time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

third order upwind finite element solutions of high reynolds number flows abstract a full upwind finite element scheme based on the petrov galerkin formulation is presented for accurate solutions of high reynolds number flows and then a simplified finite scheme with third order upwinding is developed in order to obtain a practical algorithm for numerical simulation because structures of the full upwind finite element scheme are very complicated numerical dissipation added in the proposed upwind scheme is represented by high order derivatives of flow velocities and pressure computational results for the subcritical and the supercritical reynolds number flows around a circular cylinder and for flows around twin circular cylinders are shown to illustrate the effectiveness and robustness of the simplified upwind finite element scheme

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

stereoscopic ranging by matching image modulations we apply an am fm surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system this is used to support the use of modulation based stereo matching where local image phase is used to compute stereo disparities the local image phase is an advantageous feature for image matching since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data local phase shifts however are problematic at high frequencies due to phase wrapping when disparities exceed spl plusmn spl pi we meld powerful multichannel gabor image demodulation techniques for multiscale coarse to fine computation of local image phase with a disparity channel model for depth computation the resulting framework unifies phase based matching approaches with am fm surface image models we demonstrate the concepts in a stereo algorithm that generates a dense accurate disparity map without the problems associated with phase wrapping

linear and non linear high order accurate residual distribution schemes for the discretization of the steady compressible navier stokes equations a robust and high order accurate residual distribution rd scheme for the discretization of the steady navier stokes equations is presented the proposed method is very flexible it is formulated for unstructured grids regardless the shape of the elements and the number of spatial dimensions a continuous approximation of the solution is adopted and standard lagrangian shape functions are used to construct the discrete space as in finite element methods the traditional technique for designing rd schemes is adopted evaluate for any element a total residual split it into nodal residuals sent to the degrees of freedom of the element solve the non linear system that has been assembled and then iterate up to convergence the main issue addressed by the paper is that the technique relies in depth on the continuity of the normal flux across the element boundaries this is no longer true since the gradient of the state solution appears in the flux hence continuity is lost when using standard finite element approximations naive solution methods lead to very poor accuracy to cope with the fact that the normal component of the gradient of the numerical solution is discontinuous across the faces of the elements a continuous approximation of the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution preserving the optimal accuracy of the method linear and non linear schemes are constructed and their accuracy is tested with the method of the manufactured solutions the numerical method is also used for the discretization of smooth and shocked laminar flows in two and three spatial dimensions we propose a very high order accurate methods for the approximation of the compressible navier stokes equations with residual distribution schemes the memory footprint is lower than for discontinuous galerkin like methods we show uniform accuracy for the whole range of reynolds numbers the solution technique is described in details and we show how to reach excellent convergence

a modification of the petrov galerkin method for the transient convection diffusion equation a variation of the petrov galerkin method of solution of a partial differential equation is presented in which the weight function applied to the time derivative term of the transient convection diffusion equation is different from the weight function applied to the special derivatives this allows for the formulation of fourth order explicit and centred difference schemes comparison with analytic solutions show that these methods are able to capture steep wave fronts the ability of the explicit method to capture wave fronts increases as the amount of convective transport increases

ranging through gabor logons a consistent hierarchical approach in this work the correspondence problem in stereo vision is handled by matching two sets of dense feature vectors inspired by biological evidence these feature vectors are generated by a correlation between a bank of gabor sensors and the intensity image the sensors consist of two dimensional gabor filters at various scales spatial frequencies and orientations which bear close resemblance to the receptive field profiles of simple v1 cells in visual cortex a hierarchical stochastic relaxation method is then used to obtain the dense stereo disparities unlike traditional hierarchical methods for stereo feature based hierarchical processing yields consistent disparities to avoid false matchings due to static occlusion a dual matching based on the imaging geometry is used

on a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws ii five point schemes this paper presents a family of two level five point implicit schemes for the solution of one dimensional systems of hyperbolic conservation laws which generalized the crank nicholson scheme to fourth order accuracy 4 4 in both time and space these 4 4 schemes are nondissipative and unconditionally stable special attention is given to the system of linear equations associated with these 4 4 implicit schemes the regularity of this system is analyzed and efficiency of solution algorithms is examined a two datum representation of these 4 4 implicit schemes brings about a compactification of the stencil to three mesh points at each time level this compact two datum representation is particularly useful in deriving boundary treatments numerical results are presented to illustrate some properties of the proposed scheme

