shape illumination and reflectance from shading a fundamental problem in computer vision is that of inferring the intrinsic 3d structure of the world from flat 2d images of that world traditional methods for recovering scene properties such as shape reflectance or illumination rely on multiple observations of the same scene to overconstrain the problem recovering these same properties from a single image seems almost impossible in comparison there are an infinite number of shapes paint and lights that exactly reproduce a single image however certain explanations are more likely than others surfaces tend to be smooth paint tends to be uniform and illumination tends to be natural we therefore pose this problem as one of statistical inference and define an optimization problem that searches for the most likely explanation of a single image our technique can be viewed as a superset of several classic computer vision problems shape from shading intrinsic images color constancy illumination estimation etc and outperforms all previous solutions to those constituent problems

fundamental principles on learning new features for effective dense matching in dense matching including stereo matching and optical flow nearly all existing approaches are based on simple features such as gray or rgb color gradient or simple transformations like census to calculate matching costs these features do not perform well in complex scenes that may involve radiometric changes noises overexposure and or textureless regions various problems may appear such as wrong matching at the pixel or region level flattening breaking of edges and or even entire structural collapse in this paper we propose two fundamental principles based on the consistency and the distinctiveness of features we show that almost all existing problems in dense matching are caused by features that violate one or both of these principles to systematically learn good features for dense matching we develop a general multi objective optimization based on these two principles and apply convolutional neural networks to find new features that lie on the pareto frontier by using two frame optical flow and stereo matching as applications our experimental results show that the features learned can significantly improve the performance of state of the art approaches based on the kitti benchmarks our method ranks first on the two stereo benchmarks and is the best among existing two frame optical flow algorithms on flow benchmarks

harmony potentials the hierarchical conditional random field hcrf model have been successfully applied to a number of image labeling problems including image segmentation however existing hcrf models of image segmentation do not allow multiple classes to be assigned to a single region which limits their ability to incorporate contextual information across multiple scales at higher scales in the image this representation yields an oversimplified model since multiple classes can be reasonably expected to appear within large regions this simplified model particularly limits the impact of information at higher scales since class label information at these scales is usually more reliable than at lower noisier scales neglecting this information is undesirable to address these issues we propose a new consistency potential for image labeling problems which we call the harmony potential it can encode any possible combination of labels penalizing only unlikely combinations of classes we also propose an effective sampling strategy over this expanded label set that renders tractable the underlying optimization problem our approach obtains state of the art results on two challenging standard benchmark datasets for semantic image segmentation pascal voc 2010 and msrc 21

adaptive support weight approach for correspondence search we present a new window based method for correspondence search using varying support weights we adjust the support weights of the pixels in a given support window based on color similarity and geometric proximity to reduce the image ambiguity our method outperforms other local methods on standard stereo benchmarks

shortest paths with higher order regularization this paper describes a new method of finding thin elongated structures in images and volumes we use shortest paths to minimize very general functionals of higher order curve properties such as curvature and torsion our method uses line graphs to find the optimal path on a given discretization often in the order of seconds on a single computer the curves are then refined using local optimization making it possible to recover very smooth curves we are able to place constraints on our curves such as maximum integrated curvature or a maximum curvature at any point of the curve to our knowledge we are the first to perform experiments in three dimensions with curvature and torsion regularization the largest graphs we process have over a hundred billion arcs experiments on medical images and in multi view reconstruction show the significance and practical usefulness of higher order regularization

nonexistence of positive solutions to a semilinear elliptic system and blow up estimates for a reaction diffusion system abstract we get simple conditions under which the elliptic system u u p 1 v q 1 v u p 2 v q 2 in r n n 3 with p i q i 1 i 1 2 has no positive radially symmetric solutions then by using this nonexistence result we establish blow up estimates for reaction diffusion system of fujita type u t u u p 1 v q 1 v t v u p 2 v q 2 with the homogeneous dirichlet boundary value condition

