the logarithmic sobolev inequality for discrete spin systems on a lattice for finite range lattice gases with a finite spin space it is shown that the dobrushin shlosman mixing condition is equivalent to the existence of a logarithmic sobolev inequality for the associated unique gibbs state in addition implications of these considerations for the ergodic properties of the corresponding glauber dynamics are examined

shape from focus the shape from focus method presented here uses different focus levels to obtain a sequence of object images the sum modified laplacian sml operator is developed to provide local measures of the quality of image focus the operator is applied to the image sequence to determine a set of focus measures at each image point a depth estimation algorithm interpolates a small number of focus measure values to obtain accurate depth estimates a fully automated shape from focus system has been implemented using an optical microscope and tested on a variety of industrial samples experimental results are presented that demonstrate the accuracy and robustness of the proposed method these results suggest shape from focus to be an effective approach for a variety of challenging visual inspection tasks

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

improvements in shape from focus for holographic reconstructions with regard to focus operators neighborhood size and height value interpolation this paper presents a shape from focus method which is improved with regard to the mathematical operator used for contrast measurement the selection of the neighborhood size surface refinement through interpolation and surface postprocessing three dimensional models of living human faces are presented with such a high resolution that single hairs are visible

cluster expansion for d dimensional lattice systems and finite volume factorization properties we consider classical lattice systems with finite range interactions ind dimensions by means of a block decimation procedure we transform our original system into a polymer system whose activity is small provided a suitable factorization property of finite volume partition functions holds in this way we extend a result of olivieri

depth estimation of face images using the nonlinear least squares model in this paper we propose an efficient algorithm to reconstruct the 3d structure of a human face from one or more of its 2d images with different poses in our algorithm the nonlinear least squares model is first employed to estimate the depth values of facial feature points and the pose of the 2d face image concerned by means of the similarity transform furthermore different optimization schemes are presented with regard to the accuracy levels and the training time required our algorithm also embeds the symmetrical property of the human face into the optimization procedure in order to alleviate the sensitivities arising from changes in pose in addition the regularization term based on linear correlation is added in the objective function to improve the estimation accuracy of the 3d structure further a model integration method is proposed to improve the depth estimation accuracy when multiple nonfrontal view face images are available experimental results on the 2d and 3d databases demonstrate the feasibility and efficiency of the proposed methods

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

variational depth from focus reconstruction this paper deals with the problem of reconstructing a depth map from a sequence of differently focused images also known as depth from focus dff or shape from focus we propose to state the dff problem as a variational problem including a smooth but nonconvex data fidelity term and a convex nonsmooth regularization which makes the method robust to noise and leads to more realistic depth maps in addition we propose to solve the nonconvex minimization problem with a linearized alternating directions method of multipliers allowing to minimize the energy very efficiently a numerical comparison to classical methods on simulated as well as on real data is presented

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

on the two dimensional dynamical ising model in the phase coexistence region we consider a glauber dynamics reversible with respect to the two dimensional ising model in a finite square of sidel in the absence of an external field and at large inverse temperature we first consider the gap in the spectrum of the generator of the dynamics in two different cases with plus and open boundary conditions we prove that when the symmetry under global spin flip is broken by the boundary conditions the gap is much larger than the case in which the symmetry is present for this latter we compute exactly the asymptotics of 1 l log gap asl and show that it coincides with the surface tension along one of the coordinate axes as a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin spin time correlation in the infinite volume plus phase our results establish a connection between the dynamical large deviations and those of the equilibrium gibbs measure studied by shlosman in the framework of the rigorous description of the wulff shape for the ising model finally we show that in the case of open boundary conditions it is possible to rescale the time withl in such a way that asl the finite dimensional distributions of the time rescaled magnetization converge to those of a symmetric continuous time markov chain on the two state space m m m being the spontaneous magnetization our methods rely upon a novel combination of techniques for bounding from below the gap of symmetric markov chains on complicated graphs developed by jerrum and sinclair in their markov chain approach to hard computational problems and the idea of introducing block glauber dynamics instead of the standard single site dynamics in order to put in evidence more effectively the effect of the boundary conditions in the approach to equilibrium

optimal depth estimation by combining focus measures using genetic programming three dimensional 3d shape reconstruction is a fundamental problem in machine vision applications shape from focus sff is one of the passive optical methods for 3d shape recovery that uses degree of focus as a cue to estimate 3d shape in this approach usually a single focus measure operator is applied to measure the focus quality of each pixel in the image sequence however the applicability of a single focus measure is limited to estimate accurately the depth map for diverse type of real objects to address this problem we develop optimal composite depth ocd function through genetic programming gp for accurate depth estimation the ocd function is constructed by optimally combining the primary information extracted using one or more focus measures the genetically developed composite function is then used to compute the optimal depth map of objects the performance of the developed nonlinear function is investigated using both the synthetic and the real world image sequences experimental results demonstrate that the proposed estimator is more useful in computing accurate depth maps as compared to the existing sff methods moreover it is found that the heterogeneous function is more effective than homogeneous function

