image and texture segmentation using local spectral histograms we present a method for segmenting images consisting of texture and nontexture regions based on local spectral histograms defined as a vector consisting of marginal distributions of chosen filter responses local spectral histograms provide a feature statistic for both types of regions using local spectral histograms of homogeneous regions we decompose the segmentation process into three stages the first is the initial classification stage where probability models for homogeneous texture and nontexture regions are derived and an initial segmentation result is obtained by classifying local windows in the second stage we give an algorithm that iteratively updates the segmentation using the derived probability models the third is the boundary localization stage where region boundaries are localized by building refined probability models that are sensitive to spatial patterns in segmented regions we present segmentation results on texture as well as nontexture images our comparison with other methods shows that the proposed method produces more accurate segmentation results

the helmholtz machine discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning one fruitful approach is to build a parameterized stochastic generative model independent draws from which are likely to produce the patterns for all but the simplest generative models each pattern can be generated in exponentially many ways it is thus intractable to adjust the parameters to maximize the probability of the observed patterns we describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations our method can be viewed as a form of hierarchical self supervised learning that may relate to the function of bottom up and top down cortical processing pathways

approximate maximum entropy joint feature inference consistent with arbitrary lower order probability constraints application to statistical classification we propose a new learning method for discrete space statistical classifiers similar to chow and liu 1968 and cheeseman 1983 we cast classification inference within the more general framework of estimating the joint probability mass function p m f for the feature vector class label pair cheeseman s proposal to build the maximum entropy me joint p m f consistent with general lower order probability constraints is in principle powerful allowing general dependencies between features however enormous learning complexity has severely limited the use of this approach alternative models such as bayesian networks bns require explicit determination of conditional independencies these may be difficult to assess given limited data here we propose an approximate me method which like previous methods incorporates general constraints while retaining quite tractable learning the new method restricts joint p m f support during learning to a small subset of the full feature space classification gains are realized over dependence trees tree augmented naive bayes networks bns trained by the kutato algorithm and multilayer perceptrons extensions to more general inference problems are indicated we also propose a novel exact inference method when there are several missing features

the promise and perils of near regular texture motivated by the low structural fidelity for near regular textures in current texture synthesis algorithms we propose and implement an alternative texture synthesis method for near regular texture we view such textures as statistical departures from regular patterns and argue that a thorough understanding of their structures in terms of their translation symmetries can enhance existing methods of texture synthesis we demonstrate the perils of texture synthesis for near regular texture and the promise of faithfully preserving the regularity as well as the randomness in a near regular texture sample

data driven rank breaking for efficient rank aggregation rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference rank breaking is a common practice to reduce the computational complexity of learning the global ranking the individual preferences are broken into pairwise comparisons and applied to efficient algorithms tailored for independent paired comparisons however due to the ignored dependencies in the data naive rank breaking approaches can result in inconsistent estimates the key idea to produce accurate and consistent estimates is to treat the pairwise comparisons unequally depending on the topology of the collected data in this paper we provide the optimal rank breaking estimator which not only achieves consistency but also achieves the best error bound this allows us to characterize the fundamental tradeoff between accuracy and complexity further the analysis identies how the accuracy depends on the spectral gap of a corresponding comparison graph

minimax entropy principle and its application to texture modeling this article proposes a general theory and methodology called the minimax entropy principle for building statistical models for images or signals in a variety of applications this principle consists of two parts the first is the maximum entropy principle for feature binding or fusion for a given set of observed feature statistics a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them the second part is the minimum entropy principle for feature selection among all plausible sets of feature statistics we choose the set whose maximum entropy distribution has the minimum entropy computational and inferential issues in both parts are addressed in particular a feature pursuit procedure is proposed for approximately selecting the optimal set of features the minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics and an information criterion for feature pursuit is derived the minimax entropy principle is applied to texture modeling where a novel markov random field mrf model called frame filter random field and minimax entropy is derived and encouraging results are obtained in experiments on a variety of texture images the relationship between our theory and the mechanisms of neural computation is also discussed

r matrices and the magic square the distinguished representations associated with the rows of the freudenthal magic square have a uniform tensor product graph with edges labelled by linear functions of the dimension of the corresponding division algebra

