an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

map estimation via agreement on trees message passing and linear programming we develop and analyze methods for computing provably optimal maximum a posteriori probability map configurations for a subclass of markov random fields defined on graphs with cycles by decomposing the original distribution into a convex combination of tree structured distributions we obtain an upper bound on the optimal value of the original problem i e the log probability of the map assignment in terms of the combined optimal values of the tree problems we prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common an important implication is that any such shared configuration must also be a map configuration for the original distribution next we develop two approaches to attempting to obtain tight upper bounds a a tree relaxed linear program lp which is derived from the lagrangian dual of the upper bounds and b a tree reweighted max product message passing algorithm that is related to but distinct from the max product algorithm in this way we establish a connection between a certain lp relaxation of the mode finding problem and a reweighted form of the max product min sum message passing algorithm

efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

stereo without epipolar lines a maximum flow formulation this paper describes a new algorithm for solving the stereo correspondence problem with a global 2 d optimization by transforming it into a maximum flow problem in a graph this transformation effectively removes explicit use of epipolar geometry thus allowing direct use of multiple cameras with arbitrary geometries the maximum flow solved both efficiently and globally yields a minimum cut that corresponds to a disparity surface for the whole image at once this global and efficient approach to stereo analysis allows the reconstruction to proceed in an arbitrary volume of space and provides a more accurate and coherent depth map than the traditional stereo algorithms in particular smoothness is applied uniformly instead of only along epipolar lines while the global optimality of the depth surface is guaranteed results show improved depth estimation as well as better handling of depth discontinuities while the worst case running time is o n 1 5 d 1 5 log nd the observed average running time is o n 1 2 d 1 3 for an image size of n pixels and depth resolution d

linear rank tests for interval censored data with application to pcb levels in adipose tissue of transformer repair workers linear rank statistics are described for testing for differences between groups when the data are interval censored the statistics are closely related to those described by prentice for right censored data problems in calculating the statistics are discussed and several approaches to computation including estimation of the efficient rank scores are described results from a small simulation study are presented the methods are applied to data from a study relating tissue levels of pcbs to occupational exposure

tree approximations to markov random fields methods for approximately computing the marginal probability mass functions and means of a markov random field mrf by approximating the lattice by a tree are described applied to the a posteriori mrf these methods solve bayesian spatial pattern classification and image restoration problems the methods are described several theoretical results concerning fixed point problems are proven and four numerical examples are presented including comparison with optimal estimators and the iterated conditional mode estimator and including two agricultural optical remote sensing problems

the piecewise smooth mumford shah functional on an arbitrary graph the mumford shah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and despite being introduced over two decades ago it is still in widespread use present day optimization of the mumford shah functional is predominated by active contour methods until recently these formulations necessitated optimization of the contour by evolving via gradient descent which is known for its overdependence on initialization and the tendency to produce undesirable local minima in order to reduce these problems we reformulate the corresponding mumford shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast low energy solution in contrast to traditional optimization methods use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary requiring additionally the inclusion of regularization for generating these values the energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descent based narrow band level set methods this comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time finally we demonstrate the usefulness of the graph formulation to apply the mumford shah functional to new applications such as point clustering and filtering of nonuniformly sampled images

structured prediction dual extragradient and bregman projections we present a simple and scalable algorithm for maximum margin estimation of structured output models including an important class of markov networks and combinatorial models we formulate the estimation problem as a convex concave saddle point problem that allows us to use simple projection methods based on the dual extragradient algorithm nesterov 2003 the projection step can be solved using dynamic programming or combinatorial algorithms for min cost convex flow depending on the structure of the problem we show that this approach provides a memory efficient alternative to formulations based on reductions to a quadratic program qp we analyze the convergence of the method and present experiments on two very different structured prediction tasks 3d image segmentation and word alignment illustrating the favorable scaling properties of our algorithm

a semiparametric proportional odds regression model for the analysis of current status data abstract an approach to covariate analysis of current status data is described the method is applicable when the logit of the conditional probability of survival given the covariates is some increasing function of time plus a linear combination of the covariates the approach is based on approximating the infinite dimensional nuisance parameter the baseline log odds of failure with a step function and carrying out a maximum likelihood procedure the resulting finite dimensional parameter estimates for the regression parameters are shown to be asymptotically normal and semiparametric efficient numerical studies with small and moderate samples are discussed