fuzzy cognitive maps for stereovision matching this paper outlines a method for solving the stereovision matching problem using edge segments as the primitives in stereovision matching the following constraints are commonly used epipolar similarity smoothness ordering and uniqueness we propose a new matching strategy under a fuzzy context in which such constraints are mapped the fuzzy context integrates both fuzzy clustering and fuzzy cognitive maps with such purpose a network of concepts nodes is designed each concept represents a pair of primitives to be matched each concept has associated a fuzzy value which determines the degree of the correspondence the goal is to achieve high performance in terms of correct matches the main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped initially each concept value is loaded via the fuzzy clustering and then updated by the fuzzy cognitive maps framework this updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved under this fuzzy approach we gain quantitative and qualitative matching correspondences this method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods

random walks on lattices with randomly distributed traps i the average number of steps until trapping for a random walk on a lattice with a random distribution of traps we derive an asymptotic expansion valid for smallq for the average number of steps until trapping whereq is the probability that a lattice point is a trap we study the case of perfect traps where the walk comes to an end and the extension obtained by letting the traps be imperfect i e by giving the walker a finite probability to remain free when stepping on a trap several classes of random walks of varying dimensionality are considered and special care is taken to show that the expansion derived is exact up to and including the last term calculated the numerical accuracy of the expansion is discussed

on a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws i nonstiff strongly dynamic problems an implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one dimensional systems of hyperbolic conservation laws the basic form of the method is a two level scheme which is unconditionally stable and nondissipative the scheme uses only three mesh points at level t and three mesh points at level t delta t the dissipative version of the basic method given is conditionally stable under the cfl courant friedrichs lewy condition this version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features where the cfl restriction is reasonable on accuracy grounds numerical results are provided to illustrate properties of the proposed method

a comparison of finite element and finite difference solutions of the one and two dimensional burgers equations abstract solutions to the one and two dimensional burgers equations with moderate to severe internal and boundary gradients have been used to compare minimum truncation error three five and seven point finite difference schemes with linear quadratic and cubic rectangular finite element schemes the various schemes demonstrate the theoretically predicted convergence rates if the mesh is sufficiently refined in one dimension the quadratic finite element scheme and the five point finite difference scheme are computationally the most efficient in multidimensions the finite element method is less economical than the finite difference method even if the group representation is used for the convective terms in two dimensions the linear group finite element representation and the three point finite difference scheme are computationally the most efficient on a coarse mesh or if a severe gradient is present

an introduction to finite element methods for transient advection problems abstract an introduction is presented to time accurate finite element methods recently developed for solving unsteady problems governed by linear and nonlinear advection equations this includes methods making an explicit use of the characteristic curves methods based on the taylor series in time and least squares methods

high order linear and non linear residual distribution schemes for turbulent compressible flows a high order residual distribution scheme for the solution of the compressible rans equations is developed the one equation spalart allmaras turbulence model is solved in a fully coupled approach the mean flow equations as well as the turbulence equation are solved with high order of accuracy a continuous approximation of the solution is adopted and standard lagrangian basis functions are used to construct the discrete space since viscous terms involve the gradient of the numerical solution which has a discontinuous normal component across the faces of the elements a continuous approximation of the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same basis functions used for the solution the non linear system of equations resulting from the numerical discretization is solved with the non linear lu sgs method several numerical experiments are performed to verify the accuracy of the numerical method these are based on both subsonic and transonic flows in two and three spatial dimensions

multiresolution 3 d range segmentation using focus cues this paper describes a novel system for computing a three dimensional 3 d range segmentation of an arbitrary visible scene using focus information the process of range segmentation is divided into three steps an initial range classification a surface merging process and a 3 d multiresolution range segmentation first range classification is performed to obtain quantized range estimates the range classification is performed by analyzing focus cues within a bayesian estimation framework a combined energy functional measures the degree of focus and the gibbs distribution of the class field the range classification provides an initial range segmentation second a statistical merging process is performed to merge the initial surface segments this gives a range segmentation at a coarse resolution third 3 d multiresolution range segmentation 3 d mrs is performed to refine the range segmentation into finer resolutions the proposed range segmentation method does not require initial depth estimates it allows the analysis of scenes containing multiple objects and it provides a rich description of the 3 d structure of a scene