a markov chain approximation to choice modeling assortment planning is an important problem that arises in many industries such as retailing and airlines one of the key challenges in an assortment planning problem is to identify the right model for the substitution behavior of customers from the data error in model selection can lead to highly suboptimal decisions in this paper we consider a markov chain based choice model and show that it provides a simultaneous approximation for all random utility based discrete choice models including the multinomial logit mnl the probit the nested logit and mixtures of multinomial logit models in the markov chain model substitution from one product to another is modeled as a state transition in the markov chain we show that the choice probabilities computed by the markov chain based model are a good approximation to the true choice probabilities for any random utility based choice model under mild conditions moreover they are exact if the underlying model is a generalized attraction model gam of wh

exploring texture ensembles by efficient markov chain monte carlo toward a trichromacy theory of texture presents a mathematical definition of texture the julesz ensemble spl omega h which is the set of all images defined on z sup 2 that share identical statistics h then texture modeling is posed as an inverse problem given a set of images sampled from an unknown spl omega h sub we search for the statistics h sub which define the ensemble a spl omega h has an associated probability distribution q i h which is uniform over the images in spl omega h and has zero probability outside the authors previously 1999 showed q i h to be the limit distribution of the frame filter random field and minimax entropy model as the image lattice spl lambda spl rarr z sup 2 this conclusion establishes the intrinsic link between the scientific definition of texture on z sup 2 and the mathematical models of texture on finite lattices it brings two advantages the practice of texture image synthesis by matching statistics is put on a mathematical foundation and we need not learn the expensive frame model in feature pursuit model selection and texture synthesis an efficient markov chain monte carte algorithm is proposed for sampling julesz ensembles it generates random texture images by moving along the directions of filter coefficients and thus extends the traditional single site gibbs sampler we compare four popular statistical measures in the literature in terms of their descriptive abilities our experiments suggest that a small number of bins in marginal histograms are sufficient for capturing a variety of texture patterns

finding minimum entropy codes to determine whether a particular sensory event is a reliable predictor of reward or punishment it is necessary to know the prior probability of that event if the variables of a sensory representation normally occur independently of each other then it is possible to derive the prior probability of any logical function of the variables from the prior probabilities of the individual variables without any additional knowledge hence such a representation enormously enlarges the scope of definable events that can be searched for reliable predictors finding a minimum entropy code is a possible method of forming such a representation and methods for doing this are explored in this paper the main results are 1 to show how to find such a code when the probabilities of the input states form a geometric progression as is shown to be nearly true for keyboard characters in normal text 2 to show how a minimum entropy code can be approximated by repeatedly recoding pairs triples etc of an original 7 bit code for keyboard characters 3 to prove that in some cases enlarging the capacity of the output channel can lower the entropy

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

pattern generation using likelihood inference for cellular automata cellular automata are discrete dynamical systems which evolve on a discrete grid recent studies have shown that cellular automata with relatively simple rules can produce highly complex patterns we develop likelihood based methods for estimating rules of cellular automata aimed at the re generation of observed regular patterns under noisy data our approach is equivalent to estimating the local map of a stochastic cellular automaton direct computations of the maximum likelihood estimates are possible for regular binary patterns the likelihood formulation of the problem is congenial with the use of the minimum description length principle as a model selection tool we illustrate our method with a series of examples using binary images

varying complexity in tree structured image distribution models probabilistic models of image statistics underlie many approaches in image analysis and processing an important class of such models have variables whose dependency graph is a tree if the hidden variables take values on a finite set most computations with the model can be performed exactly including the likelihood calculation training with the em algorithm etc crouse et al developed one such model the hidden markov tree hmt they took particular care to limit the complexity of their model we argue that it is beneficial to allow more complex tree structured models describe the use of information theoretic penalties to choose the model complexity and present experimental results to support these proposals for these experiments we use what we call the hierarchical image probability hip model the differences between the hip and the hmt models include the use of multivariate gaussians to model the distributions of local vectors of wavelet coefficients and the use of different numbers of hidden states at each resolution we demonstrate the broad utility of image distributions by applying the hip model to classification synthesis and compression across a variety of image types namely electrooptical synthetic aperture radar and mammograms digitized x rays in all cases we compare with the hmt

