a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

multivariate product shot noise cox point process models we introduce a new multivariate product shot noise cox process which is useful for modeling multi species spatial point patterns with clustering intra specific interactions and neutral negative or positive inter specific interactions the auto and cross pair correlation functions of the process can be obtained in closed analytical forms and approximate simulation of the process is straightforward we use the proposed process to model interactions within and among five tree species in the barro colorado island plot

a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

periodicity directionality and randomness wold features for image modeling and retrieval one of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems in applications such as database retrieval it is important that image features used in pattern comparison provide good measures of image perceptual similarities we present an image model with a new set of features that address the challenge of perceptual similarity the model is based on the 2d wold decomposition of homogeneous random fields the three resulting mutually orthogonal subfields have perceptual properties which can be described as periodicity directionality and randomness approximating what are indicated to be the three most important dimensions of human texture perception the method presented improves upon earlier wold based models in its tolerance to a variety of local inhomogeneities which arise in natural textures and its invariance under image transformation such as rotation an image retrieval algorithm based on the new texture model is presented different types of image features are aggregated for similarity comparison by using a bayesian probabilistic approach the effectiveness of the wold model at retrieving perceptually similar natural textures is demonstrated in comparison to that of two other well known pattern recognition methods the wold model appears to offer a perceptually more satisfying measure of pattern similarity while exceeding the performance of these other methods by traditional pattern recognition criteria examples of natural scene wold texture modeling are also presented

a combined estimating function approach for fitting stationary point process models a composite likelihood technique based on pairwise contributions provides a computationally simple but potentially inefficient approach for fitting spatial point process models we propose a new estimation procedure that improves the efficiency our approach combines estimating functions derived from pairwise composite likelihood estimation and estimating functions that account for correlations among the pairwise contributions our method can be used to fit a variety of parametric spatial point process models and can yield more efficient estimators for the clustering parameters than pairwise composite likelihood estimation we demonstrate the efficacy of our proposed method through a simulation study and an application to the longleaf pine data

two step estimation for inhomogeneous spatial point processes summary the paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second order properties k function regression parameters are estimated by using a poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests

pairwise likelihood methods for inference in image models summary we consider parameter estimation for certain random set models for image data for the spatial models considered here a full likelihood based approach to this problem is often difficult since the likelihood generally cannot be computed for images of typical size this has motivated the consideration of various less computationally demanding parameter estimation techniques we discuss one method based on likelihoods for small subsets of the data consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach results of a simulation study are reported for some variants of the boolean model and excursion sets of random fields the methods are illustrated for some data on the spatial incidence of heather

going off grid computationally efficient inference for log gaussian cox processes this paper introduces a new method for performing computational inference on log gaussian cox processes the likelihood is approximated directly by making novel use of a continuously specified gaussian random field we show that for sufficiently smooth gaussian random field prior distributions the approximation can converge with arbitrarily high order while an approximation based on a counting process on a partition of the domain only achieves first order convergence the given results improve on the general theory of convergence of the stochastic partial differential equation models introduced by lindgren et al 2011 the new method is demonstrated on a standard point pattern data set and two interesting extensions to the classical log gaussian cox process framework are discussed the first extension considers variable sampling effort throughout the observation window and implements the method of chakraborty et al 2011 the second extension constructs a log gaussian cox process on the world s oceans the analysis is performed using integrated nested laplace approximation for fast approximate inference

an estimating function approach to inference for inhomogeneous neyman scott processes this article is concerned with inference for a certain class of inhomogeneous neyman scott point processes depending on spatial covariates regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the mother intensity for the neyman scott process tends to infinity clustering parameter estimates are obtained using minimum contrast estimation based on the k function the approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot

natural image statistics and low complexity feature selection low complexity feature selection is analyzed in the context of visual recognition it is hypothesized that high order dependences of bandpass features contain little information for discrimination of natural images this hypothesis is characterized formally by the introduction of the concepts of conjunctive interference and decomposability order of a feature set necessary and sufficient conditions for the feasibility of low complexity feature selection are then derived in terms of these concepts it is shown that the intrinsic complexity of feature selection is determined by the decomposability order of the feature set and not its dimension feature selection algorithms are then derived for all levels of complexity and are shown to be approximated by existing information theoretic methods which they consistently outperform the new algorithms are also used to objectively test the hypothesis of low decomposability order through comparison of classification performance it is shown that for image classification the gain of modeling feature dependencies has strongly diminishing returns best results are obtained under the assumption of decomposability order 1 this suggests a generic law for bandpass features extracted from natural images that the effect on the dependence of any two features of observing any other feature is constant across image classes

