the gaussian effective potential and stochastic partial differential equations abstract we investigate arbitrary stochastic partial differential equations subject to translation invariant and temporally white noise correlations from a nonperturbative framework the method that we expose first casts the stochastic equations into a functional integral form then it makes use of the gaussian effective potential approach which is an useful tool for describing symmetry breaking we apply this method to the kardar parisi zhang equation and find that the system exhibits spontaneous symmetry breaking in 1 1 2 1 and 3 1 euclidean dimensions providing insight into the evolution of the system configuration due to the presence of noise correlations a simple and systematic approach to the renormalization without explicit regularization is employed

group theoretic structure of linear phase multirate filter banks unique lifting factorization results for group lifting structures are used to characterize the group theoretic structure of two channel linear phase fir perfect reconstruction filter bank groups for d invariant order increasing group lifting structures it is shown that the associated lifting cascade group c is isomorphic to the free product of the upper and lower triangular lifting matrix groups under the same hypotheses the associated scaled lifting group s is the semidirect product of c by the diagonal gain scaling matrix group d these results apply to the group lifting structures for the two principal classes of linear phase perfect reconstruction filter banks the whole and half sample symmetric classes since the unimodular whole sample symmetric class forms a group w that is in fact equal to its own scaled lifting group w sw the results of this paper characterize the group theoretic structure of w up to isomorphism although the half sample symmetric class does not form a group it can be partitioned into cosets of its lifting cascade group c or alternatively into cosets of its scaled lifting group s homomorphic comparisons reveal that scaled lifting groups covered by the results in this paper have a structure analogous to a noncommutative vector space

multiview image coding using depth layers and an optimized bit allocation in this paper we present a novel wavelet based compression algorithm for multiview images this method uses a layer based representation where the 3 d scene is approximated by a set of depth planes with their associated constant disparities the layers are extracted from a collection of images captured at multiple viewpoints and transformed using the 3 d discrete wavelet transform dwt the dwt consists of the 1 d disparity compensated dwt across the viewpoints and the 2 d shape adaptive dwt across the spatial dimensions finally the wavelet coefficients are quantized and entropy coded along with the layer contours to improve the rate distortion performance of the entire coding method we develop a bit allocation strategy for the distribution of the available bit budget between encoding the layer contours and the wavelet coefficients the achieved performance of our proposed scheme outperforms the state of the art codecs for several data sets of varying complexity

lifting based invertible motion adaptive transform limat framework for highly scalable video compression we propose a new framework for highly scalable video compression using a lifting based invertible motion adaptive transform limat we use motion compensated lifting steps to implement the temporal wavelet transform which preserves invertibility regardless of the motion model by contrast the invertibility requirement has restricted previous approaches to either block based or global motion compensation we show that the proposed framework effectively applies the temporal wavelet transform along a set of motion trajectories an implementation demonstrates high coding gain from a finely embedded scalable compressed bit stream results also demonstrate the effectiveness of temporal wavelet kernels other than the simple haar and the benefits of complex motion modeling using a deformable triangular mesh these advances are either incompatible or difficult to achieve with previously proposed strategies for scalable video compression video sequences reconstructed at reduced frame rates from subsets of the compressed bit stream demonstrate the visually pleasing properties expected from low pass filtering along the motion trajectories the paper also describes a compact representation for the motion parameters having motion overhead comparable to that of motion compensated predictive coders our experimental results compare favorably to others reported in the literature however our principal objective is to motivate a new framework for highly scalable video compression

a novel motion field anchoring paradigm for highly scalable wavelet based video coding existing video coders anchor motion fields at frames that are to be predicted in this paper we demonstrate how changing the anchoring of motion fields to reference frames has some important advantages over conventional anchoring we work with piecewise smooth motion fields and use breakpoints to signal discontinuities at moving object boundaries we show how discontinuity information can be used to resolve double mappings arising when motion is warped from reference to target frames we present an analytical model that allows to determine weights for texture motion and breakpoints to guide the rate allocation for scalable encoding compared with the conventional way of anchoring motion fields the proposed scheme requires fewer bits for the coding of motion furthermore the reconstructed video frames contain fewer ghosting artefacts the experimental results show the superior performance compared with the traditional anchoring and demonstrate the high scalability attributes of the proposed method

