a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

a free boundary problem for the parabolic poisson kernel abstract we study parabolic chord arc domains introduced by hofmann lewis and nystrom 14 and prove a free boundary regularity result below the continuous threshold more precisely we show that a reifenberg flat parabolic chord arc domain whose poisson kernel has logarithm in vmo must in fact be a vanishing chord arc domain i e satisfies a vanishing carleson measure condition this generalizes to the parabolic setting a result of kenig and toro 26 and answers in the affirmative a question left open in the aforementioned paper of hofmann et al a key step in this proof is a classification of flat blowups for the parabolic problem

convex and semi nonnegative matrix factorizations we present several new variations on the theme of nonnegative matrix factorization nmf considering factorizations of the form x fgt we focus on algorithms in which g is restricted to containing nonnegative entries but allowing the data matrix x to have mixed signs thus extending the applicable range of nmf methods we also consider algorithms in which the basis vectors of f are constrained to be convex combinations of the data points this is used for a kernel extension of nmf we provide algorithms for computing these new factorizations and we provide supporting theoretical analysis we also analyze the relationships between our algorithms and clustering algorithms and consider the implications for sparseness of solutions finally we present experimental results that explore the properties of these new methods

optimal doubling reifenberg flatness and operators of p laplace type in this paper we consider operators of p laplace type of the form a x u 0 concerning a we assume for p 1 fixed an appropriate ellipticity type condition holder continuity in x and that a x p 1 a x whenever x r n and r n 0 let r n be a bounded domain let d be a compact subset of we say that u up d is the a capacitary

elliptic equations with bmo nonlinearity in reifenberg domains given p 2 8 we obtain the global w1 p estimate for the weak solution of a boundary value problem for an elliptic equation with bmo nonlinearity in a reifenberg domain assuming that the nonlinearity has sufficiently small bmo seminorm and that the boundary of the domain is sufficiently flat

a global solution to sparse correspondence problems we propose a new methodology for reliably solving the correspondence problem between sparse sets of points of two or more images this is a key step inmost problems of computer vision and so far no general method exists to solve it our methodology is able to handle most of the commonly used assumptions in a unique formulation independent of the domain of application and type of features it performs correspondence and outlier rejection in a single step and achieves global optimality with feasible computation feature selection and correspondence are first formulated as an integer optimization problem this is a blunt formulation which considers the whole combinatorial space of possible point selections and correspondences to find its global optimal solution we build a concave objective function and relax the search domain into its convex hull the special structure of this extended problem assures its equivalence to the original one but it can be optimally solved by efficient algorithms that avoid combinatorial search this methodology can use any criterion provided it can be translated into cost functions with continuous second derivatives

parabolic equations in time dependent reifenberg domains in this paper we define time dependent parabolic reifenberg domains and study lp estimates for weak solutions of uniformly parabolic equations in divergence form on these domains the basic assumption is that the principal coefficients are of parabolic bmo space with small parabolic bmo seminorms it is shown that lp estimates hold for time dependent parabolic d reifenberg domains

square functions and uniform rectifiability speakers 1 vasilis chousionis university of helsinki finland square functions and uniform rectifiability 2 leonardo colzani universita degli studi di milano italy localization and convergence of fourier series and integrals 3 javier duoandikoetxea universidad del pais vasco euskal herriko unibertsitatea spain a comparison of the characterizations of a 4 bruno franchi universita degli studi di bologna italy differential forms in heisenberg groups and div curl systems 5 gustavo garrigos universidad de murcia spain maximal functions weights and convergence to initial data of certain poisson equations 6 jose ma ia martell icmat universidad autonoma de madrid spain the dirichlet problem for elliptic systems in the upper half space 7 alessio martini christian albrechts universitat zu kiel germany hypoelliptic operators and sharp multiplier theorems 8 joan mateu universitat autonoma de barcelona spain euler equation and vortex patches 9 carlos perez universidad de sevilla spain around a conjecture of e sawyer for the hilbert transform and weights 10 ezequiel rela universidad de sevilla spain optimality of weighted estimates without examples