large deviations for the empirical field of a gibbs measure on applique le principe de contraction pour obtenir un principe de grande deviation pour la distribution des distributions empiriques on donne une description detaillee de la fonction de taux resultante

the hausdorff dimension of level sets described by erdos renyi average abstract let 0 1 and be an integer function defined on n 0 satisfying 1 n n define the level set e r x 0 1 lim n a n n x where a n n x is the n n erdos renyi average of x 0 1 in this paper we will give descriptions for the hausdorff dimension of e r under the assumption n as n which complement simultaneously an early classic result of besicovitch and the new strong law of large number established by p erdos and a renyi moreover for the case n m ultimately where m 1 is an integer the hausdorff dimension of e r is also determined by us in the last section

on consistent nonparametric intensity estimation for inhomogeneous spatial point processes a common nonparametric approach to estimate the intensity function of an inhomogeneous spatial point process is through kernel smoothing when conducting the smoothing one typically uses events only in a local set around the point of interest but the resulting estimator often is inconsistent because the number of events in a fixed set is of order 1 for spatial point processes in this article we propose a new covariate based kernel smoothing method to estimate the intensity function our method defines the distance between any two points as the difference between their associated covariate values consequently we determine the kernel weight for a given event of the process as a function of its new distance to the point of interest under some suitable conditions on the covariates and the spatial point process we prove that our new estimator is consistent for the true intensity to handle the situation with high dimensional covariates we also extend sliced inverse regression a useful dimension reduc

a kpss test for stationarity for spatial point processes we propose a formal method to test stationarity for spatial point processes the proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity we show that the resulting test statistic converges in distribution to a functional of a two dimensional brownian motion to conduct the test we compare the calculated statistic with the upper tail critical values of this functional our method requires only a weak dependence condition on the process but does not assume any parametric model for it as a result it can be applied to a wide class of spatial point process models we study the efficacy of the test through both simulations and applications to two real data examples that were previously suspected to be nonstationary based on graphical evidence our test formally confirmed the suspected nonstationarity for both data

recovering relative depth from low level features without explicit t junction detection and interpretation this work presents a novel computational model for relative depth order estimation from a single image based on low level local features that encode perceptual depth cues such as convexity concavity inclusion and t junctions in a quantitative manner considering information at different scales these multi scale features are based on a measure of how likely is a pixel to belong simultaneously to different objects interpreted as connected components of level sets and hence to be occluded in some of them providing a hint on the local depth order relationships they are directly computed on the discrete image data in an efficient manner without requiring the detection and interpretation of edges or junctions its behavior is clarified and illustrated for some simple images then the recovery of the relative depth order on the image is achieved by global integration of these local features applying a non linear diffusion filtering of bilateral type the validity of the proposed features and the integration approach is demonstrated by experiments on real images and comparison with state of the art monocular depth estimation techniques

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

residual analysis for spatial point processes with discussion summary we define residuals for point process models fitted to spatial point pattern data and we propose diagnostic plots based on them the residuals apply to any point process model that has a conditional intensity the model may exhibit spatial heterogeneity interpoint interaction and dependence on spatial covariates some existing ad hoc methods for model checking quadrat counts scan statistic kernel smoothed intensity and berman s diagnostic are recovered as special cases diagnostic tools are developed systematically by using an analogy between our spatial residuals and the usual residuals for non spatial generalized linear models the conditional intensity plays the role of the mean response this makes it possible to adapt existing knowledge about model validation for generalized linear models to the spatial point process context giving recommendations for diagnostic plots a plot of smoothed residuals against spatial location or against a spatial covariate is effective in diagnosing spatial trend or co variate effects q q plots of the residuals are effective in diagnosing interpoint interaction

