rate distortion optimal fast thresholding with complete jpeg mpeg decoder compatibility we show a rate distortion optimal way to threshold or drop the dct coefficients of the jpeg and mpeg compression standards our optimal algorithm uses a fast dynamic programming recursive structure the primary advantage of our approach lies in its complete compatibility with standard jpeg and mpeg decoders

a bit allocation method for sparse source coding in this paper we develop an efficient bit allocation strategy for subband based image coding systems more specifically our objective is to design a new optimization algorithm based on a rate distortion optimality criterion to this end we consider the uniform scalar quantization of a class of mixed distributed sources following a bernoulli generalized gaussian distribution this model appears to be particularly well adapted for image data which have a sparse representation in a wavelet basis in this paper we propose new approximations of the entropy and the distortion functions using piecewise affine and exponential forms respectively because of these approximations bit allocation is reformulated as a convex optimization problem solving the resulting problem allows us to derive the optimal quantization step for each subband experimental results show the benefits that can be drawn from the proposed bit allocation method in a typical transform based coding application

invertible temporal subband wavelet filter banks with half pixel accurate motion compensation three dimensional 3 d subband wavelet coding with motion compensation has been demonstrated to be an efficient technique for video coding applications in some recent research works when motion compensation is performed with half pixel accuracy images need to be interpolated in both temporal subband analysis and synthesis stages the resulting subband filter banks developed in these former algorithms were not invertible due to image interpolation in this paper an invertible temporal analysis synthesis system with half pixel accurate motion compensation is presented we look at temporal decomposition of image sequences as a kind of down conversion of the sampling lattices the earlier motion compensated mc interlaced progressive scan conversion scheme is extended for temporal subband analysis synthesis the proposed subband wavelet filter banks allow perfect reconstruction of the decomposed video signal while retaining high energy compaction of subband transforms the invertible filter banks are then utilized in our 3 d subband video coder this video coding system does not contain the temporal dpcm loop employed in the conventional hybrid coder and the earlier mc 3 d subband coders the experimental results show a significant psnr improvement by the proposed method the generalization of our algorithm for mc temporal filtering at arbitrary subpixel accuracy is also discussed

the effect of network topology on the stability of discrete state models of genetic control boolean networks have been proposed as potentially useful models for genetic control an important aspect of these networks is the stability of their dynamics in response to small perturbations previous approaches to stability have assumed uncorrelated random network structure real gene networks typically have nontrivial topology significantly different from the random network paradigm to address such situations we present a general method for determining the stability of large boolean networks of any specified network topology and predicting their steady state behavior in response to small perturbations additionally we generalize to the case where individual genes have a distribution of expression biases and we consider a nonsynchronous update as well as extension of our method to non boolean models in which there are more than two possible gene states we find that stability is governed by the maximum eigenvalue of a modified adjacency matrix and we test this result by comparison with numerical simulations we also discuss the possible application of our work to experimentally inferred gene networks

joint optimization of run length coding huffman coding and quantization table with complete baseline jpeg decoder compatibility to maximize rate distortion performance while remaining faithful to the jpeg syntax the joint optimization of the huffman tables quantization step sizes and dct indices of a jpeg encoder is investigated given huffman tables and quantization step sizes an efficient graph based algorithm is first proposed to find the optimal dct indices in the form of run size pairs based on this graph based algorithm an iterative algorithm is then presented to jointly optimize run length coding huffman coding and quantization table selection the proposed iterative algorithm not only results in a compressed bitstream completely compatible with existing jpeg and mpeg decoders but is also computationally efficient furthermore when tested over standard test images it achieves the best jpeg compression results to the extent that its own jpeg compression performance even exceeds the quoted psnr results of some state of the art wavelet based image coders such as shapiro s embedded zerotree wavelet algorithm at the common bit rates under comparison both the graph based algorithm and the iterative algorithm can be applied to application areas such as web image acceleration digital camera image compression mpeg frame optimization and transcoding etc

galois groups of trinomials abstract galois groups of irreducible trinomials xn axs b z x are investigated assuming the classification of finite simple groups we show that under some simple yet general hypotheses bearing on the integers n s a and b only very specific groups can occur for instance if the two integers nb and as n s are coprime and if s is a prime number then already the galois group of f x is either the alternating group an or the symmetric group sn this significantly extends work of osada