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

an analysis of time discretization in the finite element solution of hyperbolic problems abstract the problem of the time discretization of hyperbolic equations when finite elements are used to represent the spatial dependence is critically examined a modified equation analysis reveals that the classical second order accurate time stepping algorithms i e the lax wendroff leap frog and crank nicolson methods properly combine with piecewise linear finite elements in advection problems only for small values of the time step on the contrary as the courant number increases the numerical phase error does not decrease uniformly at all wavelengths so that the optimal stability limit and the unit cfl property are not achieved these fundamental numerical properties can however be recovered while still remaining in the standard galerkin finite element setting by increasing the order of accuracy of the time discretization this is accomplished by exploiting the taylor series expansion in the time increment up to the third order before performing the galerkin spatial discretization using piecewise linear interpolations as a result it appears that the proper finite element equivalents of second order finite difference schemes are implicit methods of incremental type having third and fourth order global accuracy on uniform meshes taylor galerkin methods numerical results for several linear examples are presented to illustrate the properties of the taylor galerkin schemes in one and two dimensional calculations

dense features for semi dense stereo correspondence we present a new feature based algorithm for stereo correspondence most of the previous feature based methods match sparse features like edge pixels producing only sparse disparity maps our algorithm detects and matches dense features between the left and right images of a stereo pair producing a semi dense disparity map our dense feature is defined with respect to both images of a stereo pair and it is computed during the stereo matching process not a preprocessing step in essence a dense feature is a connected set of pixels in the left image and a corresponding set of pixels in the right image such that the intensity edges on the boundary of these sets are stronger than their matching error which is the difference in intensities between corresponding boundary pixels our algorithm produces accurate semi dense disparity maps leaving featureless regions in the scene unmatched it is robust requires little parameter tuning can handle brightness differences between images nonlinear errors and is fast linear complexity

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

a stereo vision technique using curve segments and relaxation matching a multichannel feature based stereo vision technique where curve segments are used as feature primitives in the matching process is described the left image and the right image are filtered by using several laplacian of gaussian operators of different widths channels curve segments are extracted by a tracking algorithm and their centroids are obtained at each channel the generalized hough transform of each curve segment in the left and the right image is evaluated the epipolar constraint on the centroids of the curve segment and the channel size is used to limit the searching space in the right image to resolve the ambiguity of the false targets multiple matches a relaxation technique is used where the initial scores of the node assignments are updated by the compatibility measures between the centroids of the curve segments the node assignments with the highest score are chosen as the matching curve segments

on learning conditional random fields for stereo until recently the lack of ground truth data has hindered the application of discriminative structured prediction techniques to the stereo problem in this paper we use ground truth data sets that we have recently constructed to explore different model structures and parameter learning techniques to estimate parameters in markov random fields mrfs via maximum likelihood one usually needs to perform approximate probabilistic inference conditional random fields crfs are discriminative versions of traditional mrfs we explore a number of novel crf model structures including a crf for stereo matching with an explicit occlusion model crfs require expensive inference steps for each iteration of optimization and inference is particularly slow when there are many discrete states we explore belief propagation variational message passing and graph cuts as inference methods during learning and compare with learning via pseudolikelihood to accelerate approximate inference we have developed a new method called sparse variational message passing which can reduce inference time by an order of magnitude with negligible loss in quality learning using sparse variational message passing improves upon previous approaches using graph cuts and allows efficient learning over large data sets when energy functions violate the constraints imposed by graph cuts

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

reformulation of gray s duality for attractive spin systems and its applications duality relations which associate two markov processes in different state spaces have been useful tools in the study of the long term behaviour of the stochastic processes of spin systems in 1986 gray introduced a new duality theory which is applicable to general spin systems with attractive transition rates the theory was developed by making full use of graphical representations in the present paper gray s duality is reformulated by studying the action of the formal generators on a newly chosen duality function and the dual processes defined in the state space upsilon a a is a finite subset of y are discussed where y is a collection of finite subsets of zd as applications of the submodularity of the survival probability sigma a of the dual processes rigorous lower bounds of the critical values are derived for the theta contact process the multi particle creation model and the sexual reproduction process