enhancing multiple point geostatistical modeling 1 graph theory and pattern adjustment in recent years higher order geostatistical methods have been used for modeling of a wide variety of large scale porous media such as groundwater aquifers and oil reservoirs their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard quantitative data which endow them with the capability for generating realistic realizations of porous formations with very complex channels as well as features that are mainly a barrier to fluid flow one group of such models consists of pattern based methods that use a set of data points for generating stochastic realizations by which the large scale structure and highly connected features are reproduced accurately the cross correlation based simulation ccsim algorithm proposed previously by the authors is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few cpu seconds the method is however sensitive to pattern s specifications such as boundaries and the number of replicates in this paper the original ccsim algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large scale patterns of heterogeneities in porous media first an effective boundary correction method based on the graph theory is presented by which one identifies the optimal cutting path surface for removing the patchiness and discontinuities in the realization of a porous medium next a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns the original ccsim algorithm is then combined with the two methods and is tested using various complex two and three dimensional examples it should however be emphasized that the methods that we propose in this paper are applicable to other pattern based geostatistical simulation methods

global minimization for continuous multiphase partitioning problems using a dual approach this paper is devoted to the optimization problem of continuous multi partitioning or multi labeling which is based on a convex relaxation of the continuous potts model in contrast to previous efforts which are tackling the optimal labeling problem in a direct manner we first propose a novel dual model and then build up a corresponding duality based approach by analyzing the dual formulation sufficient conditions are derived which show that the relaxation is often exact i e there exists optimal solutions that are also globally optimal to the original nonconvex potts model in order to deal with the nonsmooth dual problem we develop a smoothing method based on the log sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal dual model and suggests labelings with maximum entropy such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions an expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization numerical experiments also show that our method outperforms several competitive approaches in various aspects such as lower energies and better visual quality

inference based on imputed failure times for the proportional hazards model with interval censored data abstract we propose an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations that are the partial likelihood score equations for the full data proportional hazards model averaged over all rankings of imputed failure times consistent with the observed censoring intervals imputed failure times are generated using a parametric estimate of the baseline distribution the parameters of the baseline distribution are estimated simultaneously with the proportional hazards regression parameters although a parametric form for the baseline distribution must be specified simulation studies show that the method performs well even when the baseline distribution is misspecified the estimating equations are solved using monte carlo techniques we present a recursive stochastic approximation scheme that converges to the zero of the estimating equations the solution has a random error that is asymptotically normally distributed w

regression with interval censored data summary interval censored data result when survival times are not known exactly but are only known to have occurred between intermittent examination times here the accelerated failure time model is treated for interval censored data a class of score statistics that may be used for estimation and confidence procedures is proposed an adaptive procedure based on estimating the optimal member of the class of score statistics is explored

regression analysis of failure time data with informative interval censoring interval censoring arises when a subject misses prescheduled visits at which the failure is to be assessed most existing approaches for analysing interval censored failure time data assume that the censoring mechanism is independent of the true failure time however there are situations where this assumption may not hold in this paper we consider such a situation in which the dependence structure between the censoring variables and the failure time can be modelled through some latent variables and a method for regression analysis of failure time data is proposed the method makes use of the proportional hazards frailty model and an em algorithm is presented for estimation finite sample properties of the proposed estimators of regression parameters are examined through simulation studies and we illustrate the method with data from an aids study

rank invariant tests for interval censored data under the grouped continuous model this paper creates rank invariant score tests for grouped or interval censored data this generalizes finkelstein 1986 biometrics 42 845 854 who derived score tests for interval censored data assuming proportional hazards we frame the problem as a linear rank test of a shift in location with a known error distribution we discuss adjustments to the test that may be required when the number of observation times is large we offer a graphical test of the assumption of the location shift model and discuss an alternative interpretation of the test using the logistic error when the location shift assumption does not hold

dynamic graph cuts for efficient inference in markov random fields in this paper we present a fast new fully dynamic algorithm for the st mincut max flow problem we show how this algorithm can be used to efficiently compute map solutions for certain dynamically changing mrf models in computer vision such as image segmentation specifically given the solution of the max flow problem on a graph the dynamic algorithm efficiently computes the maximum flow in a modified version of the graph the time taken by it is roughly proportional to the total amount of change in the edge weights of the graph our experiments show that when the number of changes in the graph is small the dynamic algorithm is significantly faster than the best known static graph cut algorithm we test the performance of our algorithm on one particular problem the object background segmentation problem for video it should be noted that the application of our algorithm is not limited to the above problem the algorithm is generic and can be used to yield similar improvements in many other cases that involve dynamic change

penalized log likelihood estimation for partly linear transformation models with current status data we consider partly linear transformation models applied to current status data the unknown quantities are the transformation function a linear regression parameter and a nonparametric regression effect it is shown that the penalized mle for the regression parameter is asymptotically normal and efficient and converges at the parametric rate although the penalized mle for the transformation function and nonparametric regression effect are only n 1 3 consistent inference for the regression parameter based on a block jack knife is investigated we also study computational issues and demonstrate the proposed methodology with a simulation study the transformation models and partly linear regression terms coupled with new estimation and inference techniques provide flexible alternatives to the cox model for current status data analysis