motion estimation methods for overlapped block motion compensation an extension of conventional block motion compensation bmc overlapped block motion compensation obmc has been shown to reduce residual errors and blocking effects in motion compensated video however the overlap creates a noncausal spatial dependence between blocks and complicates motion estimation me for obmc iterative methods have traditionally been employed for overlapped block motion estimation obme for compression the rate for the motion vector field mvf may also be constrained this work considers several rate constrained obme algorithms both iterative and noniterative experiments demonstrate that a simple raster scan algorithm is effective as a suboptimal noniterative solution with comparable or better rate distortion performance and computational complexity than iterative obme algorithms depending on the application either this method or a simple block matching algorithm plus iteration are the most attractive of the tested obme schemes

subband coding systems incorporating quantizer models a new method for dealing with the effects of quantization in a subband system is proposed it uses the gain plus additive noise linear model for the lloyd max quantizer based on this it is demonstrated how by an appropriate choice of synthesis filters one can cancel all signal dependent errors at the output of the system the only remaining error is random in nature and not correlated with the input signal we therefore have a tradeoff between the error being only random or having signal dependent components as well since the error variances in both cases are comparable as a result of having only a random error it is possible to reduce this error using for example a noise removal technique the result is then extended to the case where the input is a multidimensional signal and arbitrary sampling lattices are used as well as to the qmf alias cancellation case to demonstrate the validity of the proposed approach two types of experiments on images are carried out in a toy example it is shown that using noise removal could be beneficial for a more realistic coding scheme however it is demonstrated that even in the case when the model is no longer valid when some of the subbands are discarded the output error is still much less correlated with the input signal as opposed to the commonly used subband system while visually the reconstructed images look very similar

lossless near lossless and refinement coding of bilevel images we present general and unified algorithms for lossy lossless coding of bilevel images the compression is realized by applying arithmetic coding to conditional probabilities as in the current jbig standard the conditioning may be specified by a template for better compression the more general free tree may be used loss may be introduced in a preprocess on the encoding side to increase compression the primary algorithm is a rate distortion controlled greedy flipping of pixels though being general the algorithms are primarily aimed at material containing half toned images as a supplement to the specialized soft pattern matching techniques that work better for text template based refinement coding is applied for lossy to lossless refinement introducing only a small amount of loss in half toned test images compression is increased by up to a factor of four compared with jbig lossy lossless and refinement decoding speed and lossless encoding speed are less than a factor of two slower than jbig the de coding method is proposed as part of jbig2 an emerging international standard for lossless lossy compression of bilevel images

an embedded still image coder with rate distortion optimization it is well known that the fixed rate coder achieves optimality when all coefficients are coded with the same rate distortion r d slope in this paper we show that the performance of the embedded coder can be optimized in a rate distortion sense by coding the coefficients with decreasing r d slope we denote such a coding strategy as rate distortion optimized embedding rde rde allocates the available coding bits first to the coefficient with the steepest r d slope i e the largest distortion decrease per coding bit the resultant coding bitstream can be truncated at any point and still maintain an optimal r d performance to avoid the overhead of coding order transmission we use the expected r d slope which can be calculated from the coded bits and is available in both the encoder and the decoder with the probability estimation table of the qm coder the calculation of the r d slope can be just a lookup table operation experimental results show that the rate distortion optimization significantly improves the coding efficiency in a wide bit rate range

an optimal quadtree based motion estimation and motion compensated interpolation scheme for video compression we propose an optimal quadtree qt based motion estimator for video compression it is optimal in the sense that for a given bit budget for encoding the displacement vector field dvf and the qt segmentation the scheme finds a dvf and a qt segmentation which minimizes the energy of the resulting displaced frame difference dfd we find the optimal qt decomposition and the optimal dvf jointly using the lagrangian multiplier method and a multilevel dynamic program we introduce a new very fast convex search for the optimal lagrangian multiplier spl lambda which results in a very fast convergence of the lagrangian multiplier method the resulting dvf is spatially inhomogeneous since large blocks are used in areas with simple motion and small blocks in areas with complex motion we also propose a novel motion compensated interpolation scheme which uses the same mathematical tools developed for the qt based motion estimator one of the advantages of this scheme is the globally optimal control of the tradeoff between the interpolation error energy and the dvf smoothness another advantage is that no interpolation of the dvf is required since we directly estimate the dvf and the qt segmentation for the frame which needs to be interpolated we present results with the proposed qt based motion estimator which show that for the same dfd energy the proposed estimator uses about 25 fewer bits than the commonly used block matching algorithm we also experimentally compare the interpolated frames using the proposed motion compensated interpolation scheme with the reconstructed original frames