fundamental limits of bayesian inference order parameters and phase transitions for road tracking there is a growing interest in formulating vision problems in terms of bayesian inference and in particular the maximum a posteriori map estimator in this paper we consider the special case of detecting roads from aerial images and demonstrate that analysis of this ensemble enables us to determine fundamental bounds on the performance of the map estimate we demonstrate that there is a phase transition at a critical value of the order parameter below this phase transition it is impossible to detect the road by any algorithm we derive closely related order parameters which determine the time and memory complexity of search and the accuracy of the solution using the n search strategy our approach can be applied to other vision problems and we briefly summarize the results when the model uses the wrong prior we comment on how our work relates to studies of the complexity of visual search and the critical behaviour in the computational cost of solving np complete problems

bayesian video dejittering by the bv image model line jittering or random horizontal displacement in video images occurs when the synchronization signals are corrupted in video storage media or by electromagnetic interference in wireless video transmission the goal of intrinsic video dejittering is to recover the ideal video directly from the observed jittered and often noisy frames the existing approaches in the literature are mostly based on local or semilocal filtering techniques and autoregressive image models and are complemented by various image processing tools in this paper based on the statistical rationale of bayesian inference we propose the first variational dejittering model based on the bounded variation bv image model which is global clean and self contained and intrinsically combines dejittering with denoising the mathematical properties of the model are studied based on the direct method of calculus of variations we design one effective algorithm and present its computational implementation based on techniques from numeri

statistical principles in image modeling images of natural scenes contain a rich variety of visual patterns to learn and recognize these patterns from natural images it is necessary to construct statistical models for these patterns in this review article we describe three statistical principles for modeling image patterns the sparse coding principle the minimax entropy principle and the meaningful alignment principle we explain these three principles and their relationships in the context of modeling images as compositions of gabor wavelets these three principles correspond to three regimes of composition patterns of gabor wavelets and these three regimes are connected by changes in scale or resolution

hierarchical mixtures of experts and the em algorithm we present a tree structured architecture for supervised learning the statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models glim s learning is treated as a maximum likelihood problem in particular we present an expectation maximization em algorithm for adjusting the parameters of the architecture we also develop an on line learning algorithm in which the parameters are updated incrementally comparative simulation results are presented in the robot dynamics domain

prior learning and gibbs reaction diffusion this article addresses two important themes in early visual computation it presents a novel theory for learning the universal statistics of natural images and it proposes a general framework of designing reaction diffusion equations for image processing we studied the statistics of natural images including the scale invariant properties then generic prior models were learned to duplicate the observed statistics based on minimax entropy theory the resulting gibbs distributions have potentials of the form u i spl lambda s spl sigma sub spl alpha 1 sup k spl sigma sub x y spl lambda sup spl alpha f sup spl alpha i x y with s f sup 1 f sup 2 f sup k being a set of filters and spl lambda spl lambda sup 1 spl lambda sup 2 spl lambda sup k the potential functions the learned gibbs distributions confirm and improve the form of existing prior models such as line process but in contrast to all previous models inverted potentials were found to be necessary we find that the partial differential equations given by gradient descent on u i spl lambda s are essentially reaction diffusion equations where the usual energy terms produce anisotropic diffusion while the inverted energy terms produce reaction associated with pattern formation enhancing preferred image features we illustrate how these models can be used for texture pattern rendering denoising image enhancement and clutter removal by careful choice of both prior and data models of this type incorporating the appropriate features