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

computationally simple accelerated failure time regression for interval censored data summary an approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals the approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals the dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients the approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred simulations are presented to assess the behaviour of the approach and the methodology is illustrated through an application to data from an aids clinical trial

quantum α determinant cyclic modules of uq gln abstract as a particular one parameter deformation of the quantum determinant we introduce a quantum determinant det q and study the u q gl n cyclic module generated by it we show that the multiplicity of each irreducible representation in this cyclic module is determined by a certain polynomial called the q content discriminant a part of the present result is a quantum counterpart for the result of matsumoto and wakayama s matsumoto m wakayama alpha determinant cyclic modules of gl n c j lie theory 16 2006 393 405 however a new distinguished feature arises in our situation specifically we determine the degeneration of the multiplicities for classical singular points and give a general conjecture for singular points involving semi classical and quantum singularities moreover we introduce a quantum permanent per q and establish another conjecture which describes a reciprocity between the multiplicities of the irreducible summands of the cyclic modules generated respectively by det q and per q

parametric maximum flow algorithms for fast total variation minimization this report studies the global minimization of anisotropically discretized total variation tv energies with an l p in particular l 1 and l 2 fidelity term using parametric maximum flow algorithms to minimize s t cut representations of these energies the tv l 2 model also known as the rudin osher fatemi rof model is suitable for restoring images contaminated by gaussian noise while the tv l 1 model is able to remove impulsive noise from grayscale images and perform multiscale decompositions of them preliminary numerical results on large scale two dimensional ct and three dimensional brain mr images are presented to illustrate the effectiveness of these approaches

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

lagrangian based methods for finding map solutions for mrf models finding maximum a posteriori map solutions from noisy images based on a prior markov random field mrf model is a huge computational task in this paper we transform the computational problem into an integer linear programming ilp problem we explore the use of lagrange relaxation lr methods for solving the map problem in particular three different algorithms based on lr are presented all the methods are competitive alternatives to the commonly used simulation based algorithms based on markov chain monte carlo techniques in all the examples including both simulated and real images that have been tested the best method essentially finds a map solution in a small number of iterations in addition lr methods provide lower and upper bounds for the posterior which makes it possible to evaluate the quality of solutions and to construct a stopping criterion for the algorithm although additive gaussian noise models have been applied any additive noise model fits into the framework

an efficient algorithm for image segmentation markov random fields and related problems problems of statistical inference involve the adjustment of sample observations so they fit some a priori rank requirements or order constraints in such problems the objective is to minimize the deviation cost function that depends on the distance between the observed value and the modify value in markov random field problems there is also a pairwise relationship between the objects the objective in markov random field problem is to minimize the sum of the deviation cost function and a penalty function that grows with the distance between the values of related pairs separation function we discuss markov random fields problems in the context of a representative application the image segmentation problem in this problem the goal is to modify color shades assigned to pixels of an image so that the penalty function consisting of one term due to the deviation from the initial color shade and a second term that penalizes differences in assigned values to neighboring pixels is minimized we present here an algorithm that solves the problem in polynomial time when the deviation function is convex and separation function is linear and in strongly polynomial time when the deviation cost function is linear quadratic or piecewise linear convex with few pieces where few means a number exponential in a polynomial function of the number of variables and constraints the complexity of the algorithm for a problem on n pixels or variables m adjacency relations or constraints and range of variable values colors u is o t n m n log u where t n m is the complexity of solving the minimum s t cut problem on a graph with n nodes and m arcs furthermore other algorithms are shown to solve the problem with convex deviation and convex separation in running time o mn log n log nu and the problem with nonconvex deviation and convex separation in running time o t nu mu the nonconvex separation problem is np hard even for fixed value of u for the family of problems with convex deviation functions and linear separation function the algorithm described here runs in polynomial time which is demonstrated to be fastest possible

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a sequence based extension of mean field annealing using the forward backward algorithm application to image segmentation optimization based on mean field theory including mean field annealing mfa is widely used for discrete optimization label assignment problems defined on the pixel sites of an image one formulation of mfa is via maximum entropy where one seeks the joint distribution over the random assignments subject to an average level of cost mfa is obtained by assuming the assignments at each pixel are statistically independent given the observed image alternatively we make the less restrictive assumption of independent row labelings the independence assumption means that at each step mfa optimizes over only one pixel whereas our method jointly optimizes over an entire row i e our method is less greedy in principle an mfa extension could be developed that explicitly re estimates the row labeling distributions but such an approach is in practice infeasible even so we can indirectly implement this re estimation by re estimating quantities that determine the row labeling distributions these quantities are the a posteriori site probabilities re estimable via the well known forward backward f b algorithm thus our algorithm which descends in the me lagrangian free energy consists of iterative application of f b to the image rows columns at convergence maximum a posteriori site labeling is performed our method was applied to segmentation of both real and synthetic noise corrupted images it achieved lower markov random field model potentials and better segmentations compared with other methods and in high noise standard mfa