criticality in random threshold networks annealed approximation and beyond random threshold networks with sparse asymmetric connections show complex dynamical behavior similar to random boolean networks with a transition from ordered to chaotic dynamics at a critical average connectivity kc in this type of model contrary to boolean networks propagation of local perturbations damage depends on the in degree of the sites kc is d eterminedanalytically using an annealedapproximation andthe results are con2rmedby numerical simulations it is shown that the statistical distributions of damage spreading near the percolation transition obey power laws andd ynamical correlations between active network clusters become maximal we investigate the e4ect of local damage suppression at highly connected nodes for networks with scale free in degree distributions possible relations of our 2ndings to properties of real world networks like robustness and non trivial degree distributions are discussed c

lossless image compression by quantization feedback in a content driven enhanced laplacian pyramid in this paper the effects of quantization noise feedback on the entropy of laplacian pyramids are investigated this technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper bounded near lossless coding and therefore allows reversible compression the entropy minimizing optimum quantizer is obtained by modeling the first order distributions of the differential signals as laplacian densities and by deriving a model for the equivalent memoryless entropy a novel approach based on an enhanced laplacian pyramid is proposed for the compression either lossless or lossy of gray scale images major details are prioritized through a content driven decision rule embedded in a uniform threshold quantizer with noise feedback lossless coding shows improvements over reversible joint photographers expert group jpeg and the reduced difference pyramid schemes while lossy coding outperforms jpeg with a significant peak signal to noise ratio psnr gain also subjective quality is higher even at very low bit rates due to the absence of the annoying impairments typical of jpeg moreover image versions having resolution and snr that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on as intermediate steps of the decoding procedure without any additional cost

framing pyramids burt and adelson 1983 introduced the laplacian pyramid lp as a multiresolution representation for images we study the lp using the frame theory and this reveals that the usual reconstruction is suboptimal we show that the lp with orthogonal filters is a tight frame and thus the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric with the forward transform in more general cases we propose an efficient filterbank fb for the reconstruction of the lp using projection that leads to a proved improvement over the usual method in the presence of noise setting up the lp as an oversampled fb we offer a complete parameterization of all synthesis fbs that provide perfect reconstruction for the lp finally we consider the situation where the lp scheme is iterated and derive the continuous domain frames associated with the lp

joint thresholding and quantizer selection for transform image coding entropy constrained analysis and applications to baseline jpeg striving to maximize baseline joint photographers expert group jpeg image quality without compromising compatibility of current jpeg decoders we develop an image adaptive jpeg encoding algorithm that jointly optimizes quantizer selection coefficient thresholding and huffman coding within a rate distortion r d framework practically speaking our algorithm unifies two previous approaches to image adaptive jpeg encoding r d optimized quantizer selection and r d optimal thresholding conceptually speaking our algorithm is a logical consequence of entropy constrained vector quantization ecvq design principles in the severely constrained instance of jpeg compatible encoding we explore both viewpoints the practical to concretely derive our algorithm and the conceptual to justify the claim that our algorithm approaches the best performance that a jpeg encoder can achieve this performance includes significant objective peak signal to noise ratio psnr improvement over previous work and at high rates gives results comparable to state of the art image coders for example coding the lena image at 1 0 b pixel our jpeg encoder achieves a psnr performance of 39 6 db that slightly exceeds the quoted psnr results of shapiro s wavelet based zero tree coder using a visually based distortion metric we can achieve noticeable subjective improvement as well furthermore our algorithm may be applied to other systems that use run length encoding including intraframe mpeg and subband or wavelet coding