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

quantum r matrix for g2 and a solvable 175 vertex model the quantum r matrix for cartan s exceptional simple lie algebra g2 in its seven dimensional minimal representation is presented the r matrix is determined through the irreducible decomposition of the tensor modules over the quantised universal enveloping algebra uq g2 this defines a new solvable seven state 175 vertex model on the planar square lattice whose boltzmann weights satisfy the yang baxter equation for the equivalent face model the local state probability is obtained in terms of a relative of a level 1 string function related to the affine lie algebra pair b3 1 contains implies g2 1

universal analytical forms for modeling image probabilities seeking probability models for images we employ a spectral approach where the images are decomposed using bandpass filters and probability models are imposed on the filter outputs also called spectral components we employ a two parameter family of probability densities called bessel k forms for modeling the marginal densities of the spectral components and demonstrate their fit to the observed histograms for video infrared and range images motivated by object based models for image analysis a relationship between the bessel parameters and the imaged objects is established using l sup 2 metric on the set of bessel k forms we propose a pseudometric on the image space for quantifying image similarities differences some applications including clutter classification and pruning of hypotheses for target recognition are presented

embedding gestalt laws in markov random fields the goal of this paper is to study a mathematical framework of 2d object shape modeling and learning for middle level vision problems such as image segmentation and perceptual organization for this purpose we pursue generic shape models which characterize the most common features of 2d object shapes in this paper shape models are learned from observed natural shapes based on a minimax entropy learning theory the learned shape models are gibbs distributions defined on markov random fields mrfs the neighborhood structures of these mrfs correspond to gestalt laws colinearity cocircularity proximity parallelism and symmetry thus both contour based and region based features are accounted for stochastic markov chain monte carlo mcmc algorithms are proposed for learning and model verification furthermore this paper provides a quantitative measure for the so called nonaccidental statistics and thus justifies some empirical observations of gestalt psychology by information theory our experiments also demonstrate that global shape properties can arise from interactions of local features

the embedding e0 and the spectrum dependent r matrix for q f4 the explicit embedding forms of e0 for the minimal representations of the quantum f4 e6 and e7 are obtained in this paper in terms of jimbo s method the spectrum dependent r matrices both trigonometric and rational for those representations are computed

computationally tractable stochastic image modeling based on symmetric markov mesh random fields in this paper the properties of a new class of causal markov random fields named symmetric markov mesh random field are initially discussed it is shown that the symmetric markov mesh random fields from the upper corners are equivalent to the symmetric markov mesh random fields from the lower corners based on this new random field a symmetric corner independent and isotropic image model is then derived which incorporates the dependency of a pixel on all its neighbors the introduced image model comprises the product of several local 1d density and 2d joint density functions of pixels in an image thus making it computationally tractable and practically feasible by allowing the use of histogram and joint histogram approximations to estimate the model parameters an image restoration application is also presented to confirm the effectiveness of the model developed the experimental results demonstrate that this new model provides an improved tool for image modeling purposes compared to the conventional markov random field models

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

statistical edge detection learning and evaluating edge cues we formulate edge detection as statistical inference this statistical edge detection is data driven unlike standard methods for edge detection which are model based for any set of edge detection filters implementing local edge cues we use presegmented images to learn the probability distributions of filter responses conditioned on whether they are evaluated on or off an edge edge detection is formulated as a discrimination task specified by a likelihood ratio test on the filter responses this approach emphasizes the necessity of modeling the image background the off edges we represent the conditional probability distributions nonparametrically and illustrate them on two different data sets of 100 sowerby and 50 south florida images multiple edges cues including chrominance and multiple scale are combined by using their joint distributions hence this cue combination is optimal in the statistical sense we evaluate the effectiveness of different visual cues using the chernoff information and receiver operator characteristic roc curves this shows that our approach gives quantitatively better results than the canny edge detector when the image background contains significant clutter in addition it enables us to determine the effectiveness of different edge cues and gives quantitative measures for the advantages of multilevel processing for the use of chrominance and for the relative effectiveness of different detectors furthermore we show that we can learn these conditional distributions on one data set and adapt them to the other with only slight degradation of performance without knowing the ground truth on the second data set this shows that our results are not purely domain specific we apply the same approach to the spatial grouping of edge cues and obtain analogies to nonmaximal suppression and hysteresis