temporal scalability of dynamic volume data using mesh compensated wavelet lifting due to their high resolution dynamic medical 2d t and 3d t volumes from computed tomography ct and magnetic resonance tomography mr reach a size which makes them very unhandy for teleradiologic applications a lossless scalable representation offers the advantage of a down scaled version which can be used for orientation or previewing while the remaining information for reconstructing the full resolution is transmitted on demand the wavelet transform offers the desired scalability a very high quality of the lowpass sub band is crucial in order to use it as a down scaled representation we propose an approach based on compensated wavelet lifting for obtaining a scalable representation of dynamic ct and mr volumes with very high quality the mesh compensation is feasible to model the displacement in dynamic volumes which is mainly given by expansion and contraction of tissue over time to achieve this we propose an optimized estimation of the mesh compensation parameters to optimally fit for dynamic volumes within the lifting structure the inversion of the motion compensation is crucial in the update step we propose to take this inversion directly into account during the estimation step and can improve the quality of the lowpass sub band by 0 63 and 0 43 db on average for our tested dynamic ct and mr volumes at the cost of an increase of the rate by 2 4 and 1 2 on average

analysis of decorrelation transform gain for uncoded wireless image and video communication an uncoded transmission scheme called softcast has recently shown great potential for wireless video transmission unlike conventional approaches softcast processes input images only by a series of transformations and modulates the coefficients directly to a dense constellation for transmission the transmission is uncoded and lossy in nature with its noise level commensurate with the channel condition this paper presents a theoretical analysis for an uncoded visual communication focusing on developing a quantitative measurements for the efficiency of decorrelation transform in a generalized uncoded transmission framework our analysis reveals that the energy distribution among signal elements is critical for the efficiency of uncoded transmission a decorrelation transform can potentially bring a significant performance gain by boosting the energy diversity in signal representation numerical results on markov random process and real image and video signals are reported to evaluate the performance gain of using different transforms in uncoded transmission the analysis presented in this paper is verified by simulated softcast transmissions this provide guidelines for designing efficient uncoded video transmission schemes

optimized update prediction assignment for lifting transforms on graphs transformations on graphs can provide compact representations of signals with many applications in denoising feature extraction or compression in particular lifting transforms have the advantage of being critically sampled and invertible by construction but the efficiency of the transform depends on the choice of a good bipartition of the graph into update mathcal u and prediction mathcal p nodes this is the update prediction mathcal u mathcal p assignment problem which is the focus of this paper we analyze this problem theoretically and derive an optimal mathcal u mathcal p assignment under assumptions about signal model and filters furthermore we prove that the best mathcal u mathcal p partition is related to the correlation between nodes on the graph and is not the one that minimizes the number of conflicts connections between nodes of same label or maximizes the weight of the cut we also provide experimental results in randomly generated graph signals and real data from image and video signals that validate our theoretical conclusions demonstrating improved performance over state of the art solutions for this problem

motion compensated 3 d subband coding of video this paper describes a video coding system based on motion compensated three dimensional 3 d subband wavelet coding mc 3dsbc which can overcome the limits of both 3 d sbc and mc prediction based coding in this new system spatio temporal subbands are generated by mc temporal analysis and a spatial wavelet transform and then encoded by 3 d subband finite state scalar quantization 3dsb fssq the rate allocation from the gop level to each class of subbands is optimized by utilizing the structural property of mc 3dsbc that additive superposition approximately holds for both rate and distortion the proposed video coding system is applied to several test video clips its performance exceeds that of both a known mpeg 1 implementation and a similar subband mc predictive coder while maintaining modest computational complexity and memory size

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

compound gauss markov random fields for image estimation algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound gauss markov random fields are discussed the authors consider both the maximum a posteriori probability map estimate and the minimum mean squared error mmse estimate for image estimation and image restoration compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels two different compound random field models are employed the doubly stochastic gaussian dsg random field and a compound gauss markov cgm random field the authors present map estimators for dsg and cgm random fields using simulated annealing a fast converging algorithm called deterministic relaxation which however converges to only a locally optimal map estimate is also presented as an alternative for reducing computational loading on sequential machines for comparison purposes the authors include results on the fixed lag smoothing mmse estimator for the dsg field and its suboptimal m algorithm approximation

simulated annealing in compound gaussian random fields image processing recently a stochastic relaxation technique called simulated annealing has been developed to search for a globally optimal solution in image estimation and restoration problems the convergence of simulated annealing has been proved only for random fields with a compact range space because of this images were modeled as random fields with bounded discrete or continuous values however in most image processing problems it is more natural to model the image as a random field with values in a noncompact space e g conditional gaussian models the proof of convergence of the stochastic relaxation method is extended to a class of compound gauss markov random fields simulation results are provided to show the power of these methods