lagrangian relaxation graph matching abstract graph matching is a fundamental problem in computer vision area graph matching problem that incorporates pair wise constraints can be formulated as an integer quadratic programming iqp problem with affine mapping constraint since it is known to be np hard approximate relaxation methods are usually required to find approximate solutions in this paper we present a new effective graph matching relaxation method called lagrangian relaxation graph matching lrgm which aims to generate a relaxation model by incorporating the affine mapping constraint into the matching objective optimization there are three main benefits of the proposed lrgm method 1 the nonnegative affine mapping constraint encoding one to one mapping is naturally incorporated in lrgm relaxation via lagrangian regularization 2 by further adding a l 1 norm constraint lrgm can generate a sparse solution empirically and thus returns a desired discrete solution for original iqp matching problem 3 an effective update algorithm is derived to solve the proposed lrgm model theoretically the converged solution can be proven to be karush kuhn tucker kkt optimal experimental results on both synthetic data and real world image datasets show the effectiveness and benefits of the proposed lrgm method

a harnack inequality approach to the regularity of free boundaries part ii flat free boundaries are lipschitz soit u une solution faible d un probleme aux limites libres du type u 0 sur u 0 et sur u 0 et soit le long de la frontiere libre f la relation u v g u x est satisfaite au sens faible alors si f est proche du graphe d une fonction de lipschitz dans la boule unite b 1 de r n f est le graphe d une fonction de lipschitz dans b 1 2

fast matching of large point sets under occlusions the problem of isometric point pattern matching can be modeled as inference in small tree width graphical models whose embeddings in the plane are said to be globally rigid although such graphical models lead to efficient and exact solutions they cannot generally handle occlusions as even a single missing point may break the rigidity of the graph in question in addition such models can efficiently handle point sets of only moderate size in this paper we propose a new graphical model that is not only adapted to handle occlusions but is much faster than previous approaches for solving the isometric point pattern matching problem we can match point patterns with thousands of points in a few seconds

null sets of harmonic measure on nta domains lipschitz approximation revisited we show the david jerison construction of big pieces of lipschitz graphs inside a corkscrew domain does not require surface measure be upper ahlfors regular thus we can study absolute continuity of harmonic measure and surface measure on nta domains of locally finite perimeter using lipschitz approximations a partial analogue of the f and m riesz theorem for simply connected planar domains is obtained for nta domains in space as one consequence every wolff snowflake has infinite surface measure

convex hull indexed gaussian mixture model ch gmm for 3d point set registration to solve the problem of rigid non rigid 3d point set registration a novel convex hull indexed gaussian mixture model ch gmm is proposed in this paper the model works by computing a weighted gaussian mixture model gmm response over the convex hull of each point set three conditions proximity area conservation and projection consistency are incorporated into the model so as to improve its performance given that the convex hull is the tightest convex set of a point set the combination of gaussian mixture and convex hull can effectively preserve the topological structure of a point set furthermore computational complexity can be significantly reduced since only the gmm of the convex hull instead of the whole point set needs to be calculated rigid registration is achieved by seeking the best rigid transformation parameters yielding the most similar ch gmm responses non rigid deformation is realized by optimizing the coordinates of the control points used by the thin plate spline model for interpolating the entire point set experiments are designed to evaluate a method s robustness to rotational changes between two point sets positional noise differences in density and partial overlap the results demonstrated better robustness and registration accuracy of ch gmm based method over state of the art methods including iterative closest point coherent point drift and the gmm method besides the computation of ch gmm is efficient a novel ch gmm method is proposed for non rigid registration of point sets the ch gmm can effectively present the topological information of point set the ch gmm matching of the point sets is very fast the registration is very robust for points with large differences