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

the blow up rate of solutions of semilinear heat equations on caracterise le comportement asymptotique de la solution de l equation de la chaleur semilineaire u t u exp u dans o t u k sur o t u x 0 x k pour xe k 0 dans un voisinage d un point d explosion quand t approche du temps d explosion fini t

multi view scene flow estimation a view centered variational approach we present a novel method for recovering the 3d structure and scene flow from calibrated multi view sequences we propose a 3d point cloud parametrization of the 3d structure and scene flow that allows us to directly estimate the desired unknowns a unified global energy functional is proposed to incorporate the information from the available sequences and simultaneously recover both depth and scene flow the functional enforces multi view geometric consistency and imposes brightness constancy and piecewise smoothness assumptions directly on the 3d unknowns it inherently handles the challenges of discontinuities occlusions and large displacements the main contribution of this work is the fusion of a 3d representation and an advanced variational framework that directly uses the available multi view information this formulation allows us to advantageously bind the 3d unknowns in time and space different from optical flow and disparity the proposed method results in a nonlinear mapping between the images coordinates thus giving rise to additional challenges in the optimization process our experiments on real and synthetic data demonstrate that the proposed method successfully recovers the 3d structure and scene flow despite the complicated nonconvex optimization problem

blowup estimates for a semilinear reaction diffusion system this paper deals with the blowup estimates of positive solutions for a semilinear reaction diffusion system ut u u vp vt v uqv with null dirichlet boundary conditions the upper and lower bounds of blowup rates are obtained

learning to refine depth for robust stereo estimation abstract traditional depth estimation from stereo images is usually formulated as a patch matching problem which requires post processing stages to impose smoothness and handle depth discontinuities and occlusions while recent deep network approaches directly learn a regressor for the entire disparity map they still suffer from large errors near the depth discontinuities in this paper we propose a novel method to refine the disparity maps generated by deep regression networks instead of relying on ad hoc post processing we learn a unified deep network model that predicts a confidence map and the disparity gradients from the learned feature representation in regression networks we integrate the initial disparity estimation the confidence map and the disparity gradients into a continuous markov random field mrf for depth refinement which is capable of representing rich surface structures our disparity mrf model can be solved via efficient global optimization in a closed form we evaluate our approach on both synthetic and real world datasets and the results show it achieves the state of art performance and produces more structure preserving disparity maps with smaller errors in the neighborhood of depth boundaries

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

multi target regression via robust low rank learning multi target regression has recently regained great popularity due to its capability of simultaneously learning multiple relevant regression tasks and its wide applications in data mining computer vision and medical image analysis while great challenges arise from jointly handling inter target correlations and input output relationships in this paper we propose multi layer multi target regression mmr which enables simultaneously modeling intrinsic inter target correlations and nonlinear input output relationships in a general framework via robust low rank learning specifically the mmr can explicitly encode inter target correlations in a structure matrix by matrix elastic nets men the mmr can work in conjunction with the kernel trick to effectively disentangle highly complex nonlinear input output relationships the mmr can be efficiently solved by a new alternating optimization algorithm with guaranteed convergence the mmr leverages the strength of kernel methods for nonlinear feature learning and the structural advantage of multi layer learning architectures for inter target correlation modeling more importantly it offers a new multi layer learning paradigm for multi target regression which is endowed with high generality flexibility and expressive ability extensive experimental evaluation on 18 diverse real world datasets demonstrates that our mmr can achieve consistently high performance and outperforms representative state of the art algorithms which shows its great effectiveness and generality for multivariate prediction

stereo matching with color weighted correlation hierarchical belief propagation and occlusion handling in this paper we formulate a stereo matching algorithm with careful handling of disparity discontinuity and occlusion the algorithm works with a global matching stereo model based on an energy minimization framework the global energy contains two terms the data term and the smoothness term the data term is first approximated by a color weighted correlation then refined in occluded and low texture areas in a repeated application of a hierarchical loopy belief propagation algorithm the experimental results are evaluated on the middlebury data sets showing that our algorithm is the top performer among all the algorithms listed there