a linear framework for region based image segmentation and inpainting involving curvature penalization we present the first method to handle curvature regularity in region based image segmentation and inpainting that is independent of initialization to this end we start from a new formulation of length based optimization schemes based on surface continuation constraints and discuss the connections to existing schemes the formulation is based on a cell complex and considers basic regions and boundary elements the corresponding optimization problem is cast as an integer linear program we then show how the method can be extended to include curvature regularity again cast as an integer linear program here we are considering pairs of boundary elements to reflect curvature moreover a constraint set is derived to ensure that the boundary variables indeed reflect the boundary of the regions described by the region variables we show that by solving the linear programming relaxation one gets reasonably close to the global optimum and that curvature regularity is indeed much better suited in the presence of long and thin objects compared to standard length regularity

semiparametric estimation of the accelerated failure time model with partly interval censored data summary partly interval censored pic data arise when some failure times are exactly observed while others are only known to lie within certain intervals in this article we consider efficient semiparametric estimation of the accelerated failure time aft model with pic data we first generalize the buckley james estimator for right censored data to pic data then we develop a one step estimator by deriving and estimating the efficient score for the regression parameters we show that under mild regularity conditions the generalized buckley james estimator is consistent and asymptotically normal and the one step estimator is consistent and asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound we conduct extensive simulation studies to examine the performance of the proposed estimators in finite samples and apply our methods to data derived from an aids study

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

power watershed a unifying graph based optimization framework in this work we extend a common framework for graph based image segmentation that includes the graph cuts random walker and shortest path optimization algorithms viewing an image as a weighted graph these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework we then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm which we term the power watershed in particular when q 2 the power watershed leads to a multilabel scale and contrast invariant unique global optimum obtained in practice in quasi linear time placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation

bayesian modeling of dynamic scenes for object detection accurate detection of moving objects is an important precursor to stable tracking or recognition in this paper we present an object detection scheme that has three innovations over existing approaches first the model of the intensities of image pixels as independent random variables is challenged and it is asserted that useful correlation exists in intensities of spatially proximal pixels this correlation is exploited to sustain high levels of detection accuracy in the presence of dynamic backgrounds by using a nonparametric density estimation method over a joint domain range representation of image pixels multimodal spatial uncertainties and complex dependencies between the domain location and range color are directly modeled we propose a model of the background as a single probability density second temporal persistence is proposed as a detection criterion unlike previous approaches to object detection which detect objects by building adaptive models of the background the foregrounds modeled to augment the detection of objects without explicit tracking since objects detected in the preceding frame contain substantial evidence for detection in the current frame finally the background and foreground models are used competitively in a map mrf decision framework stressing spatial context as a condition of detecting interesting objects and the posterior function is maximized efficiently by finding the minimum cut of a capacitated graph experimental validation of the proposed method is performed and presented on a diverse set of dynamic scenes

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

large scale integer programs in image analysis an important problem in image analysis is to segment an image into regions with different class labels this is relevant in applications in medicine and cartography in a proper statistical framework this problem may be viewed as a discrete optimization problem we present two integer linear programming formulations of the problem and study some properties of these models and associated polytopes different algorithms for solving these problems are suggested and compared on some realistic data in particular a lagrangian algorithm is shown to have a very promising performance the algorithm is based on the technique of cost splitting and uses the fact that certain relaxed problems may be solved as shortest path problems

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

sar image regularization with fast approximate discrete minimization synthetic aperture radar sar images like other coherent imaging modalities suffer from speckle noise the presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms numerous approaches have been proposed to filter speckle noise markov random field mrf modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image in this context total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges speckle noise follows heavy tailed distributions and the mrf formulation leads to a minimization problem involving nonconvex log likelihood terms such a minimization can be performed efficiently by computing minimum cuts on weighted graphs due to memory constraints exact minimization although theoretically possible is not achievable on large images required by remote sensing applications the computational burden of the state of the art algorithm for approximate minimization namely the alpha expansion is too heavy specially when considering joint regularization of several images we show that a satisfying solution can be reached in few iterations by performing a graph cut based combinatorial exploration of large trial moves this algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area sar images

self validated labeling of markov random fields for image segmentation this paper addresses the problem of self validated labeling of markov random fields mrfs namely to optimize an mrf with unknown number of labels we present graduated graph cuts ggc a new technique that extends the binary s t graph cut for self validated labeling specifically we use the split and merge strategy to decompose the complex problem to a series of tractable subproblems in terms of gibbs energy minimization a suboptimal labeling is gradually obtained based upon a set of cluster level operations by using different optimization structures we propose three practical algorithms tree structured graph cuts tsgc net structured graph cuts nsgc and hierarchical graph cuts hgc in contrast to previous methods the proposed algorithms can automatically determine the number of labels properly balance the labeling accuracy spatial coherence and the labeling cost i e the number of labels and are computationally efficient independent to initialization and able to converge to good local minima of the objective energy function we apply the proposed algorithms to natural image segmentation experimental results show that our algorithms produce generally feasible segmentations for benchmark data sets and outperform alternative methods in terms of robustness to noise speed and preservation of soft boundaries