general statistical inference for discrete and mixed spaces by an approximate application of the maximum entropy principle we propose a method for learning a general statistical inference engine operating on discrete and mixed discrete continuous feature spaces such a model allows inference on any of the discrete features given values for the remaining features applications are e g to medical diagnosis with multiple possible diseases fault diagnosis information retrieval and imputation in databases bayesian networks bns are versatile tools that possess this inference capability however bns require explicit specification of conditional independencies which may be difficult to assess given limited data alternatively cheeseman 1983 proposed finding the maximum entropy me joint probability mass function pmf consistent with arbitrary lower order probability constraints this approach is in principle powerful and does not require explicit expression of conditional independence however until now the huge learning complexity has severely limited the use of this approach here we propose an approximate me method which also encodes arbitrary low order constraints but while retaining quite tractable learning our method uses a restriction of joint pmf support during learning to a subset of the feature space results on the university of california irvine repository reveal performance gains over several bn approaches and over multilayer perceptrons

coarse to fine face detection we study visual selection detect and roughly localize all instances of a generic object class such as a face in a greyscale scene measuring performance in terms of computation and false alarms our approach is sequential testing which is coarse to fine in both in the exploration of poses and the representation of objects all the tests are binary and indicate the presence or absence of loose spatial arrangements of oriented edge fragments starting from training examples we recursively find larger and larger arrangements which are decomposable which implies the probability of an arrangement appearing on an object decays slowly with its size detection means finding a sufficient number of arrangements of each size along a decreasing sequence of pose cells at the beginning the tests are simple and universal accommodating many poses simultaneously but the false alarm rate is relatively high eventually the tests are more discriminating but also more complex and dedicated to specific poses as a result the spatial distribution of processing is highly skewed and detection is rapid but at the expense of isolated false alarms which presumably could be eliminated with localized more intensive processing

energy based models for sparse overcomplete representations we present a new way of extending independent components analysis ica to overcomplete representations in contrast to the causal generative extensions of ica which maintain marginal independence of sources we define features as deterministic linear functions of the inputs this assumption results in marginal dependencies among the features but conditional independence of the features given the inputs by assigning energies to the features a probability distribution over the input states is defined through the boltzmann distribution free parameters of this model are trained using the contrastive divergence objective hinton 2002 when the number of features is equal to the number of input dimensions this energy based model reduces to noiseless ica and we show experimentally that the proposed learning algorithm is able to perform blind source separation on speech data in additional experiments we train overcomplete energy based models to extract features from various standard data sets containing speech natural images hand written digits and faces

image segmentation by map ml estimations image segmentation plays an important role in computer vision and image analysis in this paper image segmentation is formulated as a labeling problem under a probability maximization framework to estimate the label configuration an iterative optimization scheme is proposed to alternately carry out the maximum a posteriori map estimation and the maximum likelihood ml estimation the map estimation problem is modeled with markov random fields mrfs and a graph cut algorithm is used to find the solution to the map estimation the ml estimation is achieved by computing the means of region features in a gaussian model our algorithm can automatically segment an image into regions with relevant textures or colors without the need to know the number of regions in advance its results match image edges very well and are consistent with human perception comparing to six state of the art algorithms extensive experiments have shown that our algorithm performs the best

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

representing and recognizing objects with massive local image patches natural image patches are fundamental elements for visual pattern modeling and recognition by studying the intrinsic manifold structures in the space of image patches this paper proposes an approach for representing and recognizing objects with a massive number of local image patches e g 17x17 pixels given a large collection 10 4 of proto image patches extracted from objects we map them into two types of manifolds with different metrics explicit manifolds of low dimensions for structural primitives and implicit manifolds of high dimensions for stochastic textures we define these manifolds grown from patches as the e balls where e corresponds to the perception residual or fluctuation using these e balls as features we present a novel generative learning algorithm by the information projection principle this algorithm greedily stepwise pursues the object models by selecting sparse and independent e balls say 10 3 for each category during the detection and classification phase only a small number say 20 of features are activated by a fast kd tree indexing technique the proposed method owns two characters 1 automatically generating features e balls from local image patches rather than designing marginal feature carefully and category specifically 2 unlike the weak classifiers in the boosting models these selected e ball features are used to explain object in a generative way and are mutually independent the advantage and performance of our approach is evaluated on several challenging datasets with the task of localizing objects against appearance variance occlusion and background clutter