improved recursive geodesic distance computation for edge preserving filter all known recursive filters based on the geodesic distance affinity are realized by two 1d recursions applied in two orthogonal directions of the image plane the 2d extension of the filter is not valid and has theoretically drawbacks which lead to known artifacts in this paper a maximum influence propagation method is proposed to approximate the 2d extension for the geodesic distance based recursive filter the method allows to partially overcome the drawbacks of the 1d recursion approach we show that our improved recursion better approximates the true geodesic distance filter and the application of this improved filter for image denoising outperforms the existing recursive implementation of the geodesic distance as an application we consider a geodesic distance based filter for image denoising experimental evaluation of our denoising method demonstrates comparable and for several test images better results than state of the art approaches while our algorithm is considerably faster with computational complexity o 8p

progressive match expansion via coherent subspace constraint in this paper a quasi dense matching algorithm called progressive match expansion via coherent subspace pecs is proposed our algorithm starts from a set of sparse seeds and iteratively expands potential matches in the region around the seeds until no more matches could be found the main difference from previous methods is that our method computes a coherent non rigid transformation to relate the matching pixels instead of using local planar affine model to approximate the real scene surface within the expanding region the points in the expanding region are treated as a whole and all the matches satisfying the transformation are found at once first dense sift descriptors are extracted and a subspace encoding the feature similarity between two point sets is computed this embedding pulls two points closer if they have similar features and makes the non rigid transformation learning more robust second a coherent non rigid transformation in the subspace is computed to move one point set towards the other and the spatially aligned two points denote a match the proposed model is robust to scenes with non smooth surface and experiment results reveal the good performance in both 2d image matching and 3d reconstruction

filter based mean field inference for random fields with higher order terms and product label spaces recently a number of cross bilateral filtering methods have been proposed for solving multi label problems in computer vision such as stereo optical flow and object class segmentation that show an order of magnitude improvement in speed over previous methods these methods have achieved good results despite using models with only unary and or pairwise terms however previous work has shown the value of using models with higher order terms e g to represent label consistency over large regions or global co occurrence relations we show how these higher order terms can be formulated such that filter based inference remains possible we demonstrate our techniques on joint stereo and object labelling problems as well as object class segmentation showing in addition for joint object stereo labelling how our method provides an efficient approach to inference in product label spaces we show that we are able to speed up inference in these models around 10 30 times with respect to competing graph cut move making methods as well as maintaining or improving accuracy in all cases we show results on pascalvoc 10 for object class segmentation and leuven for joint object stereo labelling

constrained optical flow estimation as a matching problem in general discretization in the motion vector domain yields an intractable number of labels in this paper we propose an approach that can reduce general optical flow to the constrained matching problem by pre estimating a 2 d disparity labeling map of the desired discrete motion vector function one of the goals of the proposed paper is estimating coarse distribution of motion vectors and then utilizing this distribution as global constraints for discrete optical flow estimation this pre estimation is done with a simple frame to frame correlation technique also known as the digital symmetric phase only filter spof we discover a strong correlation between the output of the spof and the motion vector distribution of the related optical flow a two step matching paradigm for optical flow estimation is applied pixel accuracy integer flow and subpixel accuracy estimation the matching problem is solved by global optimization experiments on the middlebury optical flow datasets confirm our intuitive assumptions about strong correlation between motion vector distribution of optical flow and maximal peaks of spof outputs the overall performance of the proposed method is promising and achieves state of the art results on the middlebury benchmark

nonexistence of global solutions to semilinear wave equations in high dimensions on considere le probleme de cauchy pour l equation d onde semi lineaire 2 t 2 u x t u x t p p 1 u x o f x u t x o g x avec f g c o r n