potential estimates of superquadratic elliptic systems with vmo coefficients in reifenberg domains abstract the purpose of this paper is to study an inhomogeneous dirichlet problem of a superquadratic nonlinear elliptic system with vmo coefficients in reifenberg flat domains we derive pointwise potential estimates for weak solution to the dirichlet problem as a consequence we derive global integrability estimates for solutions with respect to lorentz and morrey norms

robust feature point matching with sparse model feature point matching that incorporates pairwise constraints can be cast as an integer quadratic programming iqp problem since it is np hard approximate methods are required the optimal solution for iqp matching problem is discrete binary and thus sparse in nature this motivates us to use sparse model for feature point matching problem the main advantage of the proposed sparse feature point matching spm method is that it generates sparse solution and thus naturally imposes the discrete mapping constraints approximately in the optimization process therefore it can optimize the iqp matching problem in an approximate discrete domain in addition an efficient algorithm can be derived to solve spm problem promising experimental results on both synthetic points sets matching and real world image feature sets matching tasks show the effectiveness of the proposed feature point matching method

integrating graph partitioning and matching for trajectory analysis in video surveillance in order to track moving objects in long range against occlusion interruption and background clutter this paper proposes a unified approach for global trajectory analysis instead of the traditional frame by frame tracking our method recovers target trajectories based on a short sequence of video frames e g 15 frames we initially calculate a foreground map at each frame obtained from a state of the art background model an attribute graph is then extracted from the foreground map where the graph vertices are image primitives represented by the composite features with this graph representation we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching the task can be formulated by maximizing a posteriori under the bayesian framework in which we integrate the spatio temporal contexts and the appearance models the probabilistic inference is achieved by a data driven markov chain monte carlo algorithm given a period of observed frames the algorithm simulates an ergodic and aperiodic markov chain and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching in the experiments our method is tested on several challenging videos from the public datasets of visual surveillance and it outperforms the state of the art methods

a pocs based graph matching algorithm a novel projections onto convex sets pocs graph matching algorithm is presented two way assignment constraints are enforced without using elaborate penalty terms graduated nonconvexity or sophisticated annealing mechanisms to escape from poor local minima results indicate that the presented algorithm is robust and compares favorably to other well known algorithms

on an inverse type problem for the heat equation in parabolic regular graph domains in this paper we prove some results concerning inverse free boundary type problems below the continuous threshold for the heat equation in the setting of parabolic regular graph domains

chord arc surfaces with small constant i abstract we introduce a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for curves in the plane we give various equivalent operator theoretic function theoretic and geometrical characterizations of these surfaces we not know any nice potential theoretic characterizations in a companion paper we address the issue of finding good parameterizations for these surfaces

harmonic measure on locally flat domains we will review work with tatiana toro yielding a characterizati on of those domains for which the harmonic measure has a density whose logarithm has vanishing mean oscillation

free boundary regularity for harmonic measures and poisson kernels one of the basic aims of this paper is to study the relationship between the geometry of hypersurface like subsets of euclidean space and the properties of the measures they support in this context we show that certain doubling properties of a measure determine the geometry of its support a radon measure is said to be doubling with constant c if c times the measure of the ball of radius r centered on the support is greater than the measure of the ball of radius 2r and the same center we prove that if the doubling constant of a measure on r n 1 is close to the doubling constant of the ndimensional lebesgue measure then its support is well approximated by ndimensional a ne spaces provided that the support is relatively at to start with primarily we consider sets which are boundaries of domains in r n 1 the n dimensional hausdorfi measure may not be deflned on the boundary of a domain in r n 1 thus we turn our attention to the harmonic measure which is well behaved under minor assumptions see section 3 we obtain a new characterization of locally at domains in terms of the doubling properties of their harmonic measure see section 3 along these lines we investigate how the weak regularity of the poisson kernel of a domain determines the geometry of its boundary sections 5 and 6 pursue this goal as in alt and cafiarelli s work see ac c1 c2 and also jerison s j in both cases the goal is to prove that under the appropriate technical conditions at at points of the boundary the oscillation of the poisson kernel controls the oscillation of the unit normal vector the difierence between our work and the work in ac is that we measure the oscillation in an integral sense bmo estimates

