bayesian image restoration an application to edge preserving surface recovery bayesian methods for recovering a 2 d surface are discussed it is assumed that there is a textural image that can be modeled by a markov random field and that the original surface is composed of different surfaces each of which is associated with one textural state both parametric and nonparametric methods are used to enforce smoothness of these surfaces iterative procedures are examined for simultaneous restoration of the textural image and estimation of underlying parameters from the estimated textural image and the estimated parameters an estimate for the original surface is obtained two illustrative examples are presented

binary restoration of thin objects in multidimensional imagery we present a method for restoration of noisy tomographic images for detecting thin objects such as explosives use of a weighted mean square estimate optimizes the solution to place emphasis on the infrequent but significant local structure associated with thin objects experimental results show successful restoration at very high noise levels

globally convergent iterative numerical schemes for nonlinear variational image smoothing and segmentation on a multiprocessor machine we investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel a general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown we characterize various edge preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework as a by product global convergence can be proven under conditions slightly weaker than these stated in the literature efficient krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine the performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed up factors are reported

gauss markov measure field models for low level vision we present a class of models derived from classical discrete markov random fields that may be used for the solution of ill posed problems in image processing and in computational vision they lead to reconstruction algorithms that are flexible computationally efficient and biologically plausible to illustrate their use we present their application to the reconstruction of the dominant orientation and direction fields to the classification of multiband images and to image quantization and filtering

global structure of riemann solutions to a system of two dimensional hyperbolic conservation laws abstract the riemann problem for a two dimensional nonstrictly hyperbolic system of conservation laws is considered without the restriction that each jump of the initial data projects one planar elementary wave ten topologically distinct solutions are obtained by applying the method of generalized characteristic analysis some of these solutions involve the nonclassical waves i e the delta shock wave and the delta contact discontinuity for which we explicitly give the expressions of their strengths locations and propagation speeds moreover we demonstrate that the nature of our solutions is identical with that of solutions to the corresponding one dimensional cauchy problem which provides a verification that our construction produces the correct unique global solutions

feature guided biased gaussian mixture model for image matching in this article we propose a feature guided biased gaussian mixture model fgbg for image matching we formulate the matching task as a maximum a posteriori map problem by seeing one point set as the centroid of a gaussian mixture model gmm and the other point set as the data a thin plate spline tps transformation between the two point sets is learnt so that the gmm can best fit the data our main contribution is to assign each gaussian mixture component a different weight this is where our model differs from the traditional self governed balanced gaussian mixture model sgbg whose gaussian mixture components have equal coefficients the new weight is defined as a value related to feature similarity which can be computed by simply decomposing a distance matrix in the feature space in this way both feature similarity and spatial arrangement are considered the feature descriptor is introduced as a reasonable prior to guide the matching and the spatial transformation offers a global constraint so that local ambiguity can be alleviated we solve this map problem in a framework similar to 16 in which deterministic annealing and the expectation maximization em algorithms are used we show that our fgbg algorithm is robust to outliers deformation and rotation extensive experiments on self collected and the latest open access data sets show that fgbg can boost the number of correct matches

non selfsimilar solutions for a hyperbolic system of conservation laws in two space dimensions the non selfsimilar riemann problem for a two dimensional nonstrictly hyperbolic system of conservation laws is considered where the initial data are two constant states separated by a smooth curve without dimension reduction or coordinate transformation the two dimensional global solutions are constructed for six cases according to the normal velocities on both sides of the initial discontinuity moreover the interactions of non selfsimilar elementary waves are discussed by respectively taking the initial discontinuity as a parabola and a circle which enable us to provide the global structures of the entropy solutions explicitly c 2012 elsevier inc all rights reserved

distributions as initial values in a triangular hyperbolic system of conservation laws the present paper concerns the system ut u x 0 vt u v x 0 having distributions as initial conditions under certain conditions and supposing functions we explicitly solve this cauchy problem within a convenient space of distributions u v for this purpose a consistent extension of the classical solution concept defined in the setting of a distributional product not constructed by approximation processes is used shock waves shock waves and also waves defined by distributions that are not measures are presented explicitly as examples this study is carried out without assuming classical results about conservation laws for reader s convenience a brief survey of the distributional product is also included

generalized solution to a system of conservation laws which is not strictly hyperbolic abstract in this paper we study a non strictly hyperbolic system of conservation laws when viscosity is present and when viscosity is zero which has been studied in 12 we show the existence and uniqueness of the solution in the space of generalized functions of colombeau for the viscous problem and construct a solution to the inviscid system in the sense of association also we construct a solution using shadow wave approach 17 and volpert product which was partially determined as vanishing viscosity limit in 12