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

exact optimization for markov random fields with convex priors we introduce a method to solve exactly a first order markov random field optimization problem in more generality than was previously possible the mrf has a prior term that is convex in terms of a linearly ordered label set the method maps the problem into a minimum cut problem for a directed graph for which a globally optimal solution can be found in polynomial time the convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method

accurate stereo matching by two step energy minimization in stereo matching cost filtering methods and energy minimization algorithms are considered as two different techniques due to their global extent energy minimization methods obtain good stereo matching results however they tend to fail in occluded regions in which cost filtering approaches obtain better results in this paper we intend to combine both the approaches with the aim to improve overall stereo matching results we show that a global optimization with a fully connected model can be solved by cost filtering methods based on this observation we propose to perform stereo matching as a two step energy minimization algorithm we consider two markov random field mrf models 1 a fully connected model defined on the complete set of pixels in an image and 2 a conventional locally connected model we solve the energy minimization problem for the fully connected model after which the marginal function of the solution is used as the unary potential in the locally connected mrf model experiments on the middlebury stereo data sets show that the proposed method achieves the state of the arts results

joint histogram based cost aggregation for stereo matching this paper presents a novel method for performing efficient cost aggregation in stereo matching the cost aggregation problem is reformulated from the perspective of a histogram giving us the potential to reduce the complexity of the cost aggregation in stereo matching significantly differently from previous methods which have tried to reduce the complexity in terms of the size of an image and a matching window our approach focuses on reducing the computational redundancy that exists among the search range caused by a repeated filtering for all the hypotheses moreover we also reduce the complexity of the window based filtering through an efficient sampling scheme inside the matching window the tradeoff between accuracy and complexity is extensively investigated by varying the parameters used in the proposed method experimental results show that the proposed method provides high quality disparity maps with low complexity and outperforms existing local methods this paper also provides new insights into complexity constrained stereo matching algorithm design

blow up rate for a semilinear reaction diffusion system abstract this paper deals with the blow up rate of positive solution to semilinear reaction diffusion system u1 t u1 u2p1 un 1 t un 1 unpn 1 un u1 u1pn with null dirichlet boundary conditions the upper and lower bounds of blow up rate were obtained

wide baseline foreground object interpolation using silhouette shape prior we consider the synthesis of intermediate views of an object captured by two widely spaced and calibrated cameras this problem is challenging because foreshortening effects and occlusions induce significant differences between the reference images when the cameras are far apart that makes the association or disappearance appearance of their pixels difficult to estimate our main contribution lies in disambiguating this ill posed problem by making the interpolated views consistent with a plausible transformation of the object silhouette between the reference views this plausible transformation is derived from an object specific prior that consists of a nonlinear shape manifold learned from multiple previous observations of this object by the two reference cameras the prior is used to estimate the evolution of the epipolar silhouette segments between the reference views this information directly supports the definition of epipolar silhouette segments in the intermediate views as well as the synthesis of textures in those segments it permits to reconstruct the epipolar plane images epis and the continuum of views associated with the epi volume obtained by aggregating the epis experiments on synthetic and natural images show that our method preserves the object topology in intermediate views and deals effectively with the self occluded regions and the severe foreshortening effect associated with wide baseline camera configurations

the role of non linear diffusion in non simultaneous blow up we study a parabolic system of two non linear reaction diffusion equations completely coupled through source terms and with power like diffusivity under adequate hypotheses on the initial data we prove that non simultaneous blow up is sometimes possible i e one of the components blows up while the other remains bounded the conditions for non simultaneous blow up rely strongly on the diffusivity parameters and significant differences appear between the fast diffusion and the porous medium case surprisingly flat homogeneous in space solutions are not always a good guide to determine whether non simultaneous blow up is possible

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

spatial homogeneity pursuit of regression coefficients for large datasets spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest taking into account the spatial de

