infinitely divisible cascades to model the statistics of natural images we propose to model the statistics of natural images thanks to the large class of stochastic processes called infinitely divisible cascades idcs idcs were first introduced in one dimension to provide multifractal time series to model the so called intermittency phenomenon in hydrodynamical turbulence we have extended the definition of scalar idcs from one to n dimensions and commented on the relevance of such a model in fully developed turbulence in 1 in this paper we focus on the particular 2d case idcs appear as good candidates to model the statistics of natural images they share most of their usual properties and appear to be consistent with several independent theoretical and experimental approaches of the literature we point out the interest of idcs for applications to procedural texture synthesis

graph theoretical clustering based on limited neighbourhood sets abstract a method for clustering data according to a visual model of clusters is proposed the method uses either of two graphs which are defined according to relative distance and based on the gabriel graph and the relative neighbourhood graph respectively the method is locally sensitive hierarchic and based on the concept of limited neighbourhood sets clusters that are either disjoint or homogeneous and separable by sharp changes in point density may be detected

multiregion image segmentation by parametric kernel graph cuts the purpose of this study is to investigate multiregion graph cut image partitioning via kernel mapping of the image data the image data is transformed implicitly by a kernel function so that the piecewise constant model of the graph cut formulation becomes applicable the objective function contains an original data term to evaluate the deviation of the transformed data within each segmentation region from the piecewise constant model and a smoothness boundary preserving regularization term the method affords an effective alternative to complex modeling of the original image data while taking advantage of the computational benefits of graph cuts using a common kernel function energy minimization typically consists of iterating image partitioning by graph cut iterations and evaluations of region parameters via fixed point computation a quantitative and comparative performance assessment is carried out over a large number of experiments using synthetic grey level data as well as natural images from the berkeley database the effectiveness of the method is also demonstrated through a set of experiments with real images of a variety of types such as medical synthetic aperture radar and motion maps

images as occlusions of textures a framework for segmentation we propose a new mathematical and algorithmic framework for unsupervised image segmentation which is a critical step in a wide variety of image processing applications we have found that most existing segmentation methods are not successful on histopathology images which prompted us to investigate segmentation of a broader class of images namely those without clear edges between the regions to be segmented we model these images as occlusions of random images which we call textures and show that local histograms are a useful tool for segmenting them based on our theoretical results we describe a flexible segmentation framework that draws on existing work on nonnegative matrix factorization and image deconvolution results on synthetic texture mosaics and real histology images show the promise of the method

image restoration by matching gradient distributions the restoration of a blurry or noisy image is commonly performed with a map estimator which maximizes a posterior probability to reconstruct a clean image from a degraded image a map estimator when used with a sparse gradient image prior reconstructs piecewise smooth images and typically removes textures that are important for visual realism we present an alternative deconvolution method called iterative distribution reweighting idr which imposes a global constraint on gradients so that a reconstructed image should have a gradient distribution similar to a reference distribution in natural images a reference distribution not only varies from one image to another but also within an image depending on texture we estimate a reference distribution directly from an input image for each texture segment our algorithm is able to restore rich mid frequency textures a large scale user study supports the conclusion that our algorithm improves the visual realism of reconstructed images compared to those of map estimators

perfect simulation in stochastic geometry simulation plays an important role in stochastic geometry and related fields because all but the simplest random set models tend to be intractable to analysis many simulation algorithms deliver approximate samples of such random set models for example by simulating the equilibrium distribution of a markov chain such as a spatial birth and death process the samples usually fail to be exact because the algorithm simulates the markov chain for a long but finite time and thus convergence to equilibrium is only approximate the seminal work by propp and wilson made an important contribution to simulation by proposing a coupling method coupling from the past cftp which delivers perfect that is to say exact simulations of markov chains in this paper we introduce this new idea of perfect simulation and illustrate it using two common models in stochastic geometry the dead leaves model and a boolean model conditioned to cover a finite set of points

feature based image analysis according to marr s paradigm of computational vision the first process is an extraction of relevant features the goal of this paper is to quantify and characterize the information carried by features using image structure measured at feature points to reconstruct images in this way we indirectly evaluate the concept of feature based image analysis the main conclusions are that i a reasonably low number of features characterize the image to such a high degree that visually appealing reconstructions are possible ii different feature types complement each other and all carry important information the strategy is to define metamery classes of images and examine the information content of a canonical least informative representative of this class algorithms for identifying these are given finally feature detectors localizing the most informative points relative to different complexity measures derived from models of natural image statistics are given

