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

on the structure of all minimum cuts in a network and applications this paper presents a characterization of all minimum cuts separating a source from a sink in a network a binary relation is associated with any maximum flow in this network and minimum cuts are identified with closures for this relation as a consequence finding all minimum cuts reduces to a straightforward enumeration applications of this results arise in sensitivity and parametric analyses of networks the vertex packing and maximum closure problems in unconstrained pseudo boolean optimization and project selection as well as in other areas of application of minimum cuts

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

an efficient approximation algorithm for the survivable network design problem the survivable network design problem sndp is to construct a minimum cost subgraph satisfying certain given edge connectivity requirements the first polynomial time approximation algorithm was given by williamson et al combinatorica 15 1995 435 454 this paper gives an improved version that is more efficient consider a graph ofn vertices and connectivity requirements that are at mostk both algorithms find a solution that is within a factor 2k 1 of optimal fork 2 and a factor 2 of optimal fork 1 our algorithm improves the time from o k3n4 to o k 2 n 2 kn 2 sqrt log log n our algorithm shares features with those of williamson et al combinatorica 15 1995 435 454 but also differs from it at a high level necessitating a different analysis of correctness and accuracy our analysis is based on a combinatorial characterization of the redundant edges several other ideas are introduced to gain efficiency these include a generalization of padberg and rao s characterization of minimum odd cuts use of a representation of all minimum s t cuts in a network and a new priority queue system the latter also improves the efficiency of the approximation algorithm of goemans and williamson siam journal on computing 24 1995 296 317 for constrained forest problems such as minimum weight matching generalized steiner trees and others 1998 the mathematical programming society inc published by elsevier science b v

covering symmetric supermodular functions by graphs the minimum number of edges of an undirected graph covering a symmetric supermodular set function is determined as a special case we derive an extension of a theorem of j bang jensen and b jackson on hypergraph connectivity augmentation

quasistatic evolution in perfect plasticity for general heterogeneous materials inspired by some recent developments in the theory of small strain heterogeneous elastoplasticity we both revisit and generalize the formulation of the quasistatic evolutionary problem in perfect plasticity given by francfort and giacomini commun pure appl math 65 1185 1241 2012 we show that their definition of the plastic dissipation measure is equivalent to an abstract one where it is defined as the supremum of the dualities between the deviatoric parts of admissible stress fields and the plastic strains by means of this abstract definition a viscoplastic approximation and variational techniques from the theory of rate independent processes give the existence of an evolution satisfying an energy dissipation balance and consequently hill s maximum plastic work principle for an abstract and very large class of yield conditions

augmenting hypergraphs by edges of size two we give a good characterization for the minimum number of edges of size two whose addition to a given hypergraph h makes it k edge connected our result extends a previous theorem by e cheng 4 for the case when h is already k 1 edge connected we also describe a strongly polynomial algorithm to find both a minimum cardinality augmentation and a minimum cost augmentation where the cost of an edge is equal to the sum of the weights of its endvertices for some given weight function on v h our proof is based on a new splitting theorem for hypergraphs for the case when the special vertex s is only incident with edges of size two this theorem generalizes a splitting result of lovasz for graphs

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

a new approach to the minimum cut problem this paper present a new approach to finding minimum cuts in undirected graphs the fundamental principle is simple the edges in a graph s minimum cut form an extremely small fraction of the graph s edges using this idea we give a randomized strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability the algorithm runs in o n 2 log 3 n time a significant improvement over the previous o mn time bounds based on maximum flows it is simple and intuitive and uses no complex data structures our algorithm can be parallelized to run in rnc with n 2 processors this gives the first proof that the minimum cut problem can be solved in rnc the algorithm does more than find a single minimum cut it finds all of them with minor modifications our algorithm solves two other problems of interest our algorithm finds all cuts with value within a multiplicative factor of of the minimum cut s in expected o n 2 time or in rnc with n 2 processors the problem of finding a minimum multiway cut of graph into r pieces is solved in expected o n 2 r 1 time or in rnc with n 2 r 1 processors the trace of the algorithm s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph this data structure can be efficiently transformed into the more standard cactus representing for minimum cuts

dense estimation and object based segmentation of the optical flow with robust techniques we address the issue of recovering and segmenting the apparent velocity field in sequences of images as for motion estimation we minimize an objective function involving two robust terms the first one cautiously captures the optical flow constraint while the second a priori term incorporates a discontinuity preserving smoothness constraint to cope with the nonconvex minimization problem thus defined we design an efficient deterministic multigrid procedure it converges fast toward estimates of good quality while revealing the large discontinuity structures of flow fields we then propose an extension of the model by attaching to it a flexible object based segmentation device based on deformable closed curves different families of curve equipped with different kinds of prior can be easily supported experimental results on synthetic and natural sequences are presented including an analysis of sensitivity to parameter tuning

