added variable plots in linear regression this article discusses three well known methods for obtaining a graphical evaluation of the effect of adding an explanatory variable in linear regression a new method is also proposed

multiband segmentation based on a hierarchical markov model we develop a new multiscale markov segmentation model for multiband images using quadtree multiple resolution analysis of a multiband image we use both inter and intra scale spatial markov statistical dependencies bayesian inference is used to assess the appropriate number of segments we exemplify the excellent results which can be obtained with this approach using synthetic images and in two case studies involving multiband astronomical image sets

multi parameter automodels and their applications summary motivated by the modelling of non gaussian data or positively correlated data on a lattice extensions of besag s automodels to exponential families with multi dimensional parameters have been proposed recently we provide a multiple parameter analogue of besag s one dimensional result that gives the necessary form of the exponential families for the markov random field s conditional distributions we propose estimation of parameters by maximum pseudolikelihood and give a proof of the consistency of the estimators for the multi parameter automodel the methodology is illustrated with examples in particular the building of a cooperative system with beta conditional distributions we also indicate future applications of these models to the analysis of mixed state spatial data

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

random fields on a network modeling statistics and applications the theory of spatial models over lattices or random fields as they are known has developed significantly over recent years this book provides a graduate level introduction to the subject which assumes only a basic knowledge of probability and statistics finite markov chains and the spectral theory of second order processes a particular strength of this book is its emphasis on examples both to motivate the theory which is being developed and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

texture analysis through a markovian modelling and fuzzyclassification application to urban area extraction fromsatellite images herein we propose a complete procedure to analyze and classify the texture of an image we apply this scheme to solve a specific image processing problem urban areas detection in satellite images first we propose to analyze the texture through the modelling of the luminance field with eight different chain based models we then derived a texture parameter from these models the effect of the lattice anisotropy is corrected by a renormalization group technique coming from statistical physics this parameter which takes into account local conditional variances of the image is compared to classical methods of texture analysis afterwards we develop a modified fuzzy cmeans algorithm that includes an entropy term the advantage of such an algorithm is that the number of classes does not need to be known a priori besides this algorithm provides us with further information i e the probability that a given pixel belongs to a given cluster finally we introduce this information in a markovian model of segmentation some results on spot5 simulated images spot3 images and ers1 radar images are presented these images are provided by the french national space agency cnes and the european space agency esa

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

motion recognition using nonparametric image motion models estimated from temporal and multiscale co occurrence statistics a new approach for motion characterization in image sequences is presented it relies on the probabilistic modeling of temporal and scale co occurrence distributions of local motion related measurements directly computed over image sequences temporal multiscale gibbs models allow us to handle both spatial and temporal aspects of image motion content within a unified statistical framework since this modeling mainly involves the scalar product between co occurrence values and gibbs potentials we can formulate and address several fundamental issues model estimation according to the ml criterion hence model training and learning and motion classification we have conducted motion recognition experiments over a large set of real image sequences comprising various motion types such as temporal texture samples human motion examples and rigid motion situations

simultaneous motion detection and background reconstruction with a conditional mixed state markov random field in this work we present a new way of simultaneously solving the problems of motion detection and background image reconstruction an accurate estimation of the background is only possible if we locate the moving objects meanwhile a correct motion detection is achieved if we have a good available background model the key of our joint approach is to define a single random process that can take two types of values instead of defining two different processes one symbolic motion detection and one numeric background intensity estimation it thus allows to exploit the spatio temporal interaction between a decision motion detection and an estimation intensity reconstruction problem consequently the meaning of solving both tasks jointly is to obtain a single optimal estimate of such a process the intrinsic interaction and simultaneity between both problems is shown to be better modeled within the so called mixed state statistical framework which is extended here to account for symbolic states and conditional random fields experiments on real sequences and comparisons with existing motion detection methods support our proposal further implications for video sequence inpainting will be also discussed

