on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

gauss markov measure field models for low level vision we present a class of models derived from classical discrete markov random fields that may be used for the solution of ill posed problems in image processing and in computational vision they lead to reconstruction algorithms that are flexible computationally efficient and biologically plausible to illustrate their use we present their application to the reconstruction of the dominant orientation and direction fields to the classification of multiband images and to image quantization and filtering

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

entropy controlled quadratic markov measure field models for efficient image segmentation we present a new markov random field mrf based model for parametric image segmentation instead of directly computing a label map our method computes the probability that the observed data at each pixel is generated by a particular intensity model prior information about segmentation smoothness and low entropy of the probability distribution maps is codified in the form of a mrf with quadratic potentials so that the optimal estimator is obtained by solving a quadratic cost function with linear constraints although for segmentation purposes the mode of the probability distribution at each pixel is naturally used as an optimal estimator our method permits the use of other estimators such as the mean or the median which may be more appropriate for certain applications numerical experiments and comparisons with other published schemes are performed using both synthetic images and real data of brain mri for which expert hand made segmentations are available finally we show that the proposed methodology may be easily extended to other problems such as stereo disparity estimation

variational viewpoint of the quadratic markov measure field models theory and algorithms we present a framework for image segmentation based on quadratic programming i e by minimization of a quadratic regularized energy linearly constrained in particular we present a new variational derivation of the quadratic markov measure field qmmf models which can be understood as a procedure for regularizing model preferences memberships or likelihoods we also present efficient optimization algorithms in the qmmfs the uncertainty in the computed regularized probability measure field is controlled by penalizing gini s coefficient and hence it affects the convexity of the quadratic programming problem the convex case is reduced to the solution of a positive definite linear system and for that case an efficient gauss seidel gs scheme is presented on the other hand we present an efficient projected gs with subspace minimization for optimizing the nonconvex case we demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two class segmentation as well as the simultaneous estimation of segmentation and parametric and nonparametric generative models we present extensions to the original formulation for including color and texture clues as well as imprecise user scribbles in an interactive framework

logarithmic corrections in the two dimensional ising model in a random surface field in the two dimensional ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point we study this question by extensive monte carlo simulations for various strengths of disorder the calculated effective temperature or size dependent critical exponents fit with the field theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system s critical behaviour

two dimensional semi infinite multicritical ising models the order parameter correlation functions of the z2 invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi infinite plane constrained to fixed or free boundary conditions these yield the corresponding universal surface exponents which distinguish the behaviour between even and odd critical models we also make explicit the interplay between duality and boundary conditions

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

error probability for coherent and differential psk over arbitrary rician fading channels with multiple cochannel interferers this paper discusses the performance of communication systems using binary coherent and differential phase shift keyed psk modulation in correlated rician fading channels with diversity reception the presence of multiple rician faded cochannel users which may have arbitrary and nonidentical parameters is modeled exactly exact bit error probability bep expressions are derived via the moment generating functions mgfs of the relevant decision statistics which are obtained through coherent detection with maximum ratio combining for coherent psk modulation and differential detection with equal gain combining egc for differential modulation evaluating the exact expressions requires a complexity that is exponential in the number of interferers to avoid this potentially time consuming operation we derive two low complexity approximate methods each for coherent and differential modulation formats which are more accurate than the traditional gaussian approximation approach two new and interesting results of this analysis are 1 unlike in the case of rayleigh fading channels increasing correlation between diversity branches may lead to better performance in rician fading channels and 2 the phase distribution of the line of sight or static fading components of the desired user has a significant influence on the bep performance in correlated diversity channels