contextual bandits with similarity information in a multi armed bandit mab problem an online algorithm makes a sequence of choices in each round it chooses from a time invariant set of alternatives and receives the payoff associated with this alternative while the case of small strategy sets is by now well understood a lot of recent work has focused on mab problems with exponentially or infinitely large strategy sets where one needs to assume extra structure in order to make the problem tractable in particular recent literature considered information on similarity between arms we consider similarity information in the setting of contextual bandits a natural extension of the basic mab problem where before each round an algorithm is given the context a hint about the payoffs in this round contextual bandits are directly motivated by placing advertisements on web pages one of the crucial problems in sponsored search a particularly simple way to represent similarity information in the contextual bandit setting is via a similarity distance between the context arm pairs which bounds from above the difference between the respective expected payoffs prior work on contextual bandits with similarity uses uniform partitions of the similarity space so that each context arm pair is approximated by the closest pair in the partition algorithms based on uniform partitions disregard the structure of the payoffs and the context arrivals which is potentially wasteful we present algorithms that are based on adaptive partitions and take advantage of benign payoffs and context arrivals without sacrificing the worst case performance the central idea is to maintain a finer partition in high payoff regions of the similarity space and in popular regions of the context space our results apply to several other settings e g mab with constrained temporal change slivkins and upfal 2008 and sleeping bandits kleinberg et al 2008a

optimal classification for blow up phenomena in heat equations coupled via exponential sources abstract this paper deals with simultaneous and non simultaneous blow up solutions for heat equations coupled via exponential sources subject to null dirichlet boundary conditions the main results complete the previously known results on the optimal classification for simultaneous and non simultaneous blow up solutions by covering the whole ranges of exponents moreover all kinds of simultaneous and non simultaneous blow up rates are obtained

continuous 3d label stereo matching using local expansion moves we present an accurate stereo matching method using local expansion moves based on graph cuts this new move making scheme is used to efficiently infer per pixel 3d plane labels on a pairwise markov random field mrf that effectively combines recently proposed slanted patch matching and curvature regularization terms the local expansion moves are presented as many alpha expansions defined for small grid regions the local expansion moves extend traditional expansion moves by two ways localization and spatial propagation by localization we use different candidate alpha labels according to the locations of local alpha expansions by spatial propagation we design our local alpha expansions to propagate currently assigned labels for nearby regions with this localization and spatial propagation our method can efficiently infer mrf models with a continuous label space using randomized search our method has several advantages over previous approaches that are based on fusion moves or belief propagation it produces submodular moves deriving a subproblem optimality it helps find good smooth piecewise linear disparity maps it is suitable for parallelization it can use cost volume filtering techniques for accelerating the matching cost computations even using a simple pairwise mrf our method is shown to have best performance in the middlebury stereo benchmark v2 and v3

blow up rate estimates for semilinear parabolic systems abstract this paper deals with the blow up rate estimates of positive solutions for semilinear parabolic systems with null dirichlet boundary conditions the upper and lower bounds of blow up rate were obtained

stereo matching using belief propagation in this paper we formulate the stereo matching problem as a markov network and solve it using bayesian belief propagation the stereo markov network consists of three coupled markov random fields that model the following a smooth field for depth disparity a line process for depth discontinuity and a binary process for occlusion after eliminating the line process and the binary process by introducing two robust functions we apply the belief propagation algorithm to obtain the maximum a posteriori map estimation in the markov network other low level visual cues e g image segmentation can also be easily incorporated in our stereo model to obtain better stereo results experiments demonstrate that our methods are comparable to the state of the art stereo algorithms for many test cases

a pixel dissimilarity measure that is insensitive to image sampling because of image sampling traditional measures of pixel dissimilarity can assign a large value to two corresponding pixels in a stereo pair even in the absence of noise and other degrading effects we propose a measure of dissimilarity that is provably insensitive to sampling because it uses the linearly interpolated intensity functions surrounding the pixels experiments on real images show that our measure alleviates the problem of sampling with little additional computational overhead

registration and interactive planar segmentation for stereo images of polyhedral scenes we introduce a two step iterative segmentation and registration method to find coplanar surfaces among stereo images of a polyhedral environment the novelties of this paper are i to propose a user defined initialization easing the image matching and segmentation ii to incorporate color appearance and planar projection information into a bayesian segmentation scheme and iii to add consistency to the projective transformations related to the polyhedral structure of the scenes the method utilizes an assisted bayesian color segmentation scheme the initial user assisted segmentation is used to define search regions for planar homography image registration the two reliable methods cooperate to obtain probabilities for coplanar regions with similar color information that are used to get a new segmentation by means of quadratic markov measure fields qmmf we search for the best regions by iterating both steps registration and segmentation

