exponentiated gradient algorithms for conditional random fields and max margin markov networks log linear and maximum margin models are two commonly used methods in supervised machine learning and are frequently used in structured prediction problems efficient learning of parameters in these models is therefore an important problem and becomes a key factor when learning from very large data sets this paper describes exponentiated gradient eg algorithms for training such models where eg updates are applied to the convex dual of either the log linear or max margin objective function the dual in both the log linear and max margin cases corresponds to minimizing a convex function with simplex constraints we study both batch and online variants of the algorithm and provide rates of convergence for both cases in the max margin case o 1 e eg updates are required to reach a given accuracy e in the dual in contrast for log linear models only o log 1 e updates are required for both the max margin and log linear cases our bounds suggest that the online eg algorithm requires a factor of n less computation to reach a desired accuracy than the batch eg algorithm where n is the number of training examples our experiments confirm that the online algorithms are much faster than the batch algorithms in practice we describe how the eg updates factor in a convenient way for structured prediction problems allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing we perform extensive evaluation of the algorithms comparing them to l bfgs and stochastic gradient descent for log linear models and to svm struct for max margin models the algorithms are applied to a multi class problem as well as to a more complex large scale parsing task in all these settings the eg algorithms presented here outperform the other methods

convergence of the modified craig sneyd scheme for two dimensional convection diffusion equations with mixed derivative term we consider the modified craig sneyd mcs scheme which forms a prominent time stepping method of the alternating direction implicit type for multidimensional time dependent convection diffusion equations with mixed spatial derivative terms such equations arise often notably in the field of financial mathematics in this paper a first convergence theorem for the mcs scheme is proved where the obtained bound on the global temporal discretization errors has the essential property that it is independent of the arbitrarily small spatial mesh width from the semidiscretization the obtained theorem is directly pertinent to two dimensional convection diffusion equations with mixed derivative term numerical experiments are provided that illustrate our result

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

functional bregman divergence and bayesian estimation of distributions a class of distortions termed functional bregman divergences is defined which includes squared error and relative entropy a functional bregman divergence acts on functions or distributions and generalizes the standard bregman divergence for vectors and a previous pointwise bregman divergence that was defined for functions a recent result showed that the mean minimizes the expected bregman divergence the new functional definition enables the extension of this result to the continuous case to show that the mean minimizes the expected functional bregman divergence over a set of functions or distributions it is shown how this theorem applies to the bayesian estimation of distributions estimation of the uniform distribution from independent and identically drawn samples is presented as a case study

an alternating direction implicit scheme for parabolic equations with mixed derivatives abstract an alternating direction implicit method for n dimensional parabolic equations with mixed derivatives is considered the method requires the solution of n tridiagonal matrix equations per time step and combines computational simplicity with the possibility of unconditional stability for any n the regimes of conditional stability for n 6 show that the scheme is less effective for higher dimensional problems owing to the proliferation of mixed derivatives an alternative scheme requiring 2 n tridiagonal operations which involves a single iteration to time centre the mixed derivatives is shown to improve accuracy and stability in particular the iterative scheme allows second order accuracy and unconditional stability in the important special cases of two and three space dimensions

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

the entire regularization path for the support vector machine the support vector machine svm is a widely used tool for classification many efficient implementations exist for fitting a two class svm model the user has to supply values for the tuning parameters the regularization cost parameter and the kernel parameters it seems a common practice is to use a default value for the cost parameter often leading to the least restrictive model in this paper we argue that the choice of the cost parameter can be critical we then derive an algorithm that can fit the entire path of svm solutions for every value of the cost parameter with essentially the same computational cost as fitting one svm model we illustrate our algorithm on some examples and use our representation to give further insight into the range of svm solutions

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

accelerated training of max margin markov networks with kernels structured output prediction is an important machine learning problem both in theory and practice and the max margin markov network m 3n is an effective approach all state of the art algorithms for optimizing m 3n objectives take at least o 1 e number of iterations to find an e accurate solution nesterov 1 broke this barrier by proposing an excessive gap reduction technique egr which converges in o 1 e iterations however it is restricted to euclidean projections which consequently requires an intractable amount of computation for each iteration when applied to solve m 3n in this paper we show that by extending egr to bregman projection this faster rate of convergence can be retained and more importantly the updates can be performed efficiently by exploiting graphical model factorization further we design a kernelized procedure which allows all computations per iteration to be performed at the same cost as the state of the art approaches

a class of experimental designs for estimating a response surface and variance components this article introduces a new class of experimental designs called split factorials which allow for the estimation of both response surface effects fixed effects of crossed factors and variance components arising from nested random effects with an economical run size split factorials provide flexibility in dividing the degrees of freedom among the different estimations for a split factorial design it is shown that the ols estimators for the fixed effects are blue and that the variance component estimators from the mean squared errors on the anova table are minimum variance among unbiased quadratic estimators an application involving concrete mixing demonstrates the use of a split factorial experiment

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

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 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

an epsilon relaxation method for separable convex cost network flow problems we propose a new method for the solution of the single commodity separable convex cost network flow problem the method generalizes the epsilon relaxation method developed for linear cost problems and reduces to that method when applied to linear cost problems we show that the method terminates with a near optimal solution and we provide an associated complexity analysis we also present computational results showing that the method is much faster than earlier relaxation methods particularly for ill conditioned problems

unconditional convergence of some crank nicolson lod methods for initial boundary value problems in this paper convergence properties are discussed for some locally one dimensional lod splitting methods applied to linear parabolic initialboundary value problems we shall consider unconditional convergence where both the stepsize in time and the meshwidth in space tend to zero independently of each other