attributed relational graph matching based on the nested assignment structure in this paper we propose a new arg matching scheme based on the nested assignment structure to assess the similarity between two attributed relational graphs args args are represented by nodes and edges containing unary attributes and binary relations between nodes respectively the nested assignment structure consists of inner and outer steps in the inner step to form a distance matrix combinatorial differences between every pair of nodes in two args are computed by using an assignment algorithm then in the outer step a correspondence between nodes in the two args is established by using an assignment algorithm based on the distance matrix the proposed arg matching scheme consists of three procedures as follows first in the initializing procedure the nested assignment structure is performed to generate an initial correspondence between nodes in two args next the correspondence is refined by iteratively performing the updating procedure which also utilizes the nested assignment structure until the correspondence does not change finally the verifying procedure can be performed in case that some nodes to be matched in the two args are missing from experimental results the proposed arg matching scheme shows superior matching performance and localizes target objects robustly and correctly even in severely noisy and occluded scenes

cauchy integrals calderon projectors and toeplitz operators on uniformly rectifiable domains abstract we develop properties of cauchy integrals associated to a general class of first order elliptic systems of differential operators d on a bounded uniformly rectifiable ur domain in a riemannian manifold m we show that associated to such cauchy integrals are analogues of hardy spaces of functions on annihilated by d and we produce projections of calderon type onto subspaces of l p consisting of boundary values of elements of such hardy spaces we consider toeplitz operators associated to such projections and study their index properties of particular interest is a cobordism argument which often enables one to identify the index of a toeplitz operator on a rough ur domain with that of one on a smoothly bounded domain

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

improving shape retrieval by spectral matching and meta similarity we propose two computational approaches for improving the retrieval of planar shapes first we suggest a geometrically motivated quadratic similarity measure that is optimized by way of spectral relaxation of a quadratic assignment by utilizing state of the art shape descriptors and a pairwise serialization constraint we derive a formulation that is resilient to boundary noise articulations and nonrigid deformations this allows both shape matching and retrieval we also introduce a shape meta similarity measure that agglomerates pairwise shape similarities and improves the retrieval accuracy when applied to the mpeg 7 shape dataset in conjunction with the proposed geometric matching scheme we obtained a retrieval rate of 92 5

long time dynamics of highly concentrated solitary waves for the nonlinear schrodinger equation abstract in this paper we study the behavior of solutions of a nonlinear schrodinger equation in presence of an external potential which is allowed to be singular at one point we show that the solution behaves like a solitary wave for long time even if we start from an unstable solitary wave and its dynamics coincides with that of a classical particle evolving according to a natural effective hamiltonian

imposing semi local geometric constraints for accurate correspondences selection in structure from motion a game theoretic perspective most structure from motion pipelines are based on the iterative refinement of an initial batch of feature correspondences typically this is performed by selecting a set of match candidates based on their photometric similarity an initial estimate of camera intrinsic and extrinsic parameters is then computed by minimizing the reprojection error finally outliers in the initial correspondences are filtered by enforcing some global geometric property such as the epipolar constraint in the literature many different approaches have been proposed to deal with each of these three steps but almost invariably they separate the first inlier selection step which is based only on local image properties from the enforcement of global geometric consistency unfortunately these two steps are not independent since outliers can lead to inaccurate parameter estimation or even prevent convergence leading to the well known sensitivity of all filtering approaches to the number of outliers especially in the presence of structured noise which can arise for example when the images present several repeated patterns in this paper we introduce a novel stereo correspondence selection scheme that casts the problem into a game theoretic framework in order to guide the inlier selection towards a consistent subset of correspondences this is done by enforcing geometric constraints that do not depend on full knowledge of the motion parameters but rather on some semi local property that can be estimated from the local appearance of the image features the practical effectiveness of the proposed approach is confirmed by an extensive set of experiments and comparisons with state of the art techniques