on nonparametric variance estimation for second order statistics of inhomogeneous spatial point processes with a known parametric intensity form we introduce new variance estimation procedures for second order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes the statistics are defined either on a subset b of the observation window or on the whole window for the former we use subblocks that have the same size and shape as b as replicates of b in order to estimate the target variance for the latter we develop a subsampling estimator for a key component in the target variance and estimate its other components by method of moment methods under some suitable conditions we prove that the proposed variance estimators are consistent for the target variances in both cases simulations and an application to a real data example are used to demonstrate the usefulness of the proposed methods this article has supplementary material online

inference for clustered inhomogeneous spatial point processes summary we propose a method to test for significant differences in the levels of clustering between two spatial point processes cases and controls while taking into account differences in their first order intensities the key advance on earlier methods is that the controls are not assumed to be a poisson process inference and diagnostics are based around the inhomogeneous k function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach or simulating new events as in a parametric bootstrap methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest a simulation study briefly examines the accuracy and power of the inferential procedures

occlusion models for natural images a statistical study of a scale invariant dead leaves model we develop a scale invariant version of matheron s dead leaves model for the statistics of natural images the model takes occlusions into account and resembles the image formation process by randomly adding independent elementary shapes such as disks in layers we compare the empirical statistics of two large databases of natural images with the statistics of the occlusion model and find an excellent qualitative and good quantitative agreement at this point this is the only image model which comes close to duplicating the simplest elementary statistics of natural images such as the scale invariance property of marginal distributions of filter responses the full co occurrence statistics of two pixels and the joint statistics of pairs of haar wavelet responses

depth estimation from image structure in the absence of cues for absolute depth measurements as binocular disparity motion or defocus the absolute distance between the observer and a scene cannot be measured the interpretation of shading edges and junctions may provide a 3d model of the scene but it will not provide information about the actual scale of the space one possible source of information for absolute depth estimation is the image size of known objects however object recognition under unconstrained conditions remains difficult and unreliable for current computational approaches we propose a source of information for absolute depth estimation based on the whole scene structure that does not rely on specific objects we demonstrate that by recognizing the properties of the structures present in the image we can infer the scale of the scene and therefore its absolute mean depth we illustrate the interest in computing the mean depth of the scene with application to scene recognition and object detection

equivalence of maxent and poisson point process models for species distribution modeling in ecology summary modeling the spatial distribution of a species is a fundamental problem in ecology a number of modeling methods have been developed an extremely popular one being maxent a maximum entropy modeling approach in this article we show that maxent is equivalent to a poisson regression model and hence is related to a poisson point process model differing only in the intercept term which is scale dependent in maxent we illustrate a number of improvements to maxent that follow from these relations in particular a point process model approach facilitates methods for choosing the appropriate spatial resolution assessing model adequacy and choosing the lasso penalty parameter all currently unavailable to maxent the equivalence result represents a significant step in the unification of the species distribution modeling literature

exact convergence rate in the limit theorems of erdos renyi and shepp on considere le comportement asymptotique de u n sup o i n k s i k s i et on montre que le terme o k 1 2 peut etre remplace par o k 1 log k

a weighted estimating equation approach for inhomogeneous spatial point processes we introduce a new estimation method for parametric intensity function models of inhomogeneous spatial point processes based on weighted estimating equations the weights can incorporate information on both inhomogeneity and dependence of the process simulations show that significant efficiency gains can be achieved for non poisson processes compared to the poisson maximum likelihood estimator an application to tropical forest data illustrates the use of the proposed method

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

moment estimation for statistics from marked point processes in spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations in other words the data form a realization of a marked point process in this paper we formulate subsampling estimators of the moments of general statistics computed from marked point process data and we establish their l 2 consistency the variance estimator in particular can be used for the construction of confidence intervals for estimated parameters a practical data based method for choosing a subsampling parameter is given and illustrated on a data set finite sample simulation examples are also presented

aberrant crypt foci and semiparametric modeling of correlated binary data motivated by the spatial modeling of aberrant crypt foci acf in colon carcinogenesis we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent gaussian spatial process that accounts for short range dependencies the mean is modeled in a general way using regression splines the mean function can be viewed as a fixed effect and is estimated with a penalty for regularization with the latent process viewed as another random effect the model becomes a generalized linear mixed model in our motivating data set and other applications the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation reml so pairwise likelihood a special case of composite likelihood is used instead we develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications including but not limited to the problem that motivated this work the splines have penalty parameters that must converge to zero asymptotically we derive theory for this along with a data driven method for selecting the penalty parameter a method that is shown in simulations to improve greatly upon standard devices such as likelihood crossvalidation finally we apply the methods to the data from our experiment acf we discover an unexpected location for peak formation of acf