single image defogging by multiscale depth fusion restoration of fog images is important for the deweathering issue in computer vision the problem is ill posed and can be regularized within a bayesian context using a probabilistic fusion model this paper presents a multiscale depth fusion mdf method for defog from a single image a linear model representing the stochastic residual of nonlinear filtering is first proposed multiscale filtering results are probabilistically blended into a fused depth map based on the model the fusion is formulated as an energy minimization problem that incorporates spatial markov dependence an inhomogeneous laplacian markov random field for the multiscale fusion regularized with smoothing and edge preserving constraints is developed a nonconvex potential adaptive truncated laplacian is devised to account for spatially variant characteristics such as edge and depth discontinuity defog is solved by an alternate optimization algorithm searching for solutions of depth map by minimizing the nonconvex potential in the random field the mdf method is experimentally verified by real world fog images including cluttered depth scene that is challenging for defogging at finer details the fog free images are restored with improving contrast and vivid colors but without over saturation quantitative assessment of image quality is applied to compare various defog methods experimental results demonstrate that the accurate estimation of depth map by the proposed edge preserved multiscale fusion should recover high quality images with sharp details

the mean field theory in em procedures for blind markov random field image restoration a markov random field mrf model based em expectation maximization procedure for simultaneously estimating the degradation model and restoring the image is described the mrf is a coupled one which provides continuity inside regions of smooth gray tones and discontinuity at region boundaries constraints for the restoration problem which is in general ill posed the computational difficulty associated with the em procedure for mrfs is resolved by using the mean field theory from statistical mechanics an orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates experimental results on synthetic and real world images show that this approach provides good blur estimates and restored images the restored images are comparable to those obtained by a wiener filter in mean square error but are most visually pleasing

three dimensional subband coding with motion compensation three dimensional 3 d frequency coding is an alternative approach to hybrid coding concepts used in today s standards the first part of this paper presents a study on concepts for temporal axis frequency decomposition along the motion trajectory in video sequences it is shown that if a two band split is used it is possible to overcome the problem of spatial inhomogeneity in the motion vector field mvf which occurs at the positions of uncovered and covered areas in these cases original pixel values from one frame are placed into the lowpass band signal while displaced frame difference values are embedded into the highpass band this technique is applicable with arbitrary mvf s examples with block matching and interpolative motion compensation are given derivations are first performed for the example of two tap quadrature mirror filters qmf s and then generalized to any linear phase qmf s with two band analysis and synthesis stages arranged as cascade structures higher resolution frequency decompositions are realizable in the second part of the paper encoding of the temporal axis subband signals is discussed a parallel filterbank scheme was used for spatial subband decomposition and adaptive lattice vector quantization was employed to approach the entropy rate of the 3 d subband samples coding results suggest that high motion video sequences can be encoded at significantly lower rates than those achievable with conventional hybrid coders main advantages are the high energy compaction capability and the nonrecursive decoder structure in the conclusion the scheme is interpreted more generally viewed as a motion compensated short time spectral analysis of video sequences which can adapt to the quickness of changes although a 3 d multiresolution representation of the picture information is produced a true multiresolution representation of motion information based on spatio temporal decimation and interpolation of the mvf is regarded as the still missing part

effective action for stochastic partial differential equations stochastic partial differential equations spdes are the basic tool for modeling systems where noise is important spdes are used for models of turbulence pattern formation and the structural development of the universe itself it is reasonably well known that certain spdes can be manipulated to be equivalent to nonquantum field theories that nevertheless exhibit deep and important relationships with quantum field theory in this paper we systematically extend these ideas we set up a functional integral formalism and demonstrate how to extract all the one loop physics for an arbitrary spde subject to arbitrary gaussian noise it is extremely important to realize that gaussian noise does not imply that the field variables undergo gaussian fluctuations and that these nonquantum field theories are fully interacting the limitation to one loop is not as serious as might be supposed experience with quantum field theories qfts has taught us that one loop physics is often quite adequate to give a good description of the salient issues the limitation to one loop does however offer marked technical advantages because at one loop almost any field theory can be rendered finite using zeta function technology we can sidestep the complications inherent in the martin siggia rose formalism the spde analog of the becchi rouet stora tyutin formalism used in qft and instead focus attention on a minimalist approach that uses only the physical fields this direct approach is the spde analog of canonical quantization using physical fields after setting up the general formalism for the characteristic functional partition function we show how to define the effective action to all loops and then focus on the one loop effective action and its specialization to constant fields the effective potential the physical interpretation of the effective action and effective potential for spdes is addressed and we show that key features carry over from qft to the case of spdes an important result is that the amplitude of the two point function governing the noise acts as the loop counting parameter and is the analog of planck s constant in this spde context we derive a general expression for the one loop effective potential of an arbitrary spde subject to translation invariant gaussian noise and compare this with the one loop potential for qft