square functions nontangential limits and harmonic measure in codimension larger than 1 we characterize the rectifiability both uniform and not of an ahlfors regular set e of arbitrary codimension by the behavior of a regularized distance function in the complement of that set in particular we establish a certain version of the riesz transform characterization of rectifiability for lower dimensional sets we also uncover a special situation in which the regularized distance is itself a solution to a degenerate elliptic operator in the complement of e this allows us to precisely compute the harmonic measure of those sets associated to this degenerate operator and prove that in sharp contrast with the usual setting of codimension 1 a converse to dahlberg s theorem must be false on lower dimensional boundaries without additional assumptions

regularity and free boundary regularity for the p laplace operator in reifenberg flat and ahlfors regular domains regularity and free boundary regularity for the p laplace operator in reifenberg flat and ahlfors regular domains

a path following algorithm for the graph matching problem we propose a convex concave programming approach for the labeled weighted graph matching problem the convex concave programming formulation is obtained by rewriting the weighted graph matching problem as a least square problem on the set of permutation matrices and relaxing it to two different optimization problems a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices the concave relaxation has the same global minimum as the initial graph matching problem but the search for its global minimum is also a hard combinatorial problem we therefore construct an approximation of the concave problem solution by following a solution path of a convex concave problem obtained by linear interpolation of the convex and concave formulations starting from the convex relaxation this method allows to easily integrate the information on graph label similarities into the optimization problem and therefore perform labeled weighted graph matching the algorithm is compared with some of the best performing graph matching methods on four data sets simulated graphs qaplib retina vessel images and handwritten chinese characters in all cases the results are competitive with the state of the art

spectral embedding of graphs in this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern space we adopt a graph spectral approach we use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix for each eigenmode we compute vectors of spectral properties these include the eigenmode perimeter eigenmode volume cheeger number inter mode adjacency matrices and intermode edge distance we embed these vectors in a pattern space using two contrasting approaches the first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors the second approach involves performing multidimensional scaling on the l2 norm for pairs of pattern vectors we illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2d images of 3d polyhedral objects two problems are investigated the first of these is the clustering of graphs representing distinct objects viewed from different directions the second is the identification of characteristic views of single objects these two studies reveal that both embedding methods result in well structured view spaces for graph data extracted from 2d views of 3d objects

the hele shaw problem as a mesa limit of stefan problems existence uniqueness and regularity of the free boundary we study a hele shaw problem with a mushy region obtained as a mesa type limit of one phase stefan problems in exterior domains we deal with both neumann and dirichlet data and show pointwise convergence of the stefan solutions to the hele shaw solution we make no assumptions on the geometry topology or connectivity of the injection slot

global estimates for quasilinear elliptic equations on reifenberg flat domains new global regularity estimates are obtained for solutions to a class of quasilinear elliptic boundary value problems the coefficients are assumed to have small bmo seminorms and the boundary of the domain is sufficiently flat in the sense of reifenberg the main regularity estimates obtained are in weighted lorentz spaces other regularity results in lorentz morrey morrey and holder spaces are shown to follow from the main estimates

a parabolic free boundary problem with bernoulli type condition on the free boundary consider the parabolic free boundary problem u t u 0 in u 0 u 1 on u 0 for a realistic class of solutions containing for example all limits of the singular perturbation problem ue t ue e ue as e 0 we prove that one sided flatness of the free boundary implies regularity in particular we show that the topological free boundary u 0 can be decomposed into an open regular set relative to u 0 which is locally a surface with holder continuous space normal and a closed singular set our result extends the main theorem in the paper by h w alt l a caffarelli 1981 to more general solutions as well as the time dependent case our proof uses methods developed in h w alt l a caffarelli 1981 however we replace the core of that paper which relies on non positive mean curvature at singular points by an argument based on scaling discrepancies which promises to be applicable to more general free boundary or free discontinuity problems