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

sticky particles and scalar conservation laws one dimensional scalar conservation laws with nondecreasing initial conditions and general fluxes are shown to be the appropriate equations to describe large systems of free particles on the real line which stick under collision with conservation of mass and momentum

discrete shock profiles for scalar conservation laws with discontinuous fluxes abstract the paper considers a scalar conservation law with a discontinuous flux f of the form f x u h x g u 1 h x h u where h x is the heaviside function herein the fluxes g and h are supposed to have one minimum and no maximum and at most one crossing in the interior of the domain of definition the aim is to verify a weak solution of such a problem in the following way we are looking for discrete shock profiles for its continuously differentiable perturbation with a parameter e and godunov s scheme for conservation laws with spatially varying flux functions the obtained discrete shock profile satisfies a discrete entropy condition of kruzkhov type and after letting e 0 approaches an entropy weak solution of the original equation

removal of compression artifacts using projections onto convex sets and line process modeling we present a new image recovery algorithm to remove in addition to blocking ringing artifacts from compressed images and video this new algorithm is based on the theory of projections onto convex sets pocs a new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure the definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying to overcome the numerical difficulty in computing the projections onto these sets a divide and conquer dac strategy is introduced according to this strategy new smoothness sets are derived such that their projections are easier to compute the effectiveness of the proposed algorithm is demonstrated through numerical experiments using motion picture expert group based mpeg based coders decoders codecs

δ shock waves as a new type of solutions to systems of conservation laws abstract a concept of a new type of singular solutions to systems of conservation laws is introduced it is so called n shock wave where n is n th derivative of the dirac delta function n 1 2 in this paper the case n 1 is studied in details we introduce a definition of shock wave type solution for the system u t f u x 0 v t f u v x 0 w t f u v 2 f u w x 0 within the framework of this definition the rankine hugoniot conditions for shock are derived and analyzed from geometrical point of view we prove shock balance relations connected with area transportation finally a solitary shock wave type solution to the cauchy problem of the system of conservation laws u t u 2 x 0 v t 2 u v x 0 w t 2 v 2 u w x 0 with piecewise continuous initial data is constructed these results first show that solutions of systems of conservation laws can develop not only dirac measures as in the case of shocks but their derivatives as well

radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions abstract radially symmetric shadow wave solutions to the system of multidimensional pressureless gas dynamics are introduced which allow one to capture concentration of mass the transformation to a one dimensional system with source terms is performed and physically meaningful boundary conditions at the origin are determined entropy conditions are derived and applied to single out physical nonnegative mass and dissipative entropic solutions a complete solution to the pseudo riemann problem with initial data exhibiting a single delta shock on a sphere is obtained

an edge based algorithm for discontinuity adaptive color image smoothing abstract we present a new scheme to increase the performance of edge preserving image smoothing algorithm from the parameter tuning of a markov random field mrf function this method is based on an automatic control of the image smoothing strength in the mrf function in which the parameter control of the function depends on edge magnitude resulted from discontinuities of image intensity without any binary decision for the edge magnitude direct use of full edge magnitude could improve the performance of discontinuity preserving image smoothing technique

shadow waves entropies and interactions for delta and singular shocks this paper deals with two key problems for delta or singular shock solutions to systems of conservation laws that of their entropy admissibility conditions which is connected to the notorious uniqueness problem and that of their interaction we choose to represent systems of conservation laws by nets of functions which are piecewise constant or constant with respect only to the space variable here called shadow waves all the calculations can then be done on each element of such nets using only the usual rankine hugoniot conditions a 3 3 pressureless gas dynamics model is the main example in the paper

genetic algorithms for ambiguous labelling problems abstract consistent labelling problems frequently have more than one solution most work in the field has aimed at disambiguating early in the interpretation process using only local evidence this paper starts with a review of the literature on labelling problems and ambiguity based on this review we propose a strategy for simultaneously extracting multiple related solutions to the consistent labelling problem in a preliminary experimental study we show that an appropriately modified genetic algorithm is a robust tool for finding multiple solutions to the consistent labelling problem these solutions are related by common labellings of the most strongly constrained junctions we have proposed three run time measures of algorithm performance the maximum fitness of the genetic algorithm s population its shannon entropy and the total hamming distance between its distinct members the results to date indicate that when the shannon entropy falls below a certain threshold new solutions are unlikely to emerge and that most of the diversity in the population disappears within the first few generations