map based stochastic diffusion for stereo matching and line fields estimation this paper proposes a stochastic approach to estimate the disparity field combined with line field in the maximum a posteriori map method based on markov random field mrf model it is important to optimize and converge the gibbs potential function corresponding to the perturbed disparity field the proposed optimization method stochastic diffusion takes advantage of the probabilistic distribution of the neighborhood fields to diffuse the gibbs potential space iteratively by using the neighborhood distribution in the non random and non deterministic diffusion both the estimation accuracy and the convergence speed are improved in the paper the hierarchical stochastic diffusion is also applied to the disparity field the hierarchical approach reduces the memory and computational load and increases the convergence speed of the potential space the paper also proposes an effective configuration of the neighborhood to be suitable for the hierarchical disparity structure according to the experiments the stochastic diffusion shows good estimation performance the line field improves the estimation at the object boundary and coincides with the object boundary with the useful contours the stochastic diffusion is applicable to any kind of field estimation given the appropriate definition of the field and mrf models

multilevel enhancement and detection of stereo disparity surfaces abstract the problem of stereo vision has been of increasing interest to the computer vision community over the past decade this paper presents a new computational framework for matching a pair of stereo images arising from viewing the same object from two different positions in contrast to previous work this approach formulates the matching problem as detection of a bright coherent disparity surface in a 3d image called the spatio disparity space sds image the sds images represents the goodness of each and every possible match a nonlinear filter is proposed for enhancing the disparity surface in the sds image and for suppressing the noise this filter is used to construct a hyperpyramid representation of the sds image then the disparity surface is detected using a coarse to fine control structure the proposed method is robust to photometric and geometric distortions in the stereo images and has a number of computational advantages it produces good results for complex scenes

restriction of a markov random field on a graph and multiresolution statistical image modeling the association of statistical models and multiresolution data analysis in a consistent and tractable mathematical framework remains an intricate theoretical and practical issue several consistent approaches have been proposed previously to combine markov random field mrf models and multiresolution algorithms in image analysis renormalization group subsampling of stochastic processes mrfs defined on trees or pyramids etc for the simulation or a practical use of these models in statistical estimation an important issue is the preservation of the local markovian property of the representation at the different resolution levels it is shown that this key problem may be studied by considering the restriction of a markov random field defined on some simple finite nondirected graph to a part of its original site set several general properties of the restricted field are derived the general form of the distribution of the restriction is given locality of the field is studied by exhibiting a neighborhood structure with respect to which the restricted field is an mrf sufficient conditions for the new neighborhood structure to be minimal are derived several consequences of these general results related to various multiresolution mrf based modeling approaches in image analysis are presented

geometric constraints and stereo disparity computation most stereo techniques compute disparity assuming that it varies slowly along surfaces we quantify and justify this assumption using weak assumptions about surface orientation distributions in the world to derive the density of disparity surface orientations the small disparity change assumption is justified by the orientation density s heavy bias toward disparity surfaces that are nearly parallel to the image plane in addition the bias strengthens with smaller baselines larger focal lengths and as surfaces move farther from the cameras to analyze current stereo techniques we derive three densities from the first density those of the disparity gradient magnitude the directional derivative of disparity and the difference in disparity between neighboring surface points the latter may be used in bayesian algorithms computing dense disparity fields the directional derivative density and the disparity difference density both show that feature based algorithms should strongly favor small disparity changes contrary to several well known algorithms finally we use our original surface orientation density and the gradient magnitude density to derive two new surfaces from stereo techniques techniques combining feature based matching and surface reconstruction the first uses the densities to severely restrict the search range for the optimum fit the second incorporates the surface orientation density into the optimization criteria producing a bayesian formulation both algorithms are shown to be efficient and effective

finite element methods for nonlinear advection abstract the taylor galerkin method for the temporal and spatial discretization of mixed initial boundary value problems is applied to derive numerical schemes for solving a single scalar conservation law equation the discretization in time is performed before the spatial approximation by introducing second order and third order accurate generalizations of the standard two level euler scheme with the help of taylor series expansions in the time step the equations in weak form are then spatially discretized by means of the conventional galerkin finite element method to obtain a new class of parameter free one step linearly implicit schemes for the solution of nonlinear hyperbolic problems numerical results for the so called inviscid burgers equation in one and two dimensions are presented to illustrate the properties of the proposed taylor galerkin schemes

an explicit finite difference scheme with exact conservation properties abstract a finite difference scheme for the numerical study of the korteweg de vries equation is constructed it is explicit and yet conserves exactly the energy of the computed solutions the underlying idea can also be applied to more general equations or systems numerical experiments are included

a space time least square finite element scheme for advection diffusion equations abstract a space time least square finite element scheme is presented for the advection diffusion problems at moderate to high peclet numbers this scheme is designed to eliminate spurious oscillations and can be used to define the steady state solution as the asymptotic transient solution for large time numerical results using linear elements in a 1d space and bilinear elements in a 2d space demonstrate the accuracy and the stability of the new scheme