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

non parametric modeling of partially ranked data statistical models on full and partial rankings of n items are often of limited practical use for large n due to computational consideration we explore the use of non parametric models for partially ranked data and derive computationally ef cient procedures for their use for large n the derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings a bias variance analysis and an experimental study demonstrate the applicability of the proposed method

learning in gibbsian fields how accurate and how fast can it be gibbsian fields or markov random fields are widely used in bayesian image analysis but learning gibbs models is computationally expensive the computational complexity is pronounced by the recent minimax entropy frame models which use large neighborhoods and hundreds of parameters in this paper we present a common framework for learning gibbs models we identify two key factors that determine the accuracy and speed of learning gibbs models the efficiency of likelihood functions and the variance in approximating partition functions using monte carlo integration we propose three new algorithms in particular we are interested in a maximum satellite likelihood estimator which makes use of a set of precomputed gibbs models called satellites to approximate likelihood functions this algorithm can approximately estimate the minimax entropy model for textures in seconds in a hp workstation the performances of various learning algorithms are compared in our experiments

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

learning active basis model for object detection and recognition this article proposes an active basis model a shared sketch algorithm and a computational architecture of sum max maps for representing learning and recognizing deformable templates in our generative model a deformable template is in the form of an active basis which consists of a small number of gabor wavelet elements at selected locations and orientations these elements are allowed to slightly perturb their locations and orientations before they are linearly combined to generate the observed image the active basis model in particular the locations and the orientations of the basis elements can be learned from training images by the shared sketch algorithm the algorithm selects the elements of the active basis sequentially from a dictionary of gabor wavelets when an element is selected at each step the element is shared by all the training images and the element is perturbed to encode or sketch a nearby edge segment in each training image the recognition of the deformable template from an image can be accomplished by a computational architecture that alternates the sum maps and the max maps the computation of the max maps deforms the active basis to match the image data and the computation of the sum maps scores the template matching by the log likelihood of the deformed active basis

the spectrum dependent solutions to the yang baxter equation for quantum e6 and e7 both trigonometric and rational solutions to the spectrum dependent yang baxter equation are presented for the minimal representations of the quantum exceptional e6 and e7 universal enveloping algebras

when the a contrario approach becomes generative the a contrario approach is a statistical hypothesis testing based approach to detect geometric meaningful events in images the general methodology consists in computing the probability of an observed geometric event under a noise model null hypothesis h 0 h0 and then declare the event meaningful when this probability is small enough generally the noise model is taken to be the independent uniform distribution on the considered elements our aim in this paper will be to question the choice of the noise model what happens if we enrich the noise model how to characterize the noise models such that there are no meaningful events against them among them what is the one that has maximum entropy what does a sample of it look like how is this noise model related to probability distributions on the elements that would produce with high probability the same detections all these questions will be formalized and answered in two different frameworks the detection of clusters in a set of points and the detection of line segments in an image the general idea is to capture the perceptual information contained in an image and then generate new images having the same visual content we believe that such a generative approach can have applications for instance in image compression or for clutter removal

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

mm algorithms for generalized bradley terry models the bradley terry model for paired comparisons is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs among the many studies of the model in the past 75 years numerous authors have generalized it in several directions sometimes providing iterative algorithms for obtaining maximum likelihood estimates for the generalizations building on a theory of algorithms known by the initials mm for minorization maximization this paper presents a powerful technique for producing iterative maximum likelihood estimation algorithms for a wide class of generalizations of the bradley terry model while algorithms for problems of this type have tended to be custom built in the literature the techniques in this paper enable their mass production simple conditions are stated that guarantee that each algorithm described will produce a sequence that converges to the unique maximum likelihood estimator several of the algorithms and convergence results herein are new

bayes classification of online arabic characters by gibbs modeling of class conditional densities this study investigates bayes classification of online arabic characters using histograms of tangent differences and gibbs modeling of the class conditional probability density functions the parameters of these gibbs density functions are estimated following the zhu et al constrained maximum entropy formalism originally introduced for image and shape synthesis we investigate two partition function estimation methods one uses the training sample and the other draws from a reference distribution the efficiency of the corresponding bayes decision methods and of a combination of these is shown in experiments using a database of 9 504 freely written samples by 22 writers comparisons to the nearest neighbor rule method and a kohonen neural network method are provided