robust non local tv l 1 optical flow estimation with occlusion detection in this paper we propose a robust non local tv l 1 optical flow method with occlusion detection to address the problem of weak robustness of optical flow estimation with motion occlusion first a tv l 1 form for flow estimation is defined using a combination of the brightness constancy and gradient constancy assumptions in the data term and by varying the weight under the charbonnier function in the smoothing term second to handle the potential risk of the outlier in the flow field a general non local term is added in the tv l 1 optical flow model to engender the typical non local tv l 1 form third an occlusion detection method based on triangulation is presented to detect the occlusion regions of the sequence the proposed non local tv l 1 optical flow model is performed in a linearizing iterative scheme using improved median filtering and a coarse to fine computing strategy the results of the complex experiment indicate that the proposed method can overcome the significant influence of non rigid motion motion occlusion and large displacement motion results of experiments comparing the proposed method and existing state of the art methods by respectively using middlebury and mpi sintel database test sequences show that the proposed method has higher accuracy and better robustness

single machine scheduling with precedence constraints we discuss the problem of sequencing precedence constrained jobs on a single machine to minimize the average weighted completion time this problem has attracted much attention in the mathematical programming community since sidney s pioneering work in 1975 sidney j b 1975 decomposition algorithms for single machine scheduling with precedence relations and deferral costs operations research23 283 298 we look at the problem from a polyhedral perspective and uncover a relation between sidney s decomposition theorem and different linear programming relaxations more specifically we present a generalization of sidney s result which particularly allows us to reason that virtually all known 2 approximation algorithms are consistent with his decomposition moreover we establish a connection between the single machine scheduling problem and the vertex cover problem indeed in the special case of series parallel precedence constraints we prove that the sequencing problem can be seen as a special case of the vertex cover problem we also argue that this result is true for general precedence constraints if one can show that a certain integer program represents a valid formulation of the sequencing problem finally we give a 3 2 approximation algorithm for two dimensional partial orders and we also provide a characterization of the active inequalities of a linear programming relaxation in completion time variables

large displacement optical flow descriptor matching in variational motion estimation optical flow estimation is classically marked by the requirement of dense sampling in time while coarse to fine warping schemes have somehow relaxed this constraint there is an inherent dependency between the scale of structures and the velocity that can be estimated this particularly renders the estimation of detailed human motion problematic as small body parts can move very fast in this paper we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting this way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied

small strain heterogeneous elastoplasticity revisited the elastoplastic quasi static evolution of a multiphase material a material with a pointwise varying yield surface and elasticity tensor together with interfaces between the phases is revisited in the context of conservative globally minimizing movements existence is shown and classical evolutions are recovered under natural constraints on the plastic dissipation potential special attention is paid to the interfaces where the correct dissipation has to be enforced on the interfaces further the evolution is shown to be a limit of that obtained for a model with linear isotropic hardening as the hardening becomes vanishingly small the duality between plastic strains and admissible stresses is also revisited for lipschitz boundaries and its role in deriving a classical evolution is circumscribed 2012 wiley periodicals inc

regularization strategies for discontinuity preserving optical flow methods the aim of this paper is to study several strategies for the preservation of flow discontinuities in variational optical flow methods we analyze the combination of robust functionals and diffusion tensors in the smoothness assumption our study includes the use of tensors based on decreasing functions which has shown to provide good results however it presents several limitations and usually does not perform better than other basic approaches it typically introduces instabilities in the computed motion fields in the form of independent blobs of vectors with large magnitude we propose two alternatives to overcome these drawbacks first a simple approach that combines the decreasing function with a minimum isotropic smoothing and second a method that looks for the best parameter configuration that preserves the important motion contours and avoid instabilities it relies on the input images and the regularization parameter it is fully automatic providing a near optimal value for many sequences as shown in the experiments both proposals allow to detect the contours of the motion field and produce more stable solutions for a large range of parameters in the experimental results we present a detailed study and comparison of the different strategies

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

quasistatic evolution problems for linearly elastic perfectly plastic materials the problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate independent processes existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation this approach provides a new approximation result for the solutions of the quasistatic evolution problem which are shown to be absolutely continuous in time four equivalent formulations of the problem in rate form are derived a strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain

coverings and structure of crossing families the second problem we consider is to find a compact representation of f we prove that there exists a so called hypercactus k of size o v consisting of cycles and hyper edges arranged in a tree like manner and a mapping from v to v k in such a way that there is a bijection between the minimum cuts of k and the members of f if f corresponds to the minimum cuts of a k edge connected graph then k reduces to the well known cactus representation of minimum cuts due to dinitz et al