intensity and gradient based stereo matching using hierarchical gaussian basis functions we propose a stereo correspondence method by minimizing intensity and gradient errors simultaneously in contrast to conventional use of image gradients the gradients are applied in the deformed image space although a uniform smoothness constraint is imposed it is applied only to nonfeature regions to avoid local minima in the function minimization we propose to parameterize the disparity function by hierarchical gaussians both the uniqueness and the ordering constraints can be easily imposed in our minimization framework besides we propose a method to estimate the disparity map and the camera response difference parameters simultaneously experiments with various real stereo images show robust performances of our algorithm

extracting view dependent depth maps from a collection of images stereo correspondence algorithms typically produce a single depth map in addition to the usual problems of occlusions and textureless regions such algorithms cannot model the variation in scene or object appearance with respect to the viewing position in this paper we propose a new representation that overcomes the appearance variation problem associated with an image sequence rather than estimating a single depth map we associate a depth map with each input image or a subset of them our representation is motivated by applications such as view interpolation and depth based segmentation for model building or layer extraction we describe two approaches to extract such a representation from a sequence of images the first approach which is more classical computes the local depth map associated with each chosen reference frame independently the novelty of this approach lies in its combination of shiftable windows temporal selection and graph cut optimization the second approach simultaneously optimizes a set of self consistent depth maps at multiple key frames since multiple depth maps are estimated simultaneously visibility can be modeled explicitly and disparity consistency imposed across the different depth maps results which include a difficult specular scene example show the effectiveness of our approach

stochastic stereo matching over scale a stochastic optimization approach to stereo matching is presented unlike conventional correlation matching and feature matching the method provides a dense array of disparities eliminating the need for interpolation first the stereo matching problem is defined in terms of finding a disparity map that satisfies two competing constraints 1 matched points should have similar image intensity and 2 the disparity map should vary as slowly as possible these constraints are interpreted as specifying the potential energy of a system of oscillators ground states are approximated by a new variant of simulated annealing which has two important features first the microcanonical ensemble is simulated using a new algorithm that is more efficient and more easily implemented than the familiar metropolis algorithm which simulates the canonical ensemble secondly it uses a hierarchical coarse to fine control structure employing gaussian or laplacian pyramids of the stereo images in this way quickly computed results at low resolutions are used to initialize the system at higher resolutions

least squares finite elements for first order hyperbolic systems application de la methode des moindres carres a elements finis a l approximation des systemes hyperboliques du premier ordre analyse de la stabilite exemples

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

a multiple baseline stereo a stereo matching method that uses multiple stereo pairs with various baselines generated by a lateral displacement of a camera to obtain precise distance estimates without suffering from ambiguity is presented matching is performed simply by computing the sum of squared difference ssd values the ssd functions for individual stereo pairs are represented with respect to the inverse distance and are then added to produce the sum of ssds this resulting function is called the sssd in inverse distance it is shown that the sssd in inverse distance function exhibits a unique and clear minimum at the correct matching position even when the underlying intensity patterns of the scene include ambiguities or repetitive patterns the authors first define a stereo algorithm based on the sssd in inverse distance and present a mathematical analysis to show how the algorithm can remove ambiguity and increase precision experimental results with real stereo images are presented to demonstrate the effectiveness of the algorithm

progressively weighted affine adaptive correlation matching for quasi dense 3d reconstruction correlation matching has been widely accepted as a rudimentary similarity measure to obtain dense 3d reconstruction from a stereo pair in particular given a large overlapping area between images with minimal scale differences the correlation results followed by a geometrically constrained global optimisation delivers adequately dense and accurate reconstruction results in order to achieve greater reliability however correlation matching should correctly account for the geometrical distortion introduced by the different viewing angles of the stereo or multi view sensors conventional adaptive least squares correlation alsc matching addresses this by modifying the shape of a matching window iteratively assuming that the distortion can be approximated by an affine transform nevertheless since an image captured from different viewing angle is often not practically identical due to scene occlusions the matching confidence normally deteriorates subsequently it affects the density of the reconstruction results from alsc based stereo region growing algorithms to address this we propose an advanced alsc matching method that can progressively update matching weight for each pixel in an aggregating window using a relaxation labelling technique the experimental results show that the proposed method can improve matching performance which consequently enhances the quality of stereo reconstruction also the results demonstrate its ability to refine a scale invariant conjugate point pair to an affine and scale invariant point pair