detection of image structures using the fisher information and the rao metric in many detection problems the structures to be detected are parameterized by the points of a parameter space if the conditional probability density function for the measurements is known then detection can be achieved by sampling the parameter space at a finite number of points and checking each point to see if the corresponding structure is supported by the data the number of samples and the distances between neighboring samples are calculated using the rao metric on the parameter space the rao metric is obtained from the fisher information which is in turn obtained from the conditional probability density function an upper bound is obtained for the probability of a false detection the calculations are simplified in the low noise case by making an asymptotic approximation to the fisher information an application to line detection is described expressions are obtained for the asymptotic approximation to the fisher information the volume of the parameter space and the number of samples the time complexity for line detection is estimated an experimental comparison is made with a hough transform based method for detecting lines

shape from sharp and motion blurred image pair motion blur due to camera shake is a common occurrence during image capture the apparent motion of a scene point in the image plane varies according to both camera motion and scene structure our objective is to infer the camera motion and the depth map of static scenes using motion blur as a cue to this end we use an unblurred blurred image pair initially we develop a technique to estimate the transformation spread function tsf which symbolizes the camera shake this technique uses blur kernels estimated at different points across the image based on the estimated tsf we recover the complete depth map of the scene within a regularization framework

analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near ideal estimation performance in various asymptotic frameworks however image processing practice has shown that universal thresholding methods are outperformed by simple bayesian estimators assuming independent wavelet coefficients and heavy tailed priors such as generalized gaussian distributions ggds in this paper we investigate various connections between shrinkage methods and maximum a posteriori map estimation using such priors in particular we state a simple condition under which map estimates are sparse we also introduce a new family of complexity priors based upon rissanen s universal prior on integers one particular estimator in this class outperforms conventional estimators based on earlier applications of the minimum description length mdl principle we develop analytical expressions for the shrinkage rules implied by ggd and complexity priors this allows us to show the equivalence between universal hard thresholding map estimation using a very heavy tailed ggd and mdl estimation using one of the new complexity priors theoretical analysis supported by numerous practical experiments shows the robustness of some of these estimates against mis specifications of the prior a basic concern in image processing applications

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

effective solution of qualitative interval constraint problems abstract we present a fast algorithm for solving qualitative interval constraint problems which returns solutions of random problems in less than half a second on average with the hardest problem taking only half a minute on a risc workstation this is a surprising result considering the problem is np complete the fast solution time is attributed to the extraordinary pruning power of the path consistency computation and to the fact that all our randomly generated interval networks of size 14 were found to be inconsistent which is rapidly detected by a path consistency computation while inconsistency is relatively easy to prove our algorithm also solves large consistent networks with 100 edges we conclude that our algorithm suffices for solving qualitative interval constraint problems in practice other conclusions are that path consistency reduces the solution search to an almost linear selection of atomic labels and that path consistency is by itself an excellent consistency heuristic for random networks with fewer than 6 or more than 15 nodes

joint ndt image restoration and segmentation using gauss markov potts prior models and variational bayesian computation in this paper we propose a method to simultaneously restore and to segment piecewise homogeneous images degraded by a known point spread function psf and additive noise for this purpose we propose a family of nonhomogeneous gauss markov fields with potts region labels model for images to be used in a bayesian estimation framework the joint posterior law of all the unknowns the unknown image its segmentation hidden variable and all the hyperparameters is approximated by a separable probability law via the variational bayes technique this approximation gives the possibility to obtain practically implemented joint restoration and segmentation algorithm we will present some preliminary results and comparison with a mcmc gibbs sampling based algorithm we may note that the prior models proposed in this work are particularly appropriate for the images of the scenes or objects that are composed of a finite set of homogeneous materials this is the case of many images obtained in nondestructive testing ndt applications