analysis of clustered interval censored data using a class of semiparametric partly linear frailty transformation models a flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval censored data which arise naturally in complex diseases and dental research this class of models features two nonparametric components resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate the dependence among failure times within a cluster is induced by a shared unobserved frailty term a sieve maximum likelihood estimation method based on piecewise linear functions is proposed the proposed estimators of the regression dependence and transformation parameters are shown to be strongly consistent and asymptotically normal whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence an extensive simulation study is conducted to study the finite sample performance of the proposed estimators we provide an application to a dental study for illustration

a semiparametric regression cure model for interval censored data motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring we present a semiparametric nonmixture cure model for the regression analysis of interval censored time to event data we develop semiparametric maximum likelihood estimation for the model using the expectation maximization method for interval censored data the maximization step for the baseline function is nonparametric and numerically challenging we develop an efficient and numerically stable algorithm via modern convex optimization techniques yielding a self consistency algorithm for the maximization step we prove the strong consistency of the maximum likelihood estimators under the hellinger distance which is an appropriate metric for the asymptotic property of the estimators for interval censored data we assess the performance of the estimators in a simulation study with small to moderate sample sizes to illustrate the method we also analyze a real dataset

continuous global optimization in multiview 3d reconstruction in this article we introduce a new global optimization method to the field of multiview 3d reconstruction while global minimization has been proposed in a discrete formulation in form of the maxflow mincut framework we suggest the use of a continuous convex relaxation scheme specifically we propose to cast the problem of 3d shape reconstruction as one of minimizing a spatially continuous convex functional in qualitative and quantitative evaluation we demonstrate several advantages of the proposed continuous formulation over the discrete graph cut solution firstly geometric properties such as weighted boundary length and surface area are represented in a numerically consistent manner the continuous convex relaxation assures that the algorithm does not suffer from metrication errors in the sense that the reconstruction converges to the continuous solution as the spatial resolution is increased moreover memory requirements are reduced allowing for globally optimal reconstructions at higher resolutions we study three different energy models for multiview reconstruction which are based on a common variational template unifying regional volumetric terms and on surface photoconsistency the three models use data measurements at increasing levels of sophistication while the first two approaches are based on a classical silhouette based volume subdivision the third one relies on stereo information to define regional costs furthermore this scheme is exploited to compute a precise photoconsistency measure as opposed to the classical estimation all three models are compared on standard data sets demonstrating their advantages and shortcomings for the third one which gives the most accurate results a more exhaustive qualitative and quantitative evaluation is presented

dinkelbach ncut an efficient framework for solving normalized cuts problems with priors and convex constraints in this paper we propose a novel framework called dinkelbach ncut dncut which efficiently solves the normalized graph cut ncut problem under general convex constraints as well as under given priors on the nodes of the graph current ncut methods use generalized eigen decomposition which poses computational issues especially for large graphs and can only handle linear equality constraints by using an augmented graph and the iterative dinkelbach method for fractional programming fp we formulate the dncut framework to efficiently solve the ncut problem under general convex constraints and given data priors in this framework the initial problem is converted into a sequence of simpler sub problems i e convex quadratic programs qp s subject to convex constraints the complexity of finding a global solution for each sub problem depends on the complexity of the constraints the convexity of the cost function and the chosen initialization however we derive an initialization which guarantees that each sub problem is a convex qp that can be solved by available convex programming techniques we apply this framework to the special case of linear constraints where the solution is obtained by solving a sequence of sparse linear systems using the conjugate gradient method we validate dncut by performing binary segmentation on real images both with and without linear nonlinear constraints as well as multi class segmentation when possible we compare dncut to other ncut methods in terms of segmentation performance and computational efficiency even though the new formulation is applied to the problem of spectral graph based low level image segmentation it can be directly applied to other applications e g clustering

shortest path constraints for 3d multiobject semiautomatic segmentation via clustering and graph cut we derive shortest path constraints from graph models of structure adjacency relations and introduce them in a joint centroidal voronoi image clustering and graph cut multiobject semiautomatic segmentation framework the vicinity prior model thus defined is a piecewise constant model incurring multiple levels of penalization capturing the spatial configuration of structures in multiobject segmentation qualitative and quantitative analyses and comparison with a potts prior based approach and our previous contribution on synthetic simulated and real medical images show that the vicinity prior allows for the correct segmentation of distinct structures having identical intensity profiles and improves the precision of segmentation boundary placement while being fairly robust to clustering resolution the clustering approach we take to simplify images prior to segmentation strikes a good balance between boundary adaptivity and cluster compactness criteria furthermore allowing to control the trade off compared with a direct application of segmentation on voxels the clustering step improves the overall runtime and memory footprint of the segmentation process up to an order of magnitude without compromising the quality of the result