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

flexible parsimonious smoothing and additive modeling a simple method is presented for fitting regression models that are nonlinear in the explanatory variables despite its simplicity or perhaps because of it the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques especially for small data sets in the presence of high noise

unsupervised statistical segmentation of nonstationary images using triplet markov fields recent developments in statistical theory and associated computational techniques have opened new avenues for image modeling as well as for image segmentation techniques thus a host of models have been proposed and the ones which have probably received considerable attention are the hidden markov fields hmf models this is due to their simplicity of handling and their potential for providing improved image quality although these models provide satisfying results in the stationary case they can fail in the nonstationary one in this paper we tackle the problem of modeling a nonstationary hidden random field and its effect on the unsupervised statistical image segmentation we propose an original approach based on the recent triplet markov field tmf model which enables one to deal with nonstationary class fields moreover the noise can be correlated and possibly non gaussian an original parameter estimation method which uses the pearson system to find the natures of the noise margins which can vary with the class is also proposed and used to perform unsupervised segmentation of such images experiments indicate that the new model and related processing algorithm can improve the results obtained with the classical ones

some diagnostics for binary logistic regression via smoothing summary the paper discusses some diagnostic tools for binary logistic regression which use smoothing techniques smoothed binary data are employed to devise a battery of diagnostic plots from simple procedures which indicate only the adequacy or inadequacy of a maximum likelihood logistic fit to partial residual plots and delta local deviance plots which reveal the type of model inadequacy suggesting perhaps the addition of nonlinear terms or interactions properties of the methods are studied by simulation the diagnostic tools are illustrated on a set of data in which the probability of having telephone service is related to the demographic variables income and education

gibbs random fields cooccurrences and texture modeling gibbs random field grf models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination the authors show an explicit relationship between cooccurrences and a large class of grf s this result comes from a new framework based on a set theoretic concept called the aura set and on measures of this set aura measures this framework is also shown to be useful for relating different texture analysis tools the authors show how the aura set can be constructed with morphological dilation how its measure yields cooccurrences and how it can be applied to characterizing the behavior of the gibbs model for texture in particular they show how the aura measure generalizes to any number of gray levels and neighborhood order some properties previously known for just the binary nearest neighbor grf finally the authors illustrate how these properties can guide one s intuition about the types of grf patterns which are most likely to form

discriminative random fields in this research we address the problem of classification and labeling of regions given a single static natural image natural images exhibit strong spatial dependencies and modeling these dependencies in a principled manner is crucial to achieve good classification accuracy in this work we present discriminative random fields drfs to model spatial interactions in images in a discriminative framework based on the concept of conditional random fields proposed by lafferty et al 2001 the drfs classify image regions by incorporating neighborhood spatial interactions in the labels as well as the observed data the drf framework offers several advantages over the conventional markov random field mrf framework first the drfs allow to relax the strong assumption of conditional independence of the observed data generally used in the mrf framework for tractability this assumption is too restrictive for a large number of applications in computer vision second the drfs derive their classification power by exploiting the probabilistic discriminative models instead of the generative models used for modeling observations in the mrf framework third the interaction in labels in drfs is based on the idea of pairwise discrimination of the observed data making it data adaptive instead of being fixed a priori as in mrfs finally all the parameters in the drf model are estimated simultaneously from the training data unlike the mrf framework where the likelihood parameters are usually learned separately from the field parameters we present preliminary experiments with man made structure detection and binary image restoration tasks and compare the drf results with the mrf results