a stochastic method for bayesian estimation of hidden markov random field models with application to a color model we propose a new stochastic algorithm for computing useful bayesian estimators of hidden markov random field hmrf models that we call exploration selection estimation ese procedure the algorithm is based on an optimization algorithm of o francois called the exploration selection e s algorithm the novelty consists of using the a posteriori distribution of the hmrf as exploration distribution in the e s algorithm the ese procedure computes the estimation of the likelihood parameters and the optimal number of region classes according to global constraints as well as the segmentation of the image in our formulation the total number of region classes is fixed but classes are allowed or disallowed dynamically this framework replaces the mechanism of the split and merge of regions that can be used in the context of image segmentation the procedure is applied to the estimation of a hmrf color model for images whose likelihood is based on multivariate distributions with each component following a beta distribution meanwhile a method for computing the maximum likelihood estimators of beta distributions is presented experimental results performed on 100 natural images are reported we also include a proof of convergence of the e s algorithm in the case of nonsymmetric exploration graphs

patchmatch filter edge aware filtering meets randomized search for visual correspondence though many tasks in computer vision can be formulated elegantly as pixel labeling problems a typical challenge discouraging such a discrete formulation is often due to computational efficiency recent studies on fast cost volume filtering based on efficient edge aware filters provide a fast alternative to solve discrete labeling problems with the complexity independent of the support window size however these methods still have to step through the entire cost volume exhaustively which makes the solution speed scale linearly with the label space size when the label space is huge or even infinite which is often the case for subpixel accurate stereo and optical flow estimation their computational complexity becomes quickly unacceptable developed to search approximate nearest neighbors rapidly the patchmatch method can significantly reduce the complexity dependency on the search space size but its pixel wise randomized search and fragmented data access within the 3d cost volume seriously hinder the application of efficient cost slice filtering this paper presents a generic and fast computational framework for general multi labeling problems called patchmatch filter pmf we explore effective and efficient strategies to weave together these two fundamental techniques developed in isolation i e patchmatch based randomized search and efficient edge aware image filtering by decompositing an image into compact superpixels we also propose superpixel based novel search strategies that generalize and improve the original patchmatch method further motivated to improve the regularization strength we propose a simple yet effective cross scale consistency constraint which handles labeling estimation for large low textured regions more reliably than a single scale pmf algorithm focusing on dense correspondence field estimation in this paper we demonstrate pmf s applications in stereo and optical flow our pmf methods achieve top tier correspondence accuracy but run much faster than other related competing methods often giving over 10 100 times speedup

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

a multisize superpixel approach for salient object detection based on multivariate normal distribution estimation this paper presents a new method for salient object detection based on a sophisticated appearance comparison of multisize superpixels those superpixels are modeled by multivariate normal distributions in cie lab color space which are estimated from the pixels they comprise this fitting facilitates an efficient application of the wasserstein distance on the euclidean norm formula see text to measure perceptual similarity between elements saliency is computed in two ways on the one hand we compute global saliency by probabilistically grouping visually similar superpixels into clusters and rate their compactness on the other hand we use the same distance measure to determine local center surround contrasts between superpixels then an innovative locally constrained random walk technique that considers local similarity between elements balances the saliency ratings inside probable objects and background the results of our experiments show the robustness and efficiency of our approach against 11 recently published state of the art saliency detection methods on five widely used benchmark data sets

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

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

label information guided graph construction for semi supervised learning in the literature most existing graph based semi supervised learning methods only use the label information of observed samples in the label propagation stage while ignoring such valuable information when learning the graph in this paper we argue that it is beneficial to consider the label information in the graph learning stage specifically by enforcing the weight of edges between labeled samples of different classes to be zero we explicitly incorporate the label information into the state of the art graph learning methods such as the low rank representation lrr and propose a novel semi supervised graph learning method called semi supervised low rank representation this results in a convex optimization problem with linear constraints which can be solved by the linearized alternating direction method though we take lrr as an example our proposed method is in fact very general and can be applied to any self representation graph learning methods experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data and therefore is more effective for semi supervised learning tasks

learning probabilistic models for contour completion in natural images using a large set of human segmented natural images we study the statistics of region boundaries we observe several power law distributions which likely arise from both multi scale structure within individual objects and from arbitrary viewing distance accordingly we develop a scale invariant representation of images from the bottom up using a piecewise linear approximation of contours and constrained delaunay triangulation to complete gaps we model curvilinear grouping on top of this graphical geometric structure using a conditional random field to capture the statistics of continuity and different junction types quantitative evaluations on several large datasets show that our contour grouping algorithm consistently dominates and significantly improves on local edge detection