bivariate cox processes some models for bivariate spatial point patterns summary from certain points of view the range of probability models currently available for describing the joint behaviour of two point processes is rather limited in this paper we explore the structure of some further models and apply our results to the statistical analysis of bivariate spatial point patterns in many branches of science there is interest in the study and description of data which represent the locations of objects as points in an essentially planar region in the present paper we assume that the objects are of two qualitatively distinguishable types and refer to the data as a bivariate spatial point pattern a statistical analysis of such data should seek to provide some meaningful summary descriptions of the separate point patterns for each of the two types of object and of any possible inter relationship between these two patterns for example fig 1 shows the locations of 173 newly emergent and 155 1 year old bramnble 0 a a tv t to 0 x t

depth analogy data driven approach for single image depth estimation using gradient samples inferring scene depth from a single monocular image is a highly ill posed problem in computer vision this paper presents a new gradient domain approach called depth analogy that makes use of analogy as a means for synthesizing a target depth field when a collection of rgb d image pairs is given as training data specifically the proposed method employs a non parametric learning process that creates an analogous depth field by sampling reliable depth gradients using visual correspondence established on training image pairs unlike existing data driven approaches that directly select depth values from training data our framework transfers depth gradients as reconstruction cues which are then integrated by the poisson reconstruction the performance of most conventional approaches relies heavily on the training rgb d data used in the process and such a dependency severely degenerates the quality of reconstructed depth maps when the desired depth distribution of an input image is quite different from that of the training data e g outdoor versus indoor scenes our key observation is that using depth gradients in the reconstruction is less sensitive to scene characteristics providing better cues for depth recovery thus our gradient domain approach can support a great variety of training range datasets that involve substantial appearance and geometric variations the experimental results demonstrate that our depth gradient domain approach outperforms existing data driven approaches directly working on depth domain even when only uncorrelated training datasets are available

sufficient dimension reduction for spatial point processes directed by gaussian random fields summary we develop a sufficient dimension reduction paradigm for inhomogeneous spatial point processes driven by gaussian random fields specifically we introduce the notion of the kth order central intensity subspace we show that a central subspace can be defined as the combination of all central intensity subspaces for many commonly used spatial point process models we find that the central subspace is equivalent to the first order central intensity subspace to estimate the latter we propose a flexible framework under which most existing benchmark inverse regression methods can be extended to the spatial point process setting we develop novel graphical and formal testing methods to determine the structural dimension of the central subspace these methods are extremely versatile in that they do not require any specific model assumption on the correlation structures of the covariates and the spatial point process to illustrate the practical use of the methods proposed we apply them to both simulated data and two real examples

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

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

multiple depth layers and all in focus image generations by blurring and deblurring operations the depth map and all in focus generations from a single image are proposed the depth map bases on the characteristic curve of coc vs the depth characteristic curve of a camera all in focus image generation is from the estimated depth map a joint deblurring process is proposed to generate an all in focus image in this work we propose novel methods for the generation of multiple depth layers and all in focus images multiple depth layers are produced by applying a sequence of blurring and deblurring operations to determine the depth the proposed method makes no assumptions with regard to the properties of the scene in resolving depth ambiguity in complex images we also developed a method by which to generate all in focus images in which the sharpness is preserved and instabilities imposed by conventional deblurring operations largely eliminated this method involves updating outliers for which depth was over estimated while compensating for errors in the estimation of depth imposed by deblurring