on the accelerated failure time model for current status and interval censored data and tianxi cai this paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time model for current status and interval censored data the estimator is constructed by inverting a wald type test for testing a null proportional hazards model a numerically efficient markov chain monte carlo based resampling method is proposed for obtaining simultaneously the point estimator and a consistent estimator of its variance covariance matrix we illustrate our approach with interval censored datasets from two clinical studies extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators

generalized flows for optimal inference in higher order mrf map use of higher order clique potentials in mrf map problems has been limited primarily because of the inefficiencies of the existing algorithmic schemes we propose a new combinatorial algorithm for computing optimal solutions to 2 label mrf map problems with higher order clique potentials the algorithm runs in time o 2 kn 3 in the worst case k is size of clique and n is the number of pixels a special gadget is introduced to model flows in a higher order clique and a technique for building a flow graph is specified based on the primal dual structure of the optimization problem the notions of the capacity of an edge and a cut are generalized to define a flow problem we show that in this flow graph when the clique potentials are submodular the max flow is equal to the min cut which also is the optimal solution to the problem we show experimentally that our algorithm provides significantly better solutions in practice and is hundreds of times faster than solution schemes like dual decomposition 1 trws 2 and reduction 3 4 5 the framework represents a significant advance in handling higher order problems making optimal inference practical for medium sized cliques

fast approximate maximum a posteriori restoration of multicolour images we propose a new algorithm for the approximation of the maximum a posteriori map restoration of noisy images the image restoration problem is considered in a bayesian setting we assume as prior distribution multicolour markov random fields on a graph whose main restriction is the presence of only pairwise site interactions the noise is modelled as a bernoulli field computing the mode of the posterior distribution is np complete i e can very likely be done only in a time exponential in the number of sites of the underlying graph our algorithm runs in polynomial time and is based on the coding of the colours it produces an image with the following property either a pixel is coloured with one of the possible colours or it is left blank in the first case we prove that this is the colour of the site in the exact map restoration the quality of the approximation is then measured by the number of sites being left blank we assess the performance of the new algorithm by numerical experiments on the simple three colour potts model more rigorously we present a probabilistic analysis of the algorithm the results indicate that the approximation is quite often sufficiently good for the interpretation of the image

smooth semiparametric regression analysis for arbitrarily censored time to event data a general framework for regression analysis of time to event data subject to arbitrary patterns of censoring is proposed the approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models such as the baseline hazard function in the proportional hazards model have densities satisfying mild smoothness conditions densities are approximated by a truncated series expansion that for fixed degree of truncation results in a parametric representation which makes likelihood based inference coupled with adaptive choice of the degree of truncation and hence flexibility of the model computationally and conceptually straightforward with data subject to any pattern of censoring the formulation allows popular models such as the proportional hazards proportional odds and accelerated failure time models to be placed in a common framework provides a principled basis for choosing among them and renders useful extensions of the models straightforward the utility and performance of the methods are demonstrated via simulations and by application to data from time to event studies

exact solution to median surface problem using 3d graph search and application to parameter space exploration in this paper we propose the generalized median surface problem and present an exact solution by applying a 3d graph search algorithm to our knowledge this is a novel class of median computation problem which has not been considered before in the literature in addition to the theoretic interest in median surface computation we also demonstrate its practical value by means of the task of parameter space exploration without ground truth which is an effective means of dealing with the difficult parameter selection problem for image segmentation we present a concrete application for artery boundary detection in sonography ultrasound imaging it will be shown that the median computation can not only avoid the parameter training but also potentially achieve results comparable with trained parameters the median based approach can thus be a good alternate particularly in situations with no ground truth available highlightsthis paper proposes the median surface problem an optimal graph search algorithm is applied to solve the problem efficiently experimental work is conducted to demonstrate its usability it can potentially be used for segmentation parameter exploration

semiparametric bayes proportional odds models for current status data with underreporting current status data are a type of interval censored event time data in which all the individuals are either left or right censored for example our motivation is drawn from a cross sectional study which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman we propose a semiparametric bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure the proposed approach has the advantage of being straightforward to implement using a simple and efficient gibbs sampler whereas alternative semiparametric bayes event time models encounter problems for current status data the model is generalized to allow systematic underreporting in a subset of the data and the methods are applied to an epidemiologic study of uterine fibroids

a dual decomposition approach to feature correspondence in this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion such as points extracted from images of different instances of the same object category we formulate this matching task as an energy minimization problem by defining an elaborate objective function of the appearance and the spatial arrangement of the features optimization of this energy is an instance of graph matching which is in general an np hard problem we describe a novel graph matching optimization technique which we refer to as dual decomposition dd and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms in the majority of our examples dd is able to find the global minimum within a minute the ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples we show on several matching tasks that our learned model yields results superior to those of state of the art methods