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

fusion of hidden markov random field models and its bayesian estimation in this paper we present a hidden markov random field hmrf data fusion model the proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into julesz ensembles the corresponding exploration selection estimation ese procedure for the estimation of the parameters is presented this method achieves the estimation of the parameters of the gaussian kernels the mixture proportions the region labels the number of regions and the markov hyper parameter meanwhile we present a new proof of the asymptotic convergence of the ese procedure based on original finite time bounds for the rate of convergence

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

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

a novel approach to fruc using discriminant saliency and frame segmentation motion compensated frame interpolation mcfi is a technique used extensively for increasing the temporal frequency of a video sequence in order to obtain a high quality interpolation the motion field between frames must be well estimated however many current techniques for determining the motion are prone to errors in occlusion regions as well as regions with repetitive structure we propose an algorithm for improving both the objective and subjective quality of mcfi by refining the motion vector field we first utilize a discriminant saliency classifier to determine which regions of the motion field are most important to a human observer these regions are refined using a multistage motion vector refinement mvr which promotes motion vector candidates based upon their likelihood given a local neighborhood for regions which fall below the saliency threshold a frame segmentation is used to locate regions of homogeneous color and texture via normalized cuts motion vectors are promoted such that each homogeneous region has a consistent motion experimental results demonstrate an improvement over previous frame rate up conversion fruc methods in both objective and subjective picture quality

iterative kernel principal component analysis for image modeling in recent years kernel principal component analysis kpca has been suggested for various image processing tasks requiring an image model such as e g denoising or compression the original form of kpca however can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed we therefore propose a new iterative method for performing kpca the kernel hebbian algorithm which iteratively estimates the kernel principal components with only linear order memory complexity in our experiments we compute models for complex image classes such as faces and natural images which require a large number of training examples the resulting image models are tested in single frame super resolution and denoising applications the kpca model is not specifically tailored to these tasks in fact the same model can be used in super resolution with variable input resolution or denoising with unknown noise characteristics in spite of this both super resolution and denoising performance are comparable to existing methods

blobworld image segmentation using expectation maximization and its application to image querying retrieving images from large and varied collections using image content as a key is a challenging and important problem we present a new image representation that provides a transformation from the raw pixel data to a small set of image regions that are coherent in color and texture this blobworld representation is created by clustering pixels in a joint color texture position feature space the segmentation algorithm is fully automatic and has been run on a collection of 10 000 natural images we describe a system that uses the blobworld representation to retrieve images from this collection an important aspect of the system is that the user is allowed to view the internal representation of the submitted image and the query results similar systems do not offer the user this view into the workings of the system consequently query results from these systems can be inexplicable despite the availability of knobs for adjusting the similarity metrics by finding image regions that roughly correspond to objects we allow querying at the level of objects rather than global image properties we present results indicating that querying for images using blobworld produces higher precision than does querying using color and texture histograms of the entire image in cases where the image contains distinctive objects

lie group method for unsteady flows in a semi infinite expanding or contracting pipe with injection or suction through a porous wall the unsteady incompressible laminar flow in a semi infinite porous circular pipe with injection or suction through the pipe wall whose radius varies with time is considered the present analysis simulates the flow field by the burning of inner surface of cylindrical grain in a solid rocket motor in which the burning surface regresses with time we apply lie group method for determining symmetry reductions of partial differential equations lie group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant then the determining equations are derived ibragimov elementary lie group analysis and ordinary differential equations wiley new york 1999 hydon symmetry methods for differential equations cambridge university press cambridge 2000 olver applications of lie groups to differential equations springer new york 1986 seshadri na group invariance in engineering boundary value problems springer new york 1985 yi fengxiang lie symmetries of mechanical systems with unilateral holonomic constraints chinese sci bull 45 2000 1354 1358 moritz schwalm uherka finding lie groups that reduce the order of discrete dynamical systems j phys a math 31 1998 7379 7402 nucci clarkson the nonclassical method is more general than the direct method for symmetry reductions an example of the fitzhugh nagumo equation phys lett a 164 1992 49 56 basarab lahno group classification of nonlinear partial differential equations a new approach to resolving the problem proceedings of institute of mathematics of nas of ukraine vol 43 2002 pp 86 92 burde expanded lie group transformations and similarity reductions of differential equations proceedings of institute of mathematics of nas of ukraine vol 43 2002 pp 93 101 gandarias bruzon classical and nonclassical symmetries of a generalized boussinesq equation j nonlinear math phys 5 1998 8 12 hill solution of differential equations by means of one parameter groups pitman publishing co 1982 the determining equations are a set of linear differential equations the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables after the group has been determined a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system effect of the crossflow reynolds number re and the dimensionless wall expansion ratio on velocity flow streamlines axial and radial pressure drop and wall shear stress has been studied both analytically and numerically and the results are plotted