the erdos renyi strong law for pattern matching with a given proportion of mismatches 1 informal introduction the erdos bnyi law erdijs and r6nyi 1970 l for coin tossing is a strong law for the behavior of the length of long success rich runs for the length r of the longest run of pure heads in n tosses the result is that with probability l lin rjlog n 1 where p flheads 0 a more general result is quoted as formula 1 in section 2 for rz the longest head rich run in which the fraction of heads is at least a p note that r ri in many practical situations such as manufacturing or roulette observations are taken sequentially and each can be classified as success or failure for these cases it is possible to use the erdijs wnyi law to test the hypothesis that the success probability is p from another point of view the erdijs bnyi law can be used to recognize patterns of unusually long runs of succe88e8 or failures our interest is in the recognition of unusually long patterns or words common to two random sequences the patterns are unknown prior to an examination of the sequences the motivation for this work is the comparison of dna sequences which can be modeled as sequences of i i d or markov distributed letters evolution operates to conserve although imperfectly patterns important to biological function it is a task of biology to discover these patterns and their function in earlier work we generalized the erdiie bnyi law for pure head runs a 1 to exact matching patterns between two sequences in this paper we extend those results to include matchings of quality a between p and 1 the examples below illustrate the natural analogs of rz studied in this paper two words form a quality a matching if they have the same length and the

large deviations and maximum entropy principle for interacting random fields on mathbb z d we present a new approach to the principle of large deviations for the empirical field of a gibbsian random field on the integer lattice zd this approach has two main features first we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities and thus obtain estimates which are finer and more widely applicable second we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field the limits being those predicted by the maximum entropy principle this result implies a general version of the equivalence of gibbs ensembles stating that every microcanonical limiting state is a grand canonical equilibrium state we also prove a converse to the last statement and discuss some applications 0 introduction as is well known the study of the asymptotic probabilities of large fluctuations of time averages or space averages away from the mean is based on two fundamental principles the principle of large deviations and the maximum entropy principle the former provides the exact rate of exponential decay of the fluctuation probabilities whereas the latter predicts the limiting conditional distribution under the condition that the fluctuations are large it is obvious that these principles are intimately related in this paper we investigate these principles in the case of interacting random fields on the integer lattice 7zd the setup is the following first we let e 4 be any measurable space we shall assume throughout that e a is standard borel but we shall avoid making any explicit topological assumptions on e so we do not assume that e is polish next we let s zd be the d dimensional integer lattice and q f e gas the associated product space in lattice models of statistical mechanics e is called the state space or single spin space and q f the configuration space we let j s f denote the set of all probability

estimating functions for inhomogeneous spatial point processes with incomplete covariate data the r package spatstat provides a very flexible and useful framework for analysing spatial point patterns a fundamental feature is a procedure for fitting spatial point process models depending on covariates however in practice one often faces incomplete observation of the covariates and this leads to parameter estimation error which is difficult to quantify in this paper we introduce a monte carlo version of the estimating function used in spatstat for fitting inhomogeneous poisson processes and certain inhomogeneous cluster processes for this modified estimating function it is feasible to obtain the asymptotic distribution of the parameter estimators in the case of incomplete covariate information this allows a study of the loss of efficiency due to the missing covariate data

shape from texture using local spectral moments presents a non feature based solution to the problem of computing the shape of curved surfaces from texture information first the use of local spatial frequency spectra and their moments to describe texture is discussed and motivated a new more accurate method for measuring the local spatial frequency moments of an image texture using gabor elementary functions and their derivatives is presented also described is a technique for separating shading from texture information which makes the shape from texture algorithm robust to the shading effects found in real imagery second a detailed model for the projection of local spectra and spectral moments of any surface reflectance patterns not just textures is developed third the conditions under which the projection model can be solved for the orientation of the surface at each point are explored unlike earlier non feature based curved surface shape from texture approaches the assumption that the surface texture is isotropic is not required surface texture homogeneity can be assumed instead the algorithm s ability to operate on anisotropic and nondeterministic textures and on both smooth and rough textured surfaces is demonstrated

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

semi parametric multinomial logistic regression for multivariate point pattern data we propose a new method for analysis of multivariate point pattern data observed in a heterogeneous environment and with complex intensity functions we suggest semi parametric models for the inten