optimal trellis based buffered compression and fast approximations the authors formalize the description of the buffer constrained adaptive quantization problem for a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer constrained environment they formulate the optimal solution they also develop slightly suboptimal but much faster approximations these solutions are valid for any globally minimum distortion criterion which is additive over the individual elements of the sequence as a first step they define the problem as one of constrained discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming forward dynamic programming using the viterbi algorithm is shown to provide a way of computing the optimal solution then they provide a heuristic algorithm based on lagrangian optimization using an operational rate distortion framework that with computing complexity reduced by an order of magnitude approaches the optimally achievable performance the algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays video encoding for cd roms and buffered jpeg coding environments where processing delay is not a concern but decoding buffer size has to be minimized

iterative rate distortion optimization of h 264 with constant bit rate constraint in this paper we apply the primal dual decomposition and subgradient projection methods to solve the rate distortion optimization problem with the constant bit rate constraint the primal decomposition method enables spatial or temporal prediction dependency within a group of picture gop to be processed in the master primal problem as a result we can apply the dual decomposition to minimize independently the lagrangian cost of all the mbs using the reference software model of h 264 furthermore the optimal lagrange multiplier is iteratively derived from the solution of the dual problem as an example we derive the optimal bit allocation condition with the consideration of temporal prediction dependency among the pictures experimental results show that the proposed method achieves better performance than the reference software model of h 264 with rate control

an optimal polygonal boundary encoding scheme in the rate distortion sense in this paper we present fast and efficient methods for the lossy encoding of object boundaries that are given as eight connect chain codes we approximate the boundary by a polygon and consider the problem of finding the polygon which leads to the smallest distortion for a given number of bits we also address the dual problem of finding the polygon which leads to the smallest bit rate for a given distortion we consider two different classes of distortion measures the first class is based on the maximum operator and the second class is based on the summation operator for the first class we derive a fast and optimal scheme that is based on a shortest path algorithm for a weighted directed acyclic graph for the second class we propose a solution approach that is based on the lagrange multiplier method which uses the above mentioned shortest path algorithm since the lagrange multiplier method can only find solutions on the convex hull of the operational rate distortion function we also propose a tree pruning based algorithm that can find all the optimal solutions finally we present results of the proposed schemes using objects from the miss america sequence

bit allocation for dependent quantization with applications to multiresolution and mpeg video coders we address the problem of efficient bit allocation in a dependent coding environment while optimal bit allocation for independently coded signal blocks has been studied in the literature we extend these techniques to the more general temporally and spatially dependent coding scenarios of particular interest are the topical mpeg video coder and multiresolution coders our approach uses an operational rate distortion r d framework for arbitrary quantizer sets we show how a certain monotonicity property of the dependent r d curves can be exploited in formulating fast ways to obtain optimal and near optimal solutions we illustrate the application of this property in specifying intelligent pruning conditions to eliminate suboptimal operating points for the mpeg allocation problem for which we also point out fast nearly optimal heuristics additionally we formulate an efficient allocation strategy for multiresolution coders using the spatial pyramid coder as an example we then extend this analysis to a spatio temporal 3 d pyramidal coding scheme we tackle the compatibility problem of optimizing full resolution quality while simultaneously catering to subresolution bit rate or quality constraints we show how to obtain fast solutions that provide nearly optimal typically within 0 3 db full resolution quality while providing much better performance for the subresolution layer typically 2 3 db better than the full resolution optimal solution

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

optimal buffered compression and coding mode selection for mpeg 4 shape coding we propose an optimal buffered compression algorithm for shape coding as defined in the forthcoming mpeg 4 international standard the mpeg 4 shape coding scheme consists of two steps first distortion is introduced by down and up scaling then context based arithmetic encoding is applied since arithmetic coding is lossless the down up scaling step is considered as a virtual quantizer we first formulate the buffer constrained adaptive quantization problem for shape coding and then propose an algorithm for the optimal solution under buffer constraints previously the fact that a conversion ratio cr of 1 4 makes a coded image irritating to human observers for qcif size was reported for mpeg 4 shape coding therefore careful consideration for small size images such as qcif should be given to prevent coded images from being unacceptable to this end a low bit rate tuned algorithm is proposed in this paper as well experimental results are given using an mpeg 4 shape codec