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

bittracker a bitmap tracker for visual tracking under very general conditions this paper addresses the problem of visual tracking under very general conditions a possibly non rigid target whose appearance may drastically change over time general camera motion a 3d scene and no a priori information except initialization this is in contrast to the vast majority of trackers which rely on some limited model in which for example the target s appearance is known a priori or restricted the scene is planar or a pan tilt zoom camera is used their goal is to achieve speed and robustness but their limited context may cause them to fail in the more general case the proposed tracker works by approximating in each frame a pdf probability distribution function of the target s bitmap and then estimating the maximum a posteriori bitmap the pdf is marginalized over all possible motions per pixel thus avoiding the stage in which optical flow is determined this is an advantage over other general context trackers that do not use the motion cue at all or rely on the error prone calculation of optical flow using a gibbs distribution with respect to the first order neighborhood system yields a bitmap pdf whose maximization may be transformed into that of a quadratic pseudo boolean function the maximum of which is approximated via a reduction to a maximum flow problem many experiments were conducted to demonstrate that the tracker is able to track under the aforementioned general context

pseudo and conditional score approach to joint analysis of current count and current status data we develop a joint analysis approach for recurrent and nonrecurrent event processes subject to case i interval censorship which are also known in literature as current count and current status data respectively we use a shared frailty to link the recurrent and nonrecurrent event processes while leaving the distribution of the frailty fully unspecified conditional on the frailty the recurrent event is assumed to follow a nonhomogeneous poisson process and the mean function of the recurrent event and the survival function of the nonrecurrent event are assumed to follow some general form of semiparametric transformation models estimation of the models is based on the pseudo likelihood and the conditional score techniques the resulting estimators for the regression parameters and the unspecified baseline functions are shown to be consistent with rates of square and cubic roots of the sample size respectively asymptotic normality with closed form asymptotic variance is derived for the estimator of the regression parameters we apply the proposed method to a fracture osteoporosis survey data to identify risk factors jointly for fracture and osteoporosis in elders while accounting for association between the two events within a subject

message passing for graph structured linear programs proximal methods and rounding schemes the problem of computing a maximum a posteriori map configuration is a central computational challenge associated with markov random fields there has been some focus on tree based linear programming lp relaxations for the map problem this paper develops a family of super linearly convergent algorithms for solving these lps based on proximal minimization schemes using bregman divergences as with standard message passing on graphs the algorithms are distributed and exploit the underlying graphical structure and so scale well to large problems our algorithms have a double loop character with the outer loop corresponding to the proximal sequence and an inner loop of cyclic bregman projections used to compute each proximal update we establish convergence guarantees for our algorithms and illustrate their performance via some simulations we also develop two classes of rounding schemes deterministic and randomized for obtaining integral configurations from the lp solutions our deterministic rounding schemes use a re parameterization property of our algorithms so that when the lp solution is integral the map solution can be obtained even before the lp solver converges to the optimum we also propose graph structured randomized rounding schemes applicable to iterative lp solving algorithms in general we analyze the performance of and report simulations comparing these rounding schemes

a new lagrangian relaxation approach to the generalized assignment problem abstract in this paper we present a new lagrangian relaxation approach to the generalized assignment problem gap the new approach is based on a reformulation of gap into an equivalent problem which is then relaxed by traditional lagrangian relaxation techniques the reformulation is created by introducing a set of auxiliary variables and a number of coupling constraints by relaxing the coupling constraints we get subproblems where both types of constraint structures present in the gap are active the lower bound from the lagrangian dual of this approach is shown to be at least as strong as that from the best of the traditional lagrangian relaxation approaches an important feature is also the possibility of generating upper bounds quite easily the new approach has been tested on 10 problems of size m 4 n 25 i e 100 0 1 variables and the results have been compared with the traditional approaches

approximation algorithms for classification problems with pairwise relationships metric labeling and markov random fields in a traditional classification problem we wish to assign one of k labels or classes to each of n objects in a way that is consistent with some observed data that we have about the problem an active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified this issue is one of the principal motivations for the framework of markov random fields and it arises in areas such as image processing biometry and document analysis in its most basic form this style of analysis seeks to find a classification that optimizes a combinatorial function consisting of assignment costs based on the individual choice of label we make for each object and separation costs based on the pair of choices we make for two related objects we formulate a general classification problem of this type the metric labeling problem we show that it contains as special cases a number of standard classification frameworks including several arising from the theory of markov random fields from the perspective of combinatorial optimization our problem can be viewed as a substantial generalization of the multiway cut problem and equivalent to a type of uncapacitated quadratic assignment problem we provide the first nontrivial polynomial time approximation algorithms for a general family of classification problems of this type our main result is an o log k log log k approximation algorithm for the metric labeling problem with respect to an arbitrary metric on a set of k labels and an arbitrary weighted graph of relationships on a set of objects for the special case in which the labels are endowed with the uniform metric all distances are the same our methods provide a 2 approximation algorithm