completely analytical interactions constructive description an interactionu is called a completely analytical ca interaction if it satisfies one of 12 given conditions formulated in terms of analyticity properties of the partition functions zv u or correlation decay or truncated correlation bounds or asymptotic behavior of ln zv u v the 12 conditions are presented together with part of the proof of their equivalence the main result of the paper is that each condition is constructive in the following sense instead of checking it in all finite volumesv v it is enough to consider only a finite amount of volumes with restricted size in particular the partition functions z v u for the complex perturbationsu ofu do not vanish for all v v and all with provided this is true only forv with diam v c and but with

analysis of focus measure operators for shape from focus shape from focus sff has widely been studied in computer vision as a passive depth recovery and 3d reconstruction method one of the main stages in sff is the computation of the focus level for every pixel of an image by means of a focus measure operator in this work a methodology to compare the performance of different focus measure operators for shape from focus is presented and applied the selected operators have been chosen from an extensive review of the state of the art the performance of the different operators has been assessed through experiments carried out under different conditions such as image noise level contrast saturation and window size such performance is discussed in terms of the working principles of the analyzed operators

the logarithmic sobolev inequality for continuous spin systems on a lattice abstract in this article we give cf theorem 1 6 a sufficient condition on a local specification for the associated gibbs state to satisfy a logarithmic sobolev inequality in the final section cf theorem 3 10 we relate our condition to the type of mixing condition introduced by dobrushin and shlosman in connection with their work on complete analyticity

a fully implicit domain decomposition algorithm for shallow water equations on the cubed sphere popular approaches for solving shallow water equations swes for climate modeling are explicit and semiimplicit methods and both have certain constraints on the time step size in this paper we propose and study a fully implicit method which imposes no limit on the time step size but requires the solution of a large sparse nonlinear system of equations at every time step the focus of the paper is a parallel fully coupled newton krylov ras algorithm with a jacobian matrix explicitly calculated on a weakly nonmatching cubed sphere mesh here ras is a restricted additive schwarz method we show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the cfl condition and we report superlinear speedup of the algorithm on machines with thousands of processors for problems with smooth and nonsmooth solutions

the equivalence of the logarithmic sobolev inequality and the dobrushin shlosman mixing condition given a finite range lattice gas with a compact continuous spin space it is shown cf theorem 1 2 that a uniform logarithmic sobolev inequality cf 1 4 holds if and only if the dobrushin shlosman mixing condition cf 1 5 holds as a consequence of our considerations we also show cf theorems 3 2 and 3 6 that these conditions are equivalent to a statement about the uniform rate at which the associated glauber dynamics tends to equilibrium in this same direction we show cf theorem 3 19 that these ideas lead to a surprisingly strong large deviation principle for the occupation time distribution of the glauber dynamics

log sobolev inequalities for infinite one dimensional lattice systems it is shown that a unique gibbs measure of infinite spin system with short range interaction on one dimensional lattice satisfies log sobolev inequality

improved mixing condition on the grid for counting and sampling independent sets the hard core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics a multicast model of calls in communication networks and as a weighted independent set problem in combinatorics probability and theoretical computer science in this model each independent set i in a graph g is weighted proportionally to i for a positive real parameter for large computing the partition function namely the normalizing constant which makes the weighting a probability distribution on a finite graph on graphs of maximum degree 3 is a well known computationally challenging problem more concretely let lambda c mathbb t delta denote the critical value for the so called uniqueness threshold of the hard core model on the infinite regular tree recent breakthrough results of weitz proceedings of the 38th annual acm symposium on theory of computing stoc pp 140 149 2006 and sly proceedings of the 51st annual ieee symposium on foundations of computer science focs pp 287 296 2010 have identified lambda c mathbb t delta as a threshold where the hardness of estimating the above partition function undergoes a computational transition we focus on the well studied particular case of the square lattice mathbb z 2 and provide a new lower bound for the uniqueness threshold in particular taking it well above lambda c mathbb t 4 our technique refines and builds on the tree of self avoiding walks approach of weitz resulting in a new technical sufficient criterion of wider applicability for establishing strong spatial mixing and hence uniqueness for the hard core model our new criterion achieves better bounds on strong spatial mixing when the graph has extra structure improving upon what can be achieved by just using the maximum degree applying our technique to mathbb z 2 we prove that strong spatial mixing holds for all 2 3882 improving upon the work of weitz that held for 27 16 1 6875 our results imply a fully polynomial deterministic approximation algorithm for estimating the partition function as well as rapid mixing of the associated glauber dynamics to sample from the hard core distribution

selecting the optimal focus measure for autofocusing and depth from focus a method is described for selecting the optimal focus measure with respect to gray level noise from a given set of focus measures in passive autofocusing and depth from focus applications the method is based on two new metrics that have been defined for estimating the noise sensitivity of different focus measures the first metric the autofocusing uncertainty measure aum is useful in understanding the relation between gray level noise and the resulting error in lens position for autofocusing the second metric autofocusing root mean square error arms error is an improved metric closely related to aum aum and arms error metrics are based on a theoretical noise sensitivity analysis of focus measures and they are related by a monotonic expression the theoretical results are validated by actual and simulation experiments for a given camera the optimally accurate focus measure may change from one object to the other depending on their focused images therefore selecting the optimal focus measure from a given set involves computing all focus measures in the set