arc and path consistence revisited mackworth and freuder have analyzed the time complexity of several constraint satisfaction algorithms 5 we present here new algorithms for arc and path consistency and show that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms a refined solution for the path consistency problem is proposed however the space complexity of the path consistency algorithm makes it practicable only for small problems these algorithms are the result of the synthesis techniques used in image a general constraint satisfaction system and local consistency methods 3

image denoising by averaging of piecewise constant simulations of image partitions this paper investigates the problem of image denoising when the image is corrupted by additive white gaussian noise we herein propose a spatial adaptive denoising method which is based on an averaging process performed on a set of markov chain monte carlo simulations of region partition maps constrained to be spatially piecewise uniform i e constant in the grey level value sense for each estimated constant value regions for the estimation of these region partition maps we have adopted the unsupervised markovian framework in which parameters are automatically estimated in the least square sense this sequential averaging allows to obtain under our image model an approximation of the image to be recovered in the minimal mean square sense error the experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state of the art wavelet based denoising methods in benchmark tests

probabilistic framework for the characterization of surfaces and edges in range images with application to edge detection we develop a powerful probabilistic framework for the local characterization of surfaces and edges in range images we use the geometrical nature of the data to derive an analytic expression for the joint probability density function pdf for the random variables used to model the ranges of a set of pixels in a local neighborhood of an image we decompose this joint pdf by considering independently the cases where two real world points corresponding to two neighboring pixels are locally on the same real world surface or not in particular we show that this joint pdf is linked to the voigt pdf and not to the gaussian pdf as it is assumed in some applications we apply our framework to edge detection and develop a locally adaptive algorithm that is based on a probabilistic decision rule we show in an objective evaluation that this new edge detector performs better than prior art edge detectors this proves the benefits of the probabilistic characterization of the local neighborhood as a tool to improve applications that involve range images

enhanced figure ground classification with background prior propagation we present an adaptive figure ground segmentation algorithm that is capable of extracting foreground objects in a generic environment starting from an interactively assigned background mask an initial background prior is defined and multiple soft label partitions are generated from different foreground priors by progressive patch merging these partitions are fused to produce a foreground probability map the probability map is then binarized via threshold sweeping to create multiple hard label candidates a set of segmentation hypotheses is formed using different evaluation scores from this set the hypothesis with maximal local stability is propagated as the new background prior and the segmentation process is repeated until convergence similarity voting is used to select a winner set and the corresponding hypotheses are fused to yield the final segmentation result experiments indicate that our method performs at or above the current state of the art on several data sets with particular success on challenging scenes that contain irregular or multiple connected foregrounds

symmetry groups and similarity solutions for the system of equations for a viscous compressible fluid here using lie group transformations we consider the problem of finding similarity solutions to the system of partial differential equations pdes governing one dimensional unsteady motion of a compressible fluid in the presence of viscosity and thermal conduction using the general form of the equation of state the symmetry groups admitted by the governing system of pdes are obtained and the complete lie algebra of infinitesimal symmetries is established indeed with the use of the entailed similarity solution the problem is transformed to a system of ordinary differential equations odes which in general is nonlinear in some cases it is possible to solve these odes to determine some special exact solutions