two armed restless bandits with imperfect information stochastic control and indexability we present a two armed bandit model of decision making under uncertainty where the expected return to investing in the risky arm increases when choosing that arm and decreases when choosing the safe arm these dynamics are natural in applications such as human capital development job search and occupational choice using new insights from stochastic control along with a monotonicity condition on the payoff dynamics we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with gittins index our result implies the indexability of a new class of restless bandit models

blowup in diffusion equations a survey this paper deals with quasilinear reaction diffusion equations for which a solution local in time exists if the solution ceases to exist for some finite time we say that it blows up in contrast to linear equations blowup can occur even if the data are smooth and well defined for all times depending on the equation either the solution or some of its derivatives become singular we shall concentrate on those cases where the solution becomes unbounded in finite time this can occur in quasilinear equations if the heat source is strong enough there exist many theoretical studies on the question on the occurrence of blowup in this paper we shall recount some of the most interesting criteria and most important methods for analyzing blowup the asymptotic behavior of solutions near their singularities is only completely understood in the special case where the source is a power a better knowledge would be useful also for their numerical treatment thus not surprisingly the numerical analysis of this type of problems is still at a rather early stage the goal of this paper is to collect some of the known results and algorithms and to direct the attention to some open problems

global existence and blow up for a nonlinear reaction diffusion system abstract we consider the nonlinear reaction diffusion system u t u u m 1 v n 1 v t v u m 2 v n 2 subject to dirichlet boundary conditions andm2 m1 1 n1 n2 1 we prove that ifm1 1 n2 1 andm2n1 1 m1 1 n2 all nonnegative solutions are global while ifm1 1 orn2 1 orm2n1 1 m1 1 n2 both global existence and finite time blow up coexist

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

blow up properties of solutions for a multi coupled parabolic system this paper deals with the blow up behavior of radial solutions to a parabolic system multi coupled via inner sources and boundary flux we first obtain a necessary and sufficient condition for the existence of non simultaneous blow up and then find five regions of exponent parameters where both non simultaneous and simultaneous blow up may happen in particular nine simultaneous blow up rates are established for different regions of parameters it is interesting to observe that different initial data may lead to different simultaneous blow up rates even with the same exponent parameters

global color sparseness and a local statistics prior for fast bilateral filtering the property of smoothing while preserving edges makes the bilateral filter a very popular image processing tool however its non linear nature results in a computationally costly operation various works propose fast approximations to the bilateral filter however the majority does not generalize to vector input as is the case with color images we propose a fast approximation to the bilateral filter for color images the filter is based on two ideas first the number of colors which occur in a single natural image is limited we exploit this color sparseness to rewrite the initial non linear bilateral filter as a number of linear filter operations second we impose a statistical prior to the image values that are locally present within the filter window we show that this statistical prior leads to a closed form solution of the bilateral filter finally we combine both ideas into a single fast and accurate bilateral filter for color images experimental results show that our bilateral filter based on the local prior yields an extremely fast bilateral filter approximation but with limited accuracy which has potential application in real time video filtering our bilateral filter which combines color sparseness and local statistics yields a fast and accurate bilateral filter approximation and obtains the state of the art results

bandit problems with infinitely many arms we consider a bandit problem consisting of a sequence of n choices from an infinite number of bernoulli arms with n the objective is to minimize the long run failure rate the bernoulli parameters are independent observations from a distribution f we first assume f to be the uniform distribution on 0 1 and consider various extensions in the uniform case we show that the best lower bound for the expected failure proportion is between 2 n and 2 n and we exhibit classes of strategies that achieve the latter