dobrushin uniqueness theorem and logarithmic sobolev inequalities we formulate a condition on a local specification e on a countable product space m m being a riemannian manifold or a discrete set 1 1 assuring that the corresponding set of gibbs measures consists of a unique measure satisfying a logarithmic sobolev inequality

a very simple proof of the lsi for high temperature spin systems abstract we present a very simple proof that the o n model satisfies a uniform logarithmic sobolev inequality lsi if the difference between the largest and the smallest eigenvalue of the coupling matrix is less than n this condition applies in particular to the sk spin glass model at inverse temperature 1 4 it is the first result of rapid relaxation for the sk model and requires significant cancellations between the ferromagnetic and anti ferromagnetic spin couplings that cannot be obtained by existing methods to prove log sobolev inequalities the proof also applies to more general bounded and unbounded spin systems it uses a single step of zero range renormalisation and bakry emery theory for the renormalised measure

nonlinear approach for enhancement of image focus volume in shape from focus mostly shape from focus algorithms use local averaging using a fixed rectangle window to enhance the initial focus volume in this linear filtering the window size affects the accuracy of the depth map a small window is unable to suppress the noise properly whereas a large window oversmoothes the object shape moreover the use of any window size smoothes focus values uniformly consequently an erroneous depth map is obtained in this paper we suggest the use of iterative 3 d anisotropic nonlinear diffusion filtering andf to enhance the image focus volume in contrast to linear filtering andf utilizes the local structure of the focus values to suppress the noise while preserving edges the proposed scheme is tested using image sequences of synthetic and real objects and results have demonstrated its effectiveness

critical ising on the square lattice mixes in polynomial time the ising model is widely regarded as the most studied model of spin systems in statistical physics the focus of this paper is its dynamic stochastic version the glauber dynamics introduced in 1963 and by now the most popular means of sampling the ising measure intensive study throughout the last three decades has yielded a rigorous understanding of the spectral gap of the dynamics on mathbb z 2 everywhere except at criticality while the critical behavior of the ising model has long been the focus for physicists mathematicians have only recently developed an understanding of its critical geometry with the advent of sle cle and new tools to study conformally invariant systems

approach to equilibrium of glauber dynamics in the one phase region ii the general case we develop a new method based on renormalization group ideas block decimation procedure to prove under an assumption of strong mixing in a finite cube 0 a logarithmic sobolev inequality for the gibbs state of a discrete spin system as a consequence we derive the hypercontractivity of the markov semigroup of the associated glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes multiples of the cube 0

exponential relaxation of glauber dynamics with some special boundary conditions we consider attractive finite range glauber dynamics and show that if a certain mixing condition is satisfied then the system evolving on arbitrary subsets of the lattice with appropriate boundary conditions converges to equilibrium exponentially fast in the uniform sense uniformly over the subsets of the lattice this result applies for instance to the ferromagnetic nearest neighbor ising model in the so called basuev region where complete analyticity is expected to fail

for 2 d lattice spin systems weak mixing implies strong mixing we prove that for finite range discrete spin systems on the two dimensional latticez2 the weak mixing condition which follows for instance from the dobrushin shlosman uniqueness condition for the gibbs state implies a stronger mixing property of the gibbs state similar to the dobrushin shlosman complete analyticity condition but restricted to all squares in the lattice or more generally to all sets multiple of a large enough square the key observation leading to the proof is that a change in the boundary conditions cannot propagate either in the bulk because of the weak mixing condition or along the boundary because it is one dimensional as a consequence we obtain for ferromagnetic ising type systems proofs that several nice properties hold arbitrarily close to the critical temperature these properties include the existence of a convergent cluster expansion and uniform boundedness of the logarithmic sobolev constant and rapid convergence to equilibrium of the associated glauber dynamics on nice subsets ofz2 including the full lattice

cutoff for general spin systems with arbitrary boundary conditions the cutoff phenomenon describes a sharp transition in the convergence of a markov chain to equilibrium in recent work the authors established cutoff and its location for the stochastic ising model on the d dimensional torus n d for any d 1 the proof used the symmetric structure of the torus and monotonicity in an essential way here we enhance the framework and extend it to general geometries boundary conditions and external fields to derive a cutoff criterion that involves the growth rate of balls and the log sobolev constant of the glauber dynamics in particular we show there is cutoff for the stochastic ising model on any sequence of bounded degree graphs with subexponential growth under arbitrary external fields provided the inverse log sobolev constant is bounded for lattices with homogenous boundary such as all plus we identify the cutoff location explicitly in terms of spectral gaps of infinite volume dynamics on half plane intersections analogous results establishing cutoff are obtained for nonmonotone spin systems at high temperatures including the gas hard core model the potts model the antiferromagnetic potts model and the coloring model 2014 wiley periodicals inc