field theory renormalization approach to the kardar parisi zhang equation the long wavelength scaling properties of the kardar parisi zhang equation have been studied using a field theory renormalization technique the perturbation expansions are carried out to two loop order for both 1 1 and 2 1 dimensions in substrate dimension d 1 we find that the perturbation formalism obeys the fluctuation dissipation theorem order by order so that the exact results ensuremath chi 1 2 z 3 2 are recovered in every order for substrate dimension d 2 which is the critical dimension of this equation an infrared stable strong coupling fixed point is found and the dynamic scaling exponents of this fixed point are obtained to be ensuremath chi ensuremath simeq 0 16 z ensuremath simeq 1 84 which are roughly halfway between the free field exponents and those determined by simulations of discrete models the possible reasons for this discrepancy are discussed

parameter reduction for the compound gauss markov model the efficacy of the compound gauss markov cgm model initially proposed by jeng and woods 1990 has been demonstrated in several image processing applications however parameter estimation for the cgm model is difficult since it is not clear as to how the constraints or interdependence amongst the model parameters can be incorporated into the estimation procedures as result the parameter estimates tend to be inconsistent it is shown that under some reasonable symmetry constraints the 80 interdependent parameters of the cgm model can be reduced to seven independent ones this guarantees the consistency of model parameters obtained from parameter estimation algorithms thereby removing a main obstacle for the parameter estimation of the cgm model

three dimensional subband coding of video we describe and show the results of video coding based on a three dimensional 3 d spatio temporal subband decomposition the results include a 1 mbps coder based on a new adaptive differential pulse code modulation scheme adpcm and adaptive bit allocation this rate is useful for video storage on cd rom coding results are also shown for a 384 kbps rate that are based on adpcm for the lowest frequency band and a new form of vector quantization geometric vector quantization gvq for the data in the higher frequency bands gvq takes advantage of the inherent structure and sparseness of the data in the higher bands results are also shown for a 128 kbps coder that is based on an unbalanced tree structured vector quantizer utsvq for the lowest frequency band and gvq for the higher frequency bands the results are competitive with traditional video coding techniques and provide the motivation for investigating the 3 d subband framework for different coding schemes and various applications

action principle in nonequilibrium statistical dynamics we introduce a variational method for approximating distribution functions of dynamics with a liouville operator l in terms of a nonequilibriumaction functional for two independent left and right trial states the method is valid for deterministic or stochastic markov dynamics and for stationary or time dependent distributions a practical rayleigh ritz procedure is advanced whose inputs are a finitely parametrized ansatz for the trial states leading to a parametric action for their evolution the euler lagrange equations of the action principle are hamiltonian in form generally noncanonical this permits a simple identification of fixed points as critical points of the parametric hamiltonian we also establish a variational principle for low order statistics such as mean values and correlation functions by means of the least effective action the latter is a functional of the given variable which is positive and convex as a consequence of h older realizability inequalities its value measures the cost for a fluctuation from the average to occur and in a weak noise limit it reduces to the onsager machlup action in general the effective action is shown to arise from the nonequilibrium action functional by a constrained variation this result provides a rayleigh ritz scheme for calculating just the desired low order statistics with internal consistency checks less demanding than for the full distribution textcopyright 1996 the american physical society

two loop renormalization group analysis of the burgers kardar parisi zhang equation a systematic analysis of the burgers kardar parisi zhang equation in d 1 dimensions by dynamic renormalization group theory is described the fixed points and exponents are calculated to two loop order we use the dimensional regularization scheme carefully keeping the full d dependence originating from the angular parts of the loop integrals for dimensions less than mathit d mathit c 2 we find a strong coupling fixed point which diverges at d 2 indicating that there is nonperturbative strong coupling behavior for all d ensuremath ge 2 at d 1 our method yields the identical fixed point as in the one loop approximation and the two loop contributions to the scaling functions are nonsingular for dg2 dimensions there is no finite strong coupling fixed point in the framework of a 2 ensuremath epsilon expansion we find the dynamic exponent corresponding to the unstable fixed point which described the nonequilibrium roughening transition to be z 2 o mathrm ensuremath epsilon 3 in agreement with a recent scaling argument by doty and kosterlitz phys rev lett 69 1979 1992 similarly our result for the correlation length exponent at the transition is 1 ensuremath nu ensuremath epsilon o mathrm ensuremath epsilon 3 for the smooth phase some aspects of the crossover from gaussian to critical behavior are discussed

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

renormalization group analysis of a quivering string model of posture control scaling concepts and renormalization group methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces the string is driven by uncorrelated white gaussian noise intended to model the corrections of the physiological control system we find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space representing the dynamics with various nontrivial fixed points and basins of attraction the transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon and the robustness of the linear model with respect to weak nonlinearities is confirmed correlations in posture fluctuations are obtained in both time and space domains there is an attractive fixed point identified with falling the scaling of the correlations in the front back displacement which can be measured in the laboratory is predicted for both large separation along the string and long time regimes of posture control