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

statistics of natural stochastic textures and their application in image denoising natural stochastic textures nsts characterized by their fine details are prone to corruption by artifacts introduced during the image acquisition process by the combined effect of blur and noise while many successful algorithms exist for image restoration and enhancement the restoration of natural textures and textured images based on suitable statistical models has yet to be further improved we examine the statistical properties of nst using three image databases we show that the gaussian distribution is suitable for many nst while other natural textures can be properly represented by a model that separates the image into two layers one of these layers contains the structural elements of smooth areas and edges while the other contains the statistically gaussian textural details based on these statistical properties an algorithm for the denoising of natural images containing nst is proposed using patch based fractional brownian motion model and regularization by means of anisotropic diffusion it is illustrated that this algorithm successfully recovers both missing textural details and structural attributes that characterize natural images the algorithm is compared with classical as well as the state of the art denoising algorithms

a bottom up approach for pancreas segmentation using cascaded superpixels and deep image patch labeling robust organ segmentation is a prerequisite for computer aided diagnosis quantitative imaging analysis pathology detection and surgical assistance for organs with high anatomical variability e g the pancreas previous segmentation approaches report low accuracies compared with well studied organs such as the liver or heart we present an automated bottom up approach for pancreas segmentation in abdominal computed tomography ct scans the method generates a hierarchical cascade of information propagation by classifying image patches at different resolutions and cascading segments superpixels the system contains four steps 1 decomposition of ct slice images into a set of disjoint boundary preserving superpixels 2 computation of pancreas class probability maps via dense patch labeling 3 superpixel classification by pooling both intensity and probability features to form empirical statistics in cascaded random forest frameworks and 4 simple connectivity based post processing dense image patch labeling is conducted using two methods efficient random forest classification on image histogram location and texture features and more expensive but more accurate deep convolutional neural network classification on larger image windows i e with more spatial contexts over segmented 2 d ct slices by the simple linear iterative clustering approach are adopted through model parameter calibration and labeled at the superpixel level for positive pancreas or negative non pancreas or background classes the proposed method is evaluated on a data set of 80 manually segmented ct volumes using six fold cross validation its performance equals or surpasses other state of the art methods evaluated by leave one patient out with a dice coefficient of 70 7 and jaccard index of 57 9 in addition the computational efficiency has improved significantly requiring a mere 6 8 min per testing case versus 10 h for other methods the segmentation framework using deep patch labeling confidences is also more numerically stable as reflected in the smaller performance metric standard deviations finally we implement a multi atlas label fusion malf approach for pancreas segmentation using the same data set under six fold cross validation our bottom up segmentation method significantly outperforms its malf counterpart 70 7 13 0 versus 52 51 20 84 in dice coefficients

robust image regression based on the extended matrix variate power exponential distribution of dependent noise dealing with partial occlusion or illumination is one of the most challenging problems in image representation and classification in this problem the characterization of the representation error plays a crucial role in most current approaches the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted this ignores the dependence between the elements of error in this paper it is assumed that the error image caused by partial occlusion or illumination changes is a random matrix variate and follows the extended matrix variate power exponential distribution this has the heavy tailed regions and can be used to describe a matrix pattern of l times m dimensional observations that are not independent this paper reveals the essence of the proposed distribution it actually alleviates the correlations between pixels in an error matrix e and makes e approximately gaussian on the basis of this distribution we derive a schatten p norm based matrix regression model with l q regularization alternating direction method of multipliers is applied to solve this model to get a closed form solution in each step of the algorithm two singular value function thresholding operators are introduced in addition the extended schatten p norm is utilized to characterize the distance between the test samples and classes in the design of the classifier extensive experimental results for image reconstruction and classification with structural noise demonstrate that the proposed algorithm works much more robustly than some existing regression based methods

the flow of a micropolar fluid through a porous expanding channel in this paper the flow of a micropolar fluid through a porous channel with deforming walls is investigated the lie group method is applied to determine symmetry reductions of partial differential equations compared with previous work the similar variable for the microrotation velocity also is obtained which is an extension of the case corresponding to the newtonian fluids boutros et al 2007 this problem we study here can be considered as an extension of the model discussed in boutros et al 2007 the effect of the permeation reynolds number re the micropolar parameter k and the expansion ratio are studied numerically and the results are plotted furthermore the multiple solutions also can be found for some values of parameters