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

phase transitions in random networks simple analytic determination of critical points the standard method for determining the critical points in random networks such as boolean nets is based on the derrida approximation this method leads to the critical points based on the so called annealed approximation in this paper we present a very simple annealed approximation based on the study of damage spreading when single elements are modified several examples are analyzed

order disorder phase transition in random walk networks in this paper we study in detail the behavior of random walk networks rwn s these networks are a generalization of the well known random boolean networks rbn s a classical approach to the study of the genome rwn s are also discrete networks but their response is defined by small variations in the state of each gene thus being a more realistic representation of the genome and a natural bridge between discrete and continuous models rwn s show a clear transition between order and disorder here we explicitly deduce the formula of the critical line for the annealed model and compute numerically the transition points for quenched and annealed models we show that rbn s and the annealed model of rwn s act as an upper and a lower limit for the quenched model of rwn s finally we calculate the limit of the annealed model for the continuous case

optimization of mpeg 2 snr scaleable codecs it is shown how the signal to noise snr scaleable coder can benefit from optimizing quantified discrete cosine transform dct coefficients in a rate distortion context in order to reduce bit rate overheads the technique is based on adjusting the quantized coefficients rather than dropping them since the former gives finer control over rate distortion trade offs the widely used lagrangian optimization technique is then applied to arrive at the optimally adjusted coefficients block we show that such an optimization is very efficient for the second layer but has little effect on the base layer

compression of laplacian pyramids through orthogonal transforms and improved prediction scalable representation of visual signals such as image and video signals has become a subject of active research since early 1980s scalability allows the adaptation of the bit rate and or the resolution of the transmitted data to the network bandwidth and or the rendering capability of the receiving device for many years spatial scalability has been achieved through wavelets but recently the laplacian pyramid lp has become an alternative choice because of reduced aliasing in the lower resolutions in this paper we focus on the coding efficiency of the lp with a view to transmitting it over a communication channel in particular we aim to improve the compression efficiency of the lp detail layers through improved interlayer prediction and orthogonal spatial transforms first we consider an lp in the open loop configuration and propose to improve its rate distortion performance by compressing it to a critically sampled representation we derive four different orthogonal spatial transforms from the upsampling and downsampling filters that can achieve this representation and apply them on the detail layers the application of these transforms to the detail layers renders a fixed number of transform coefficients either zero or redundant thus making their transmission unnecessary then we consider the compression of an lp in the closed loop configuration through similar spatial transforms because of the introduction of quantization in the prediction loop these spatial transforms applied on the detail layers do not produce the same number of zero or redundant transform coefficients as in the open loop case nevertheless the insight obtained from the open loop coding leads us to enhance the interlayer prediction and the subsequent application of the spatial transforms to the new detail layers aims to achieve better energy compaction

consistent picture quality control strategy for dependent video coding typically a video rate control algorithm minimizes the average distortion denoted as minave at the cost of large temporal quality variation especially for videos with high motion and frequent scene changes to alleviate the negative effect on subjective video quality another criterion that restricts a small amount of quality variation among adjacent frames is preferred for practical applications as pointed out by although some existing proposals can produce consistent quality videos they often fail to fully utilize the available bits to minimize the global total distortion in this paper we would like to achieve the triple goal of consistent quality video minimizing the total distortion and meeting the bit budget strictly all at the same time on the interframe dependent coding structure two approaches are taken to accomplish this goal in the first algorithm a trellis based framework is proposed one of our contributions is to derive an equivalent condition between the distortion minimization problem and the budget minimization problem second our trellis state tree node is defined in terms of distortion which facilitates the consistent quality control third by adjusting one key parameter in our algorithm a solution in between the minave and the constant quality criteria can be obtained the second approach is to combine the lagrange multipliers method together with the consistent quality control the psnr performance is degraded slightly but the computational complexity is significantly reduced simulation results show that both our approaches produce a much smaller psnr variation at a slight average psnr loss as compared to the mpeg jm rate control when they are compared to the other consistent quality proposals only the proposed algorithms can strictly meet the target bit budget requirement no more no less and produce the largest average psnr at a small psnr variation