separation dimension and facet algorithms for node flow polyhedra production planning problems such as an available to promise atp model of chen et al 2002 can involve material compatibility constraints that specify when components from various suppliers can be feasibly assembled into a final product in a companion paper to chen et al 2002 ball et al 2003 showed that in many cases such constraints can be modeled as the set of feasible source sink flows through an acyclic network the flow through a node is the sum of the flows on all paths containing it the number of paths is often exponential in the number of nodes and so it is more computationally tractable to consider the set of node flows in place of that of path flows here nodes represent components and paths represent product configurations in the context of np hard mixed integer programming models such as the atp model when the description of the set of node flows is too complicated to be explicitly written out the material compatibility constraints can be handled in a cutting plane framework by using a separation algorithm ball et al characterized the polyhedron of node flows for some special cases we extend this work in various practical and theoretical directions we allow arbitrary directed networks we allow both upper and lower bounds on flows we characterize which valid inequalities are facets we give fast algorithms for separation violation and dimension and we put all the pieces together into an algorithm for facet separation all algorithms are very efficient as they are based on max flow and min cost flow subroutines

the general structure of edge connectivity of a vertex subset in a graph and its incremental maintenance odd case let g v e be an undirected graph s be a subset of its vertices frak c s be the set of minimum edge cuts partitioning s and lambda s be the cardinality of such a cut we suggest a graph structure called the connectivity carcass of s that represents both cuts in frak c s and the partition of v by all these cuts its size is o min e lambda s v in this paper we present general constructions and study in detail the case lambda s odd the specifics of the case lambda s even are considered elsewhere for an adequate description of the connectivity carcass we introduce a new type of graph locally orientable graphs which generalize digraphs the connectivity carcass consists of a locally orientable quotient graph of g a cactus tree in case lambda s odd just a tree representing all distinct partitions of s by cuts in frak c s and a mapping connecting them one can build it in o s max flow computations in g for an arbitrary sequence of u edge insertions not changing lambda s the connectivity carcass can be maintained in time o v min e lambda s v u for two vertices of g queries asking whether they are separated by a cut in frak c s are answered in o 1 worst case time per query another possibility is to maintain the carcass in o s min e lambda s v u time but to answer the queries in o 1 time only if at least one of the vertices belongs to s

parallel and fast sequential algorithms for undirected edge connectivity augmentation e2 such that i ei optmially increases the connectivity by for any integer the main result of the paper is that this sequence of edge sets can be divided into o n groups such that within one group all ei are basically the same using this result we improve on the running time of edge connectivity augmentation as well as we give the first parallel rnc augmentation algorithm we also present new efficient subroutines for finding the so called extreme sets and the cactus representation of min cuts required in our algorithms augmenting the connectivity of hypergraphs with ordinary edges is known to be structurally harder than that of ordinary graphs in a weaker version when one exceptional hyperedge is allowed in the augmenting edge set we derive similar results as for ordinary graphs

sparse occlusion detection with optical flow we tackle the problem of detecting occluded regions in a video stream under assumptions of lambertian reflection and static illumination the task can be posed as a variational optimization problem and its solution approximated using convex minimization we describe efficient numerical schemes that reach the global optimum of the relaxed cost functional for any number of independently moving objects and any number of occlusion layers we test the proposed algorithm on benchmark datasets expanded to enable evaluation of occlusion detection performance in addition to optical flow

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

hypergraph connectivity augmentation the hypergraph augmentation problem is to augment a hypergraph by hyperedges to meet prescribed local connectivity requirements we provide here a minimax theorem for this problem the result is derived from the degree constrained version of the problem by a standard method we shall construct the required hypergraph for the latter problem by a greedy type algorithm a similar minimax result will be given for the problem of augmenting a hypergraph by weighted edges hyperedges of size two with weights to meet prescribed local connectivity requirements moreover a special case of an earlier result of schrijver on supermodular colourings shall be derived from our theorem

optic flow in harmony most variational optic flow approaches just consist of three constituents a data term a smoothness term and a smoothness weight in this paper we present an approach that harmonises these three components we start by developing an advanced data term that is robust under outliers and varying illumination conditions this is achieved by using constraint normalisation and an hsv colour representation with higher order constancy assumptions and a separate robust penalisation our novel anisotropic smoothness is designed to work complementary to the data term to this end it incorporates directional information from the data constraints to enable a filling in of information solely in the direction where the data term gives no information yielding an optimal complementary smoothing behaviour this strategy is applied in the spatial as well as in the spatio temporal domain finally we propose a simple method for automatically determining the optimal smoothness weight this method bases on a novel concept that we call optimal prediction principle opp it states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence the benefits of our optic flow in harmony ofh approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used middlebury optic flow benchmark

decompositions network flows and a precedence constrained single machine scheduling problem we present an in depth theoretical algorithmic and computational study of a linear programming lp relaxation to the precedence constrained single machine scheduling problem 1 prec s jw jc jto minimize a weighted sum of job completion times on the theoretical side we study the structure of tight parallel inequalities in thelp relaxation and show thatevery permutation schedule that is consistent with sidney s decomposition has total cost no more than twice the optimum on the algorithmic side we provide a parametric extension to sidney s decomposition and show that a finest decomposition can be obtained by essentially solving a parametric minimum cut problem finally we report results obtained by an algorithm based on these developments on randomly generated instances with up to 2 000 jobs