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

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

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

optimal design of blocked and split plot experiments for fixed effects and variance component estimation in general modeling data from blocked and split plot response surface experiments requires the use of generalized least squares and the estimation of two variance components the literature on the optimal design of blocked and split plot response surface experiments however focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well to overcome this problem we propose a new bayesian optimal design criterion which focuses on both the variance components and the fixed effects a novel feature of the criterion is that it incorporates prior information about the variance components through log normal or beta prior distributions the resulting designs allow for a more powerful statistical inference than traditional optimal designs in our algorithm for generating optimal blocked and split plot designs we implement efficient quadrature approaches for the numerical approximation of the new optimal design criterion

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

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

a new matrix method for solving two dimensional time dependent diffusion equations with dirichlet boundary conditions abstract this paper is devoted to develop a new matrix scheme for solving two dimensional time dependent diffusion equations with dirichlet boundary conditions we first transform these equations into equivalent integro partial differential equations pdes such these integro pdes contain both of the initial and boundary conditions and can be solved numerically in a more appropriate manner subsequently all the existing known and unknown functions in the latter equations are approximated by bernoulli polynomials and operational matrices of differentiation and integration together with the completeness of these polynomials can be used to reduce the integro pdes into the associated algebraic generalized sylvester equations for solving these algebraic equations an efficient krylov subspace iterative method i e bicgstab is implemented two numerical examples are given to demonstrate the efficiency accuracy and versatility of the proposed method

polynomial time approximation algorithms for the ising model the paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic ising system to any specified degree of accuracy the running time of the algorithm in

dual extrapolation and its applications to solving variational inequalities and related problems in this paper we suggest new dual methods for solving variational inequalities with monotone operators we show that with an appropriate step size strategy our method is optimal both for lipschitz continuous operators o 1 over epsilon iterations and for the operators with bounded variations o 1 over epsilon 2 iterations our technique can be applied for solving non smooth convex minimization problems with known structure in this case the worst case complexity bound is o 1 over epsilon iterations

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

adaptive fuzzy filtering in a deterministic setting many real world applications involve the filtering and estimation of process variables this study considers the use of interpretable sugeno type fuzzy models for adaptive filtering our aim in this study is to provide different adaptive fuzzy filtering algorithms in a deterministic setting the algorithms are derived and studied in a unified way without making any assumptions on the nature of signals i e process variables the study extends in a common framework the adaptive filtering algorithms usually studied in signal processing literature and p norm algorithms usually studied in machine learning literature to semilinear fuzzy models a mathematical framework is provided that allows the development and an analysis of the adaptive fuzzy filtering algorithms we study a class of nonlinear lms like algorithms for the online estimation of fuzzy model parameters a generalization of the algorithms to the p norm is provided using bregman divergences a standard tool for online machine learning algorithms

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

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

discriminative learning of max sum classifiers the max sum classifier predicts n tuple of labels from n tuple of observable variables by maximizing a sum of quality functions defined over neighbouring pairs of labels and observable variables predicting labels as map assignments of a random markov field is a particular example of the max sum classifier learning parameters of the max sum classifier is a challenging problem because even computing the response of such classifier is np complete in general estimating parameters using the maximum likelihood approach is feasible only for a subclass of max sum classifiers with an acyclic structure of neighbouring pairs recently the discriminative methods represented by the perceptron and the support vector machines originally designed for binary linear classifiers have been extended for learning some subclasses of the max sum classifier besides the max sum classifiers with the acyclic neighbouring structure it has been shown that the discriminative learning is possible even with arbitrary neighbouring structure provided the quality functions fulfill some additional constraints in this article we extend the discriminative approach to other three classes of max sum classifiers with an arbitrary neighbourhood structure we derive learning algorithms for two subclasses of max sum classifiers whose response can be computed in polynomial time i the max sum classifiers with supermodular quality functions and ii the max sum classifiers whose response can be computed exactly by a linear programming relaxation moreover we show that the learning problem can be approximately solved even for a general max sum classifier

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

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

fractional resolution and minimum aberration in blocked 2 n k designs systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks this is accomplished through the use of blocking factors the concepts of resolution and minimum aberration design optimization criteria ordinarily used to rank unblocked fractional factorial designs are extended to such blocked fractional factorial designs by treating the treatment and blocking factors differently in terms of their contribution to word length in the defining contrast subgroup some limited theoretical results are derived and tables of minimumaberration blocked two level fractional factorial designs are presented and considered the relationship between clear effects effects that are estimable when higher order effects are assumed negligible and minimum aberration in the presence of blocking is discussed

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

multi output regression on the output manifold multi output regression aims at learning a mapping from an input feature space to a multivariate output space previous algorithms define the loss functions using a fixed global coordinate of the output space which is equivalent to assuming that the output space is a whole euclidean space with a dimension equal to the number of the outputs so the underlying structure of the output space is completely ignored in this paper we consider the output space as a riemannian submanifold to incorporate its geometric structure into the regression process to this end we propose a novel mechanism called locally linear transformation llt to define the loss functions on the output manifold in this way currently existing regression algorithms can be improved in particular we propose an algorithm under the support vector regression framework our experimental results on synthetic and real life data are satisfactory