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

probabilistic relaxation and the hough transform abstract we discuss the recent developments in probabilistic relaxation which is used as a tool for contextual sensory data interpretation the relationship of this technique with the hough transform is then established focusing on the generalised hough transform ght we show that the label probability updating formula of the probabilistic relaxation process exploiting binary relations between object primitives under the assumption that the primitives convey weak context exhibits very close similarity to the voting function employed by a computationally efficient ght we argue that the relationship could be exploited by importing the positive features of the respective techniques to benefit one another specific suggestions for enhancing the respective techniques are mentioned they include the adoption of the representational efficiency of the hough transform to reduce the computational complexity of probabilistic relaxation vice versa in the case of the generalised hough transform it is pointed out that the effect of an unknown object transformation could be dealt with by means of a parallel cooperative interpretation rather than by means of an exhaustive search through the parameter space of a transformation group this has implications in terms of both the storage and computational requirements of the ght it also opens the possibility of using the ght for detecting objects subject to more complex transformations such as affine or perspective the relationship also suggests the possibility of using alternative voting functions which may speed up the object detection process

the riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws abstract in this paper we solve the riemann problem with the initial data containing dirac delta functions for a class of coupled hyperbolic systems of conservation laws under suitably generalized rankine hugoniot relation and entropy condition the existence and uniqueness of solutions involving delta shock waves are proved further four kinds of different structure for solutions are established uniquely

the riemann problem admitting δ δ shocks and vacuum states the vanishing viscosity approach in this paper using the vanishing viscosity method we construct a solution of the riemann problem for the system of conservation laws ut u2 x 0 vt 2 uv x 0 wt 2 v2 uw x 0 with the initial data u x 0 v x 0 w x 0 u v w x 0 this problem admits shock wave type solutions and vacuum states shock is a new type of singular solutions to systems of conservation laws first introduced in e yu panov v m shelkovich shock waves as a new type of solutions to systems of conservation laws j differential equations 228 2006 49 86 it is a distributional solution of the riemann problem such that for t 0 its second component v may contain dirac measures the third component w may contain a linear combination of dirac measures and their derivatives while the first component u has bounded variation using the above mentioned results we also solve the shock cauchy problem for the first two equations of the above system since shocks can be constructed by the vanishing viscosity method they are natural solutions to systems of conservation laws we describe the formation of the shocks and the vacuum states from smooth solutions of the parabolic problem the results of this paper as well as those of the above mentioned paper show that solutions of systems of conservation laws can develop not only dirac measures as in the case of shocks but their derivatives as well

generalized variational principles global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics we study systems of conservation laws arising in two models of adhesion particle dynamics the first is the system of free particles which stick under collision the second is a system of gravitationally interacting particles which also stick under collision in both cases mass and momentum are conserved at the collisions so the dynamics is described by 2 2 systems of conservations laws we show that for these systems global weak solutions can be constructed explicitly using the initial data by a procedure analogous to the lax oleinik variational principle for scalar conservation laws however this weak solution is not unique among weak solutions satisfying the standard entropy condition we also study a modified gravitational model in which instead of momentum some other weighted velocity is conserved at collisions for this model we prove both existence and uniqueness of global weak solutions we then study the qualitative behavior of the solutions with random initial data we show that for continuous but nowhere differentiable random initial velocities all masses immediately concentrate on points even though they were continuously distributed initially and the set of shock locations is dense

spaces of weighted measures for conservation laws with singular shock solutions abstract we study a model system of two strictly hyperbolic conservation laws which is genuinely nonlinear but for which the riemann problem has no global solution singular solutions are defined by means of a generalized rankine hugoniot relation and an overcompressive condition on the discontinuity we show that approximate solutions which can be constructed by several standard methods converge in a weighted measure space and that the error in the approximation converges to zero viscous approximations satisfy approximate entropy inequalities which imply the overcompressive condition

interactions of delta shock waves in a strictly hyperbolic system of conservation laws we study interaction of generalized solutions to a strictly hyperbolic system of two conservation laws from magnetohydrodynamics the riemann problem of this system is known to be solvable by a combination of shock waves contact discontinuities rarefaction waves and delta shock waves we derive how the solutions continue beyond points of interaction of these types of solutions we introduce a type of generalized solution a delta contact discontinuity a complete description of all global solutions with initial data given by two jump points and three constant states is obtained

parallel and deterministic algorithms from mrfs surface reconstruction deterministic approximations to markov random field mrf models are derived one of the models is shown to give in a natural way the graduated nonconvexity gnc algorithm proposed by a blake and a zisserman 1987 this model can be applied to smooth a field preserving its discontinuities a class of more complex models is then proposed in order to deal with a variety of vision problems all the theoretical results are obtained in the framework of statistical mechanics and mean field techniques a parallel iterative algorithm to solve the deterministic equations of the two models is presented together with some experiments on synthetic and real images