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

the tractability of segmentation and scene analysis one of the fundamental problems in computer vision is the segmentation of an image into semantically meaningful regions based only on image characteristics a single segmentation can be determined using a linear number of evaluations of a uniformity predicate however minimising the number of regions is shown to be an np complete problem we also show that the variational approach to segmentation based on minimising a criterion combining the overall variance of regions and the number of regions also gives rise to an np complete problem when a library of object models is available segmenting the image becomes a problem of scene analysis a sufficient condition for the reconstruction of a 3d scene from a 2d image to be solvable in polynomial time is that the scene contains no cycles of mutually occluding objects and that no range information can be deduced from the image it is known that relaxing the no cycles condition renders the problem np complete we show that relaxing the no range information condition also produces an np complete problem

ctex an adaptive unsupervised segmentation algorithm based on color texture coherence this paper presents the development of an unsupervised image segmentation framework referred to as ctex that is based on the adaptive inclusion of color and texture in the process of data partition an important contribution of this work consists of a new formulation for the extraction of color features that evaluates the input image in a multispace color representation to achieve this we have used the opponent characteristics of the rgb and yiq color spaces where the key component was the inclusion of the self organizing map som network in the computation of the dominant colors and estimation of the optimal number of clusters in the image the texture features are computed using a multichannel texture decomposition scheme based on gabor filtering the major contribution of this work resides in the adaptive integration of the color and texture features in a compound mathematical descriptor with the aim of identifying the homogenous regions in the image this integration is performed by a novel adaptive clustering algorithm that enforces the spatial continuity during the data assignment process a comprehensive qualitative and quantitative performance evaluation has been carried out and the experimental results indicate that the proposed technique is accurate in capturing the color and texture characteristics when applied to complex natural images

a tree structured framework for purifying complex clusters with structural roles of individual data how can we find a natural clustering of a complex dataset which may contain an unknown number of overlapping clusters of arbitrary shape and be contaminated by noise a tree structured framework is proposed in this paper to purify such clusters by exploring the structural role of each data in practice each individual object within the internal organization of the data has its own specific role centroid hub or outlier due to distinctive associations with their respective neighbors adjacent centroids always interact on each other and serve as mediate nodes of one tree being members of some cluster hubs closed to some centroid become leaf nodes responsible for the termination of the growth of trees outliers that weakly touch with any centroid are often discarded from any trees as global noise all the data can thus be labeled by a specified criterion of centroids connected structural consistency ccsc free of domain specific information our framework with ccsc could widely adapt to many clustering related applications theoretical and experimental contributions both confirm that our framework is easy to interpret and implement efficient and effective in complex clustering

multispectral image denoising with optimized vector bilateral filter vector bilateral filtering has been shown to provide good tradeoff between noise removal and edge degradation when applied to multispectral hyperspectral image denoising it has also been demonstrated to provide dynamic range enhancement of bands that have impaired signal to noise ratios snrs typical vector bilateral filtering described in the literature does not use parameters satisfying optimality criteria we introduce an approach for selection of the parameters of a vector bilateral filter through an optimization procedure rather than by ad hoc means the approach is based on posing the filtering problem as one of nonlinear estimation and minimization of the stein s unbiased risk estimate of this nonlinear estimator along the way we provide a plausibility argument through an analytical example as to why vector bilateral filtering outperforms band wise 2d bilateral filtering in enhancing snr experimental results show that the optimized vector bilateral filter provides improved denoising performance on multispectral images when compared with several other approaches

distribution matching with the bhattacharyya similarity a bound optimization framework we present efficient graph cut algorithms for three problems 1 finding a region in an image so that the histogram or distribution of an image feature within the region most closely matches a given model 2 co segmentation of image pairs and 3 interactive image segmentation with a user provided bounding box each algorithm seeks the optimum of a global cost function based on the bhattacharyya measure a convenient alternative to other matching measures such as the kullback leibler divergence our functionals are not directly amenable to graph cut optimization as they contain non linear functions of fractional terms which make the ensuing optimization problems challenging we first derive a family of parametric bounds of the bhattacharyya measure by introducing an auxiliary labeling then we show that these bounds are auxiliary functions of the bhattacharyya measure a result which allows us to solve each problem efficiently via graph cuts we show that the proposed optimization procedures converge within very few graph cut iterations comprehensive and various experiments including quantitative and comparative evaluations over two databases demonstrate the advantages of the proposed algorithms over related works in regard to optimality computational load accuracy and flexibility