series analysis of the generalized contact process abstract we study critical behavior in a one parameter family of generalized contact processes using series expansions our results show that the entire family belongs to a single universality class and permit a more accurate assessment of exponent uncertainties

using chromatic information in dense stereo correspondence abstract the use of chromatic information in dense stereo correspondence is investigated specifically the chromatic photometric constraint which is used to specify a mathematical optimality criterion for solving the dense stereo correspondence problem is developed the result is a theoretical construction for developing dense stereo correspondence algorithms which use chromatic information the efficacy of using chromatic information via this construction is tested by implementing single and multi resolution versions of a stereo correspondence algorithm that uses simulated annealing as a means of solving the optimization problem results demonstrate that the use of chromatic information can significantly improve the performance of dense stereo correspondence

efficient stereoscopic ranging via stochastic sampling of match quality we present an efficient method that computes dense stereo correspondences by stochastically sampling match quality values nonexhaustive sampling facilitates the use of quality metrics that take unique values at noninteger disparities depth estimates are iteratively refined with a stochastic cooperative search by perturbing the estimates sampling match quality and reweighting and aggregating the perturbations the approach gains significant efficiencies when applied to video where initial estimates are seeded using information from the previous pair in a novel application of the z buffering algorithm this significantly reduces the number of search iterations required we present a quantitative accuracy evaluation wherein the proposed method outperforms a microcanonical annealing approach by barnard and a cooperative approach by zitnick and kanade while using fewer match quality evaluations than either the approach is shown to have more attractive memory usage and scaling than alternatives based on exhaustive sampling

time accurate solution of advection diffusion problems by finite elements abstract the taylor galerkin method recently proposed for the spatial and temporal discretization of hyperbolic equations is employed to derive accurate and efficient numerical schemes for the solution of time dependent advection diffusion problems two distinct numerical strategies are discussed the first is suitable for evolutionary problems while the second is appropriate for situations in which a steady state is eventually reached for purely evolutionary problems the taylor galerkin method is applied to the complete advection diffusion equation and through modifications of the standard mass matrix is shown to generate an incremental form of the crank nicolson time stepping method such an incremental form also lends itself to the derivation of computationally simple but accurate explicit algorithms to deal with transient situations which evolve towards a highly convective steady state the global taylor galerkin method is found to be ineffective since it reduces to the standard galerkin formulation as the temporal term vanishes for such cases we suggest the use of a splitting up method in which advection and diffusion are treated separately by appropriate taylor galerkin methods the proposed methods are illustrated first for linear constant coefficient equations they are successively extended to deal with nonlinear and multi dimensional problems numerical applications indicate their effectiveness

a comparative study of energy minimization methods for markov random fields with smoothness based priors among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel labeling tasks such as depth or texture computation it has been known for decades that such problems can be elegantly expressed as markov random fields yet the resulting energy minimization problems have been widely viewed as intractable algorithms such as graph cuts and loopy belief propagation lbp have proven to be very powerful for example such methods form the basis for almost all the top performing stereo methods however the trade offs among different energy minimization algorithms are still not well understood in this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and runtime of several common energy minimization algorithms we investigate three promising methods graph cuts lbp and tree reweighted message passing in addition to the well known older iterated conditional mode icm algorithm our benchmark problems are drawn from published energy functions used for stereo image stitching interactive segmentation and denoising we also provide a general purpose software interface that allows vision researchers to easily switch between optimization methods the benchmarks code images and results are available at http vision middlebury edu mrf

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

bounds for the critical line of the theta contact processes with 1 or theta or 2 we study a family of the one dimensional contact processes introduced by durrett and griffeath 1983 which is parametrized by theta for each theta or 1 there is a unique critical value lambda c theta so that any process becomes extinct with probability 1 for lambda lambda c theta in this paper we give rigorous upper and lower bounds for the critical line lambda lambda c theta for 1 or theta or 2 in order to obtain the upper bound we extend the holley liggett argument which was originally given for the case theta 2 the basic contact process we construct a new class of attractive renewal measures with positive densities and the upper bound of lambda c theta is given as the largest root of a cubic equation theta lambda 3 3 theta 2 lambda 2 3 2 theta lambda 2 theta 0 recently liggett 1991 reported an upper bound of the critical value for the case theta 1 the threshold contact process by a modified version of the holley liggett argument our result includes these previous results as special cases