denumerable armed bandits this paper studies the class of denumerable armed i e finite or countably infinitearmed bandit problems with independent arms and geometric discounting over an infinite horizon in which each arm generates rewards according to one of a finite number of distributions or types the number of types in the support of an arm as also the types themselves are allowed to vary across the arms we derive certain continuity and curvature properties of the dynamic allocation or gittins index of gittins and jones 1974 and provide necessary and sufficient conditions under which the gittins jones result identifying all optimal strategies for finite armed bandits may be extended to infinite armed bandits we then establish our central result at each point in time the arm selected by an optimal strategy will with strictly positive probability remain an optimal selection forever more specifically for every such arm there exists at least one type of that arm such that when conditioned on that type being the arm s true type the arm will survive forever and continuously with nonzero probability when the reward distributions of an arm satisfy the monotone likelihood ratio property mlrp the survival prospects of an arm improve when conditioned on types generating higher expected rewards however we show how this need not be the case in the absence of mlrp implications of these results are derived for the theories of job search and matching as well as other applications of the bandit paradigm

switching costs and the gittins index the theorem of gittins and jones 1974 is perhaps the single most powerful result in the literature on bandit problems this result establishes that in independent armed bandit problems with geometric discounting over an infinite horizon all optimal strategies may be obtained by solving a family of simple optimal stopping problems that associate with each arm an index known as the dynamic allocation index or more popularly as the gittins index importantly the gittins index of an arm depends solely on the characteristics of that arm and the rate of discounting and is otherwise completely independent of the problem under consideration these features simplify significantly the task of characterizing optimal strategies in this class of problems

kernel based tests for joint independence summary we investigate the problem of testing whether d possibly multivariate random variables which may or may not be continuous are jointly or mutually independent our method builds on ideas of the two variable hilbert schmidt independence criterion but allows for an arbitrary number of variables we embed the joint distribution and the product of the marginals in a reproducing kernel hilbert space and define the d variable hilbert schmidt independence criterion dhsic as the squared distance between the embeddings in the population case the value of dhsic is 0 if and only if the d variables are jointly independent as long as the kernel is characteristic on the basis of an empirical estimate of dhsic we investigate three non parametric hypothesis tests a permutation test a bootstrap analogue and a procedure based on a gamma approximation we apply non parametric independence testing to a problem in causal discovery and illustrate the new methods on simulated and real data sets

single point blow up for a semilinear initial value problem abstract the initial value problem on r r is considered u t t x u xx t x u t x u t r 0 u 0 x x where 0 and is a fixed large number it is known that for some initial values the solution u t x exists only up to some finite time t and that u t as t t for the specific initial value k where 0 xx 0 r 0 k is sufficiently large it is shown that if x 0 then lim t t u t x and lim t t u x t x exist and are finite in other words blow up occurs only at the point x 0

global stereo reconstruction under second order smoothness priors second order priors on the smoothness of 3d surfaces are a better model of typical scenes than first order priors however stereo reconstruction using global inference algorithms such as graph cuts has not been able to incorporate second order priors because the triple cliques needed to express them yield intractable nonsubmodular optimization problems this paper shows that inference with triple cliques can be effectively performed our optimization strategy is a development of recent extensions to alpha expansion based on the ldquo qpbordquo algorithm the strategy is to repeatedly merge proposal depth maps using a novel extension of qpbo proposal depth maps can come from any source for example frontoparallel planes as in alpha expansion or indeed any existing stereo algorithm with arbitrary parameter settings

depth estimation with occlusion modeling using light field cameras light field cameras have become widely available in both consumer and industrial applications however most previous approaches do not model occlusions explicitly and therefore fail to capture sharp object boundaries a common assumption is that for a lambertian scene a pixel will exhibit photo consistency which means all viewpoints converge to a single point when focused to its depth however in the presence of occlusions this assumption fails to hold making most current approaches unreliable precisely where accurate depth information is most important at depth discontinuities in this paper an occlusion aware depth estimation algorithm is developed the method also enables identification of occlusion edges which may be useful in other applications it can be shown that although photo consistency is not preserved for pixels at occlusions it still holds in approximately half the viewpoints moreover the line separating the two view regions occluded object versus occluder has the same orientation as that of the occlusion edge in the spatial domain by ensuring photo consistency in only the occluded view region depth estimation can be improved occlusion predictions can also be computed and used for regularization experimental results show that our method outperforms current state of the art light field depth estimation algorithms especially near occlusion boundaries