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

recognition without correspondence using multidimensionalreceptive field histograms the appearance of an object is composed of local structure this local structure can be described and characterized by a vector of local features measured by local operators such as gaussian derivatives or gabor filters this article presents a technique where appearances of objects are represented by the joint statistics of such local neighborhood operators as such this represents a new class of appearance based techniques for computer vision based on joint statistics the paper develops techniques for the identification of multiple objects at arbitrary positions and orientations in a cluttered scene experiments show that these techniques can identify over 100 objects in the presence of major occlusions most remarkably the techniques have low complexity and therefore run in real time

characteristics of natural scenes related to the fractal dimension many objects in images of natural scenes are so complex and erratic that describing them by the familiar models of classical geometry is inadequate in this paper we exploit the power of fractal geometry to generate global characteristics of natural scenes in particular we are concerned with the following two questions 1 can we develop a measure which can distinguish between different global backgrounds e g mountains and trees and 2 can we develop a measure that is sensitive to change in distance or scale we present a model based on fractional brownian motion which will allow us to recover two characteristics related to the fractal dimension from silhouettes the first characteristic is an estimate of the fractal dimension based on a least squares linear fit we show that this feature is stable under a variety of real image conditions and use it to distinguish silhouettes of trees from silhouettes of mountains next we introduce a new theoretical concept called the average holder constant and relate it mathematically to the fractal dimension it is shown that this measurement is sensitive to scale in a predictable manner and hence provides the potential for use as a range indicator corroborating experimental results are presented

a thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns when modeling inhomogeneous spatial point patterns it is of interest to fit a parametric model for the first order intensity function foif of the process in terms of some measured covariates estimates for the regression coefficients say can be obtained by maximizing a poisson maximum likelihood criterion little work has been done on the asymptotic distribution of except in some special cases in this article we show that is asymptotically normal for a general class of mixing processes to estimate the variance of we propose a novel thinned block bootstrap procedure that assumes that the point process is second order reweighted stationary to apply this procedure only the foif and not any high order terms of the process needs to be estimated we establish the consistency of the resulting variance estimator and demonstrate its efficacy through simulations and an application to a real data example

color constancy using 3d scene geometry derived from a single image the aim of color constancy is to remove the effect of the color of the light source as color constancy is inherently an ill posed problem most of the existing color constancy algorithms are based on specific imaging assumptions e g gray world and white patch assumption in this paper 3d geometry models are used to determine which color constancy method to use for the different geometrical regions depth layer found in images the aim is to classify images into stages rough 3d geometry models according to stage models images are divided into stage regions using hard and soft segmentation after that the best color constancy methods are selected for each geometry depth to this end we propose a method to combine color constancy algorithms by investigating the relation between depth local image statistics and color constancy image statistics are then exploited per depth to select the proper color constancy method our approach opens the possibility to estimate multiple illuminations by distinguishing nearby light source from distant illuminations experiments on state of the art data sets show that the proposed algorithm outperforms state of the art single color constancy algorithms with an improvement of almost 50 of median angular error when using a perfect classifier i e all of the test images are correctly classified into stages the performance of the proposed method achieves an improvement of 52 of the median angular error compared with the best performing single color constancy algorithm

on the voronoi estimator for the intensity of an inhomogeneous planar poisson process summary the voronoi estimator may be defined for any location as the inverse of the area of the corresponding voronoi cell we investigate the statistical properties of this estimator for the intensity of an inhomogeneous poisson process and demonstrate it is approximately unbiased with a gamma sampling distribution we also introduce the centroidal voronoi estimator a simple extension based on spatial regularization of the point pattern simulations show the voronoi estimator has remarkably low bias while the centroidal voronoi estimator has slightly more bias but much less variability the performance is compared to kernel estimators using two simulated data sets and a dataset consisting of earthquakes within the continental united states

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

quasi likelihood for spatial point processes fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates when cox or cluster process models are used to accommodate clustering not accounted for by the available covariates likelihood based inference becomes computationally cumbersome due to the complicated nature of the likelihood function and the associated score function it is therefore of interest to consider alternative more easily computable estimating functions we derive the optimal estimating function in a class of first order estimating functions the optimal estimating function depends on the solution of a certain fredholm integral equation which in practise is solved numerically the derivation of the optimal estimating function has close similarities to the derivation of quasi likelihood for standard data sets the approximate solution is further equivalent to a quasi likelihood score for binary spatial data we therefore use the term quasi likelihood for our optimal estimating function approach we demonstrate in a simulation study and a data example that our quasi likelihood method for spatial point processes is both statistically and computationally efficient