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

semi infinite two dimensional ising model with marginally inhomogeneous couplings and conformal invariance the authors consider a semi infinite two dimensional ising model with nearest neighbour couplings that deviate from the bulk critical couplings by al 2 where l is the distance from the surface the surface critical exponents of this system are non universal under a conformal mapping onto a strip of width l the al 1 inhomogeneity transforms into a l pi sin pi l l 1 for the square lattice the spectrum of the transfer matrix in the strip geometry is calculated exactly in the extreme anisotropic limit the analytical results and numerical results for the triangular lattice are compared with predictions of conformal invariance

logarithmic corrections to finite size scaling in strips abstract the corrections to the finite size scaling behaviour of the eigenvalues of the transfer matrix of a critical theory defined on an infinitely long strip of finite width which occur when the hamiltonian contains a marginal operator are computed using conformal invariance they show a calculable universal logarthmic character for the four state potts model they agree with numerical data

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

new simple closed form ber expressions for mrc diversity bpsk in correlated rayleigh fading and cci exact closed form expressions are derived for the bit error rate of binary phase shift keying in rayleigh fading channels with maximal ratio combining diversity in the presence of cochannel interference and additive white gaussian noise the desired signal and the interferer signals are subject to correlated rayleigh fading and binary phase shift keying modulation is used by all users

critical behaviour near multiple junctions and dirty surfaces in the two dimensional ising model the authors consider m two dimensional semi infinite planes of ising spins joined together through surface spins and study the critical behaviour near to the junction the m 0 limit of the model according to the replica trick corresponds to the semi infinite ising model in the presence of a random surface field rsfi using conformal mapping second order perturbation expansion around the weak and strong coupled planes limits and a differential renormalization group they show that the surface critical behaviour of the rsfi model is described by ising critical exponents with logarithmic corrections to scaling while at multiple junctions m 2 the transition is of first order there is a spontaneous junction magnetization at the bulk critical point

spectral matting we present spectral matting a new approach to natural image matting that automatically computes a basis set of fuzzy matting components from the smallest eigenvectors of a suitably defined laplacian matrix thus our approach extends spectral segmentation techniques whose goal is to extract hard segments to the extraction of soft matting components these components may then be used as building blocks to easily construct semantically meaningful foreground mattes either in an unsupervised fashion or based on a small amount of user input

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

critical phenomena at perfect and non perfect surfaces the effect of imperfections on surface critical properties is studied for ising models with nearest neighbour ferromagnetic couplings on simple cubic lattices in particular results of monte carlo simulations for flat perfect surfaces are compared to those for flat surfaces with random weak or strong interactions between neighbouring spins in the surface layer and for surfaces with steps of monoatomic height surface critical exponents at the ordinary transition in particular are found to be robust against these perturbations

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

mixed order phase transition of the contact process near multiple junctions we have studied the phase transition of the contact process near a multiple junction of m semi infinite chains by monte carlo simulations as opposed to the continuous transitions of the translationally invariant m 2 and semi infinite m 1 system the local order parameter is found to be discontinuous for m 2 furthermore the temporal correlation length diverges algebraically as the critical point is approached but with different exponents on the two sides of the transition in the active phase the estimate is compatible with the bulk value while in the inactive phase it exceeds the bulk value and increases with m the unusual local critical behavior is explained by a scaling theory with an irrelevant variable which becomes dangerous in the inactive phase quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results

calculating error probabilities for intersymbol and cochannel interference the probability of error in a binary symmetric channel with intersymbol interference and additive noise is efficiently calculated by numerical quadrature of a laplace inversion integral along a contour in the complex plane passing through a saddlepoint of the integrand for gaussian noise a bound is set on the truncation error incurred by necessarily restricting the integration to a finite interval the probability of error resulting from cochannel interference is calculated by a similar technique

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

quadratic forms in random variables theory and applications textbook for a one semester graduate course for students specializing in mathematical statistics or in multivariate analysis or reference for theoretical as well as applied statisticians confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

a closed form ber expression for bpsk using mrc in correlated cci and rayleigh fading an exact closed form expression for the average bit error rate ber of coherent bpsk using maximal ratio combining mrc with correlated branches in the presence of cochannel interference cci and noise is derived this expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated rayleigh fading with the same correlation eigenvector matrix