surfaces with occlusions from layered stereo we propose a new binocular stereo algorithm that estimates scene structure as a collection of smooth surface patches the disparities within each patch are modeled by a continuous valued spline while the extent of each patch is represented via a pixelwise partitioning of the images disparities and extents are alternately estimated in an iterative energy minimization framework experimental results demonstrate that for scenes consisting of smooth surfaces the proposed algorithm significantly improves upon the state of the art

on a penalty finite element cfd algorithm for high speed flow abstract the expanding interest in finite element discrete approximation techniques applied to high speed flow prediction has engendered derivation of many distinct theoretical statements quantization of algorithm robustness has focused on accuracy assessment for non smooth solutions i e those containing shocks and or contact discontinuities to reduced forms of the navier stokes equations specifically the euler equation system and the transonic potential flow equation this paper presents derivation of a penalty finite element algorithm applicable to both problem statements with penalty functional derived as a reduced form of a taylor galerkin weak statement numerical results for shocked transonic and euler solutions are cited to document aspects of accuracy convergence and stability

duality for general attractive spin systems with applications in one dimension on developpe une theorie des processus duaux qui s applique aux systemes de spin generaux a taux de transition attractifs on illustre l applicabilite de ces processus en generalisant les resultats de durrett et griffeath 1983

joint reconstruction of multiview compressed images distributed representation of correlated multiview images is an important problem that arises in vision sensor networks this paper concentrates on the joint reconstruction problem where the distributively compressed images are decoded together in order to take benefit from the image correlation we consider a scenario where the images captured at different viewpoints are encoded independently using common coding solutions e g jpeg with a balanced rate distribution among different cameras a central decoder first estimates the inter view image correlation from the independently compressed data the joint reconstruction is then cast as a constrained convex optimization problem that reconstructs total variation tv smooth images which comply with the estimated correlation model at the same time we add constraints that force the reconstructed images to be as close as possible to their compressed versions we show through experiments that the proposed joint reconstruction scheme outperforms independent reconstruction in terms of image quality for a given target bit rate in addition the decoding performance of our algorithm compares advantageously to state of the art distributed coding schemes based on motion learning and on the discover algorithm

a finite element algorithm for computational fluid dynamics an implicit finite element numerical algorithm is derived for the compressible navier stokes equations expressed in generalized coordinates the theoretical basis utilizes a galerkin weighted residuals formulation and extremization of approximation error within the context of a multipole expansion a simplified yon neumann analysis indicates the algorithm fourth order phase accurate with third order dissipation for the elementary linear basis construction algorithm performance is nominally improved using a quadratic basis numerical experiments for shocked duct flows are employed to refine the several algorithm parameters

shape and the stereo correspondence problem we examine the implications of shape on the process of finding dense correspondence and half occlusions for a stereo pair of images the desired property of the disparity map is that it should be a piecewise continuous function which is consistent with the images and which has the minimum number of discontinuities to zeroth order piecewise continuity becomes piecewise constancy using this approximation we first discuss an approach for dealing with such a fronto parallel shapeless world and the problems involved therein we then introduce horizontal and vertical slant to create a first order approximation to piecewise continuity in particular we emphasize the following geometric fact a horizontally slanted surface i e having depth variation in the direction of the separation of the two cameras will appear horizontally stretched in one image as compared to the other image thus while corresponding two images n pixels on a scanline in one image may correspond to a different number of pixels m in the other image this leads to three important modifications to existing stereo algorithms a due to unequal sampling existing intensity matching metrics must be modified b unequal numbers of pixels in the two images must be allowed to correspond to each other and c the uniqueness constraint which is often used for detecting occlusions must be changed to an interval uniqueness constraint we also discuss the asymmetry between vertical and horizontal slant and the central role of non horizontal edges in the context of vertical slant using experiments we discuss cases where existing algorithms fail and how the incorporation of these new constraints provides correct results

stereo matching with nonlinear diffusion one of the central problems in stereo matching and other image registration tasks is the selection of optimal window sizes for comparing image regions this paper addresses this problem with some novel algorithms based on iteratively diffusing support at different disparity hypotheses and locally controlling the amount of diffusion based on the current quality of the disparity estimate it also develops a novel bayesian estimation technique which significantly outperforms techniques based on area based matching ssd and regular diffusion we provide experimental results on both synthetic and real stereo image pairs