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

alpha determinant cyclic modules and jacobi polynomials for positive integers n and l we study the cyclic u gl n module generated by the l th power of the determinant det x this cyclic module is isomorphic to the n th tensor space s l n n of the symmetric l th tensor space of n for all but finitely many exceptional values of if is exceptional then the cyclic module is equivalent to a proper submodule of s l n n i e the multiplicities of several irreducible subrepresentations in the cyclic module are smaller than those in s l n n the degeneration of each isotypic component of the cyclic module is described by a matrix whose size is given by a kostka number and whose entries are polynomials in with rational coefficients in particular we determine the matrix completely when n 2 in this case the matrix becomes a scalar and is essentially given by a classical jacobi polynomial moreover we prove that these polynomials are unitary in the appendix we consider a variation of the spherical fourier transformation for o nl o n l as a main tool for analyzing the same problems and describe the case where n 2 by using the zonal spherical functions of the gelfand pair o 2l o 2 l

interactively multiphase image segmentation based on variational formulation and graph cuts in this paper the multiple piecewise constant mpc active contour model is extended to deal with multiphase case this proposed multiphase model can be effectively optimized by solving the minimum cuts problem of a specially devised multilayer graph based on the proposed energy functional and its graph cuts optimization an interactively multiphase partition method for image segmentation is presented the user places some scribbles with different colors on the image according to the practical application demand and each group of scribbles with the same color corresponds to a potential image region the distribution of each region can be learned from the input scribbles with some particular color then the corresponding multilayer graph can be constructed and its minimum cuts can be computed to determine the segmentation result of the image numerical experiments show that the proposed interactively multiphase segmentation method can accurately segment the image into different regions according to the input scribbles with different color

pm pm patchmatch with potts model for object segmentation and stereo matching this paper presents a unified variational formulation for joint object segmentation and stereo matching which takes both accuracy and efficiency into account in our approach depth map consists of compact objects each object is represented through three different aspects 1 the perimeter in image space 2 the slanted object depth plane and 3 the planar bias which is to add an additional level of detail on top of each object plane in order to model depth variations within an object compared with traditional high quality solving methods in low level we use a convex formulation of the multilabel potts model with patchmatch stereo techniques to generate depth map at each image in object level and show that accurate multiple view reconstruction can be achieved with our formulation by means of induced homography without discretization or staircasing artifacts our model is formulated as an energy minimization that is optimized via a fast primal dual algorithm which can handle several hundred object depth segments efficiently performance evaluations in the middlebury benchmark data sets show that our method outperforms the traditional integer valued disparity strategy as well as the original patchmatch algorithm and its variants in subpixel accurate disparity estimation the proposed algorithm is also evaluated and shown to produce consistently good results for various real world data sets kitti benchmark data sets and multiview benchmark data sets

minimization of monotonically levelable higher order mrf energies via graph cuts a feature of minimizing images of submodular binary markov random field mrf energies is introduced using this novel feature the collection of minimizing images of levels of higher order monotonically levelable multilabel mrf energies is shown to constitute a monotone collection this implies that these minimizing binary images can be combined to give minimizing images of the multilabel mrf energies thanks to the graph cuts framework the mentioned class of binary mrf energies is known to be minimized by maximum flow computations on appropriately constructed graphs with the aid of these developments an exact and efficient algorithm to minimize monotonically levelable multilabel mrf energies of any order which is composed of a series of maximum flow computations is proposed and an application of the proposed algorithm to image denoising is given

new loss functions in bayesian imaging abstract unlike the development of more accurate prior distributions for use in bayesian imaging the design of more sensible estimators through loss functions has been neglected in the literature we discuss the design of loss functions with a local structure that depend only on a binary misclassification vector the proposed approach is similar to modeling with a markov random field the bayes estimate is calculated in a two step algorithm using markov chain monte carlo and simulated annealing algorithms we present simulation experiments with the ising model where the observations are corrupted with gaussian and flip noise

empirical estimation of a distribution function with truncated and doubly interval censored data and its application to aids studies in this paper we discuss the non parametric estimation of a distribution function based on incomplete data for which the measurement origin of a survival time or the date of enrollment in a study is known only to belong to an interval also the survival time of interest itself is observed from a truncated distribution and is known only to lie in an interval to estimate the distribution function a simple self consistency algorithm a generalization of turnbull s 1976 journal of the royal statistical association series b 38 290 295 self consistency algorithm is proposed this method is then used to analyze two aids cohort studies for which direct use of the em algorithm dempster laird and rubin 1976 journal of the royal statistical association series b 39 1 38 which is computationally complicated has previously been the usual method of the analysis