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

partial residual plots in generalized linear models abstract in this article we explore the structure and usefulness of partial residual plots as tools for visualizing curvature as a function of selected predictors x 2 in a generalized linear model glm where the vector of predictors x is partitioned as x t x t 1 x t 2 the glm extension of ceres plots is discussed but to a lesser extent the usefulness of these plots for obtaining a good visual impression of curvature may be limited by the specified glm the link function and the stochastic behavior of the predictors partial residual plots seem to work well when modeling is in a region where the conditional mean of the response given x stays well away from its extremes so that the link is essentially linear and e x 1 x 2 is linear in x 2 ceres plots however require only the first condition the behavior of these plots is contrasted with their behavior in additive error models

a segmentation model using compound markov random fields based on a boundary model markov random field mrf theory has been widely applied to the challenging problem of image segmentation in this paper we propose a new nontexture segmentation model using compound mrfs in which the original label mrf is coupled with a new boundary mrf to help improve the segmentation performance the boundary model is relatively general and does not need prior training on boundary patterns unlike some existing related work the proposed method offers a more compact interaction between label and boundary mrfs furthermore our boundary model systematically takes into account all the possible scenarios of a single edge existing in a 3times3 neighborhood and thus incorporates sophisticated prior information about the relation between label and boundary it is experimentally shown that the proposed model can segment objects with complex boundaries and at the same time is able to work under noise corruption the new method has been applied to medical image segmentation experiments on synthetic images and real clinical datasets show that the proposed model is able to produce more accurate segmentation results and satisfactorily keep the delicate boundary it is also less sensitive to noise in both high and low signal to noise ratio regions than some of the existing models in common use

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

exploring partial residual plots partial residual plots have a long history and judging from their prominence in the literature are frequently used in this article i explore the structure and usefulness of partial residual plots and augmented partial residual plots as basic tools for dealing with curvature as a function of selected covariates x 2 in regression problems in which the covariate vector x is partitioned as x t x 1 t x 2 t the usefulness of these plots for obtaining a good impression of curvature can depend on the behavior of the covariates through the conditional expectation e x 1 x 2 partial residual plots seem to perform best under linear conditional expectations augmented partial residual plots allow e x 1 x 2 to be a quadratic function of x 2 this development leads to a new class of plots called ceres plots that includes partial and augmented partial residual plots as special cases ceres plots may be useful for obtaining an impression of curvature as a function of x 2 when the conditional expectations

augmented partial residuals a simple way of encouraging a nonlinear effect in a regression model to show itself in a partial residual parres plot component plus residual plot is to include a single quadratic term in the regression it is computationally cheap to do this for each of the independent variables examples show that the resulting set of augmented partial residual plots gives insights that are not available from standard parres or added variable plots

an a contrario decision framework for region based motion detection the aim of motion detection is to decide whether a given part of an image belongs to a moving object or to the static background this paper proposes an automatic decision rule for the detection of moving regions the proposed framework is derived from a perceptual grouping principle namely the helmholtz principle this principle basically states that perceptually relevant events are perceived because they deviate from a model of complete randomness detections are then said to be performed a contrario moving regions appear as low probability events in a model corresponding to the absence of moving objects in the scene a careful design of the events considered under the hypothesis of absence of moving objects results in a general and robust motion detection algorithm no posterior parameter tuning is necessary furthermore a confidence level is attached to each detected region

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

singular perturbation results for a class of stochastic control problems composite control originally proposed in a deterministic context is generalized to the problem with white noise inputs however the approach used here is radically different from the deterministic approach presence of noise smoothes the system behavior and allows a more complete solution than in the deterministic case

fuzzy markov random fields versus chains for multispectral image segmentation this paper deals with a comparison of recent statistical models based on fuzzy markov random fields and chains for multispectral image segmentation the fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data in this framework we assume the dependence between bands and we express the general model for the covariance matrix a fuzzy markov chain model is developed in an unsupervised way this method is compared with the fuzzy markovian field model previously proposed by one of the authors the segmentation task is processed with bayesian tools such as the well known mpm mode of posterior marginals criterion our goal is to compare the robustness and rapidity for both methods fuzzy markov fields versus fuzzy markov chains indeed such fuzzy based procedures seem to be a good answer e g for astronomical observations when the patterns present diffuse structures moreover these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy to validate both models we perform and compare the segmentation on synthetic images and raw multispectral astronomical data