an operational rate distortion optimal single pass snr scalable video coder we introduce a new methodology for signal to noise ratio snr video scalability based on the partitioning of the dct coefficients the dct coefficients of the displaced frame difference dfd for inter blocks or the intensity for intra blocks are partitioned into a base layer and one or more enhancement layers thus producing an embedded bitstream subsets of this bitstream can be transmitted with increasing video quality as measured by the snr given a bit budget for the base and enhancement layers the partitioning of the dct coefficients is done in a way that is optimal in the operational rate distortion sense the optimization is performed using lagrangian relaxation and dynamic programming dp experimental results are presented and conclusions are drawn

random walk networks abstract random boolean networks are among the best known systems used to model genetic networks they show an on off dynamics and it is easy to obtain analytical results with them unfortunately very few genes are strictly on off switched on the other hand continuous methods are in principle more suitable to capture the real behavior of the genome but have difficulties when trying to obtain analytical results in this work we introduce a new model of random discrete network random walk networks where the state of each gene is changed by small discrete variations being thus a natural bridge between discrete and continuous models

cellular automata model for gene networks in order to study the overall behavior of gene networks we propose a simple cellular automata ca model in which each binary gene is connected to k other inputs including itself interacting through asymmetric short and long range couplings using numerical simulations and mean field calculations collective dynamical properties of this ca model were investigated it is shown that the ca exhibits three different dynamical regimes a frozen a marginal and a chaotic phase where an initial damage vanishes remains limited and grows to a finite fraction of the lattice sites respectively the results presented are also consistent with the observed biological scaling laws for the number of differentiated cells and cell length cycles as a function of the number of genes in an organism s1063 651x 97 03303 5

rate distortion optimization for h 264 interframe coding a general framework and algorithms rate distortion rd optimization for h 264 interframe coding with complete baseline decoding compatibility is investigated on a frame basis using soft decision quantization sdq rather than the standard hard decision quantization we first establish a general framework in which motion estimation quantization and entropy coding in h 264 for the current frame can be jointly designed to minimize a true rd cost given previously coded reference frames we then propose three rd optimization algorithms a graph based algorithm for near optimal sdq in h 264 baseline encoding given motion estimation and quantization step sizes an algorithm for near optimal residual coding in h 264 baseline encoding given motion estimation and an iterative overall algorithm to optimize h 264 baseline encoding for each individual frame given previously coded reference frames with them embedded in the indicated order the graph based algorithm for near optimal sdq is the core given motion estimation and quantization step sizes it is guaranteed to perform optimal sdq if the weak adjacent block dependency utilized in the context adaptive variable length coding of h 264 is ignored for optimization the proposed algorithms have been implemented based on the reference encoder jm82 of h 264 with complete compatibility to the baseline profile experiments show that for a set of typical video testing sequences the graph based algorithm for near optimal sdq the algorithm for near optimal residual coding and the overall algorithm achieve on average 6 8 and 12 respectively rate reduction at the same psnr ranging from 30 to 38 db when compared with the rd optimization method implemented in the h 264 reference software

a video compression scheme with optimal bit allocation among segmentation motion and residual error we present a theory for the optimal bit allocation among quadtree qt segmentation displacement vector field dvf and displaced frame difference dfd the theory is applicable to variable block size motion compensated video coders vbsmcvc where the variable block sizes are encoded using the qt structure the dvf is encoded by first order differential pulse code modulation dpcm the dfd is encoded by a block based scheme and an additive distortion measure is employed we derive an optimal scanning path for a qt that is based on a hilbert curve we consider the case of a lossless vbsmcvc first for which we develop the optimal bit allocation algorithm using dynamic programming dp we then consider a lossy vbsmcvc for which we use lagrangian relaxation and show how an iterative scheme which employs the dp based solution can be used to find the optimal solution we finally present a vbsmcvc which is based on the proposed theory which employs a dct based dfd encoding scheme we compare the proposed coder with h 263 the results show that it outperforms h 263 significantly in the rate distortion sense as well as in the subjective sense

entropy based distortion measure and bit allocation for wavelet image compression quality criteria for image coding are often based on mean square error however this is not always a relevant measure of visual quality at low bit rates here we investigate the properties of a distortion measure based on the conditional differential entropy of the input signal given its quantized value the proposed measure appears to be a correct representation of the amount of information lost by quantization an adaptive bit allocation algorithm is proposed in order to take advantage of this criterion experimental results illustrate the behavior of the proposed distortion measure and exhibit interesting visual properties for low bit rate subband image coding