on a regularization of a scalar conservation law with discontinuous coefficients this paper is devoted to a scalar conservation law with a linear flux function involving discontinuous coefficients it is clear that the delta standing wave should be introduced into the riemann solution in some nonclassical situation in order to study the formation of delta standing wave we consider a regularization of the discontinuous coefficient with the helmholtz mollifier and then obtain a regularized system which depends on a regularization parameter 0 the regularization mechanism is a nonlinear bending of characteristic curves that prevents their finite time intersection it is proved rigorously that the solutions of regularized system converge to the delta standing wave solution in the 0 limit compared with the classical method of vanishing viscosity here it is clear to see how the delta standing wave forms naturally along the characteristics

a markov model for blind image separation by a mean field em algorithm this paper deals with blind separation of images from noisy linear mixtures with unknown coefficients formulated as a bayesian estimation problem this is a flexible framework where any kind of prior knowledge about the source images and the mixing matrix can be accounted for in particular we describe local correlation within the individual images through the use of markov random field mrf image models these are naturally suited to express the joint pdf of the sources in a factorized form so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained our model also includes edge variables to preserve intensity discontinuities mrf models have been proved to be very efficient in many visual reconstruction problems such as blind image restoration and allow separation and edge detection to be performed simultaneously we propose an expectation maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix the sources and their edge maps we tested this procedure on both synthetic and real images in the fully blind case i e no prior information on mixing is exploited and found that a source model accounting for local autocorrelation is able to increase robustness against noise even space variant furthermore when the model closely fits the source characteristics independence is no longer a strict requirement and cross correlated sources can be separated as well

hierarchical unsupervised learning with growing via phase transitions we address unsupervised learning subject to structural constraints with particular emphasis placed on clustering with an imposed decision tree structure most known methods are greedy optimizing one node of the tree at a time to minimize a local cost by constrast we develop a joint optimization method derived based on information theoretic principles and closely related to known methods in statistical physics the approach is inspired by the deterministic annealing algorithm for unstructured data clustering which was based on maximum entropy inference the new approach is founded on the principle of minimum cross entropy using informative priors to approximate the unstructured clustering solution while imposing the structural constraint the resulting method incorporates supervised learning principles applied in an unsupervised problem setting in our approach the tree grows by a sequence of bifurcations that occur while optimizing an effective free energy cost at decreasing temperature scales thus estimates of the tree size and structure are naturally obtained at each temperature in the process examples demonstrate considerable improvement over known methods

the plus closure of an ideal abstract if r is a local integral domain let r denote the integral closure of r in an algebraic closure of its quotient field if z r we would like to understand the conditions under which z ir where i is an ideal of r necessary and sufficient conditions on the coefficients of the minimal irreducible polynomial for z are known when i is generated by two elements of a regular system of parameters and when z is in a degree two extension of r in this article we obtain results for the case when z 3 r as well as a sufficient condition for z to be in ir when z a r for a 1 and i has a finite number of generators

dynamics of propagation and interaction of δ shock waves in conservation law systems abstract we introduce a new definition of a shock wave type solution for a class of systems of conservation laws in the one dimensional case the weak asymptotics method developed by the authors is used to construct formulas describing the propagation and interaction of shock waves the dynamics of merging two shocks is described by explicit formulas continuously in time

concentration and cavitation in the vanishing pressure limit of solutions to the euler equations for nonisentropic fluids numerical simulations 2 d riemann problem in gas dynamics and formation of spiral in nonlinear problems in engineering and science numerical and analytical approach beijing 1991 science press beijing 1992 pp 167 179 discrete contin dyn syst 1 1995 555 584 6 2000 419 430 for the euler equations for gas dynamics in the regime of small pressure showed that for one case the particles seem to be more sticky and tend to concentrate near some shock locations and for the other case in the region of rarefaction waves the particles seem to be far apart and tend to form cavitation in the region in this paper we identify and analyze the phenomena of concentration and cavitation by studying the vanishing pressure limit of solutions of the full euler equations for nonisentropic compressible fluids with a scaled pressure it is rigorously shown that any riemann solution containing two shocks and possibly one contact discontinuity to the euler equations for nonisentropic fluids tends to a shock solution to the corresponding transport equations and the intermediate densities between the two shocks tend to a weighted measure that along with the two shocks and possibly contact discontinuity forms the shock as the pressure vanishes by contrast it is also shown that any riemann solution containing two rarefaction waves and possibly one contact discontinuity to the euler equations for nonisentropic fluids tends to a two contact discontinuity solution to the transport equations and the nonvacuum intermediate states between the two rarefaction waves tend to a vacuum state as the pressure vanishes some numerical results exhibiting the processes of concentration and cavitation are presented as the pressure decreases 2003 elsevier b v all rights reserved msc 35l65 35b30 76e19 35q35 35l67 35b25 65m06