intriguing problems in video processing is the removal of the redundancy or the compression of a video signal. There are a large number of applications which depend on video compression. Data compression represents the enabling technology behind the multimedia and digital television revolution. In motion compensated lossy video compression the original video sequence is first split into three new sources of information, segmentation, motion and residual error. These three information sources are then quantized, leading to a reduced rate for their representation but also to a distorted reconstructed video sequence. After the decomposition of the original source into segmentation, mo tion and residual error information is decided, the key remaining problem is the allocation of the available bits into these three sources of information. In this monograph a theory is developed which provides a solution to this fundamental bit allocation problem. It can be applied to all quad-tree-based motion com pensated video coders which use a first order differential pulse code modulation (DPCM) scheme for the encoding of the displacement vector field (DVF) and a block-based transform scheme for the encoding of the displaced frame differ ence (DFD). An optimal motion estimator which results in the smallest DFD energy for a given bit rate for the encoding of the DVF is also a result of this theory. Such a motion estimator is used to formulate a motion compensated interpolation scheme which incorporates a global smoothness constraint for the DVF."