on least squares fitting for stationary spatial point processes summary the k function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability in this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the k function by using subsampling we demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures this is done through asymptotic theory simulation experiments and an application to a data set on long leaf pine trees

window subsampling of estimating functions with application to regression models abstract we propose a subsampling method for estimating the asymptotic standard error of a statistic n that is the solution to an estimating equation 1 n n j 1 uj y j xj 0 where the data yj may be temporally or spatially correlated and the estimating function may depend on covariates xj a key statistic that we consider in detail is a generalized linear model regression coefficient computed under the assumption of independence the availability of a consistent variance estimator allows semiparametric regression approaches for clustered and longitudinal data to be used with time series and spatial data the methods that we develop extend the subsampling ideas of carlstein sherman and garcia soidan and hall to estimating functions our approach provides an attractive alternative to the jackknife method of lele particularly for large datasets because we do not require parameter reestimation

a composite likelihood approach in fitting spatial point process models we propose a new likelihood based approach in fitting spatial point process models a composite likelihood is first formed by adding some pairwise composite likelihood functions that are defined in terms of the second order intensity function of the underlying process and then used for estimating the unknown parameters the estimation procedure is computationally simple and yields consistent and asymptotically normal estimators under some mild conditions we demonstrate through a simulation study and applications to two real data examples that the proposed approach may lead to improved estimations compared with the commonly used minimum contrast estimation approach

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

bayesian semiparametric intensity estimation for inhomogeneous spatial point processes summary in this work we propose a fully bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process the basic idea is to first convert intensity estimation into a poisson regression setting via binning data points on a regular grid and then model the log intensity semiparametrically using an adaptive version of gaussian markov random fields to smooth the corresponding counts the inference is carried by an efficient markov chain monte carlo simulation algorithm compared to existing methods for intensity estimation for example parametric modeling and kernel smoothing the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates but also uses information from the data to adaptively determine the amount of smoothing at the local level the effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

monocular depth ordering using t junctions and convexity occlusion cues this paper proposes a system that relates objects in an image using occlusion cues and arranges them according to depth the system does not rely on a priori knowledge of the scene structure and focuses on detecting special points such as t junctions and highly convex contours to infer the depth relationships between objects in the scene the system makes extensive use of the binary partition tree as hierarchical region based image representation jointly with a new approach for candidate t junction estimation since some regions may not involve t junctions occlusion is also detected by examining convex shapes on region boundaries combining t junctions and convexity leads to a system which only relies on low level depth cues and does not rely on semantic information however it shows a similar or better performance with the state of the art while not assuming any type of scene as an extension of the automatic depth ordering system a semi automatic approach is also proposed if the user provides the depth order for a subset of regions in the image the system is able to easily integrate this user information to the final depth order for the complete image for some applications user interaction can naturally be integrated improving the quality of the automatically generated depth map

on the central limit theorem for stationary mixing random fields a simple proof of a central limit theorem for stationary random fields under mixing conditions is given generalizing some results obtained by more complicated methods e g bernstein s method

the cylindrical k function and poisson line cluster point processes the analysis of point patterns with linear structures is of interest in many applications to detect anisotropy in such patterns in particular in the case of a columnar structure we introduce a functional summary statistic the cylindrical k function which is a directional k function whose structuring element is a cylinder we further introduce a class of anisotropic cox point processes called poisson line cluster point processes the points of such a process are random displacements of poisson point processes defined on the lines of a poisson line process parameter estimation for this model based on moment methods or bayesian inference is discussed in the case where the underlying poisson line process is latent to illustrate the proposed methods we analyse two and three dimensional point pattern datasets the three dimensional dataset is of particular interest as it relates to the minicolumn hypothesis in neuroscience which claims that pyramidal and other brain cells have a columnar arrangement perpendicular to the surface of the brain

erdős renyi laws for gibbs measures can one detect a phase transition from a single large sample of a gibbs measure what information does one get on the other gibbs distributions with the same potential we approach these questions via erd s renyi laws in particular we prove almost sure limit theorems for sets of empirical distributions of sub samples of the given one for suitable sub samples size this set converges to the set of stationary gibbs measures moreover we formulate erd s renyi laws for general families of random variables with suitable large deviation principles