directed connected operators asymmetric hierarchies for image filtering and segmentation connected operators provide well established solutions for digital image processing typically in conjunction with hierarchical schemes in graph based frameworks such operators basically rely on symmetric adjacency relations between pixels in this article we introduce a notion of directed connected operators for hierarchical image processing by also considering non symmetric adjacency relations the induced image representation models are no longer partition hierarchies i e trees but directed acyclic graphs that generalize standard morphological tree structures such as component trees binary partition trees or hierarchical watersheds we describe how to efficiently build and handle these richer data structures and we illustrate the versatility of the proposed framework in image filtering and image segmentation

processing disjunctions in temporal constraint networks temporal constraint satisfaction problems tcsps provide a formal framework for representing and processing temporal knowledge deciding the consistency of tcsps is known to be intractable we demonstrate that even local consistency algorithms like path consistency pc can be exponential on tcsps due to the fragmentation problem we present two new polynomial approximation algorithms upper lower tightening ult and loose path consistency lpc which are efficient yet effective in detecting inconsistencies and reducing fragmentation our experiments on hard problems in the transition region show that lpc has the best effectiveness efficiency tradeoff for processing tcsps when incorporated within backtrack search lpc is capable of improving search performance by orders of magnitude

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

statistics of natural images scaling in the woods we study the statistics of an ensemble of images taken in the woods distributions of local quantities such as contrast are scale invariant and have nearly exponential tails power spectra exhibit scaling with a nontrivial exponent these data limit the information content of natural images and point to the importance of gain control strategies in visual processing

geometrically induced force interaction for three dimensional deformable models in this paper we propose a novel 3 d deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions this external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient the evolution of the deformable model is solved using the level set method so that topological changes are handled automatically the relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves the geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries and it gives the deformable model a high invariancy in initialization configurations the voxel interactions across the whole image domain provide a global view of the object boundary representation giving the external force a long attraction range the bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross boundary initializations and facilitates the handling of weak edges and broken boundaries in addition we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm the new deformable model can effectively overcome image noise we provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images and show that the proposed method achieves significant improvements against existing image gradient techniques

a variational method for geometric regularization of vascular segmentation in medical images in this paper a level set based geometric regularization method is proposed which has the ability to estimate the local orientation of the evolving front and utilize it as shape induced information for anisotropic propagation we show that preserving anisotropic fronts can improve elongations of the extracted structures while minimizing the risk of leakage to that end for an evolving front using its shape offset level set representation a novel energy functional is defined it is shown that constrained optimization of this functional results in an anisotropic expansion flow which is useful for vessel segmentation we have validated our method using synthetic data sets 2 d retinal angiogram images and magnetic resonance angiography volumetric data sets a comparison has been made with two state of the art vessel segmentation methods quantitative results as well as qualitative comparisons of segmentations indicate that our regularization method is a promising tool to improve the efficiency of both techniques

automatic image segmentation by dynamic region merging this paper addresses the automatic image segmentation problem in a region merging style with an initially oversegmented image in which many regions or superpixels with homogeneous color are detected an image segmentation is performed by iteratively merging the regions according to a statistical test there are two essential issues in a region merging algorithm order of merging and the stopping criterion in the proposed algorithm these two issues are solved by a novel predicate which is defined by the sequential probability ratio test and the minimal cost criterion starting from an oversegmented image neighboring regions are progressively merged if there is an evidence for merging according to this predicate we show that the merging order follows the principle of dynamic programming this formulates the image segmentation as an inference problem where the final segmentation is established based on the observed image we also prove that the produced segmentation satisfies certain global properties in addition a faster algorithm is developed to accelerate the region merging process which maintains a nearest neighbor graph in each iteration experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm

factorization based texture segmentation this paper introduces a factorization based approach that efficiently segments textured images we use local spectral histograms as features and construct an m times n feature matrix using m dimensional feature vectors in an n pixel image based on the observation that each feature can be approximated by a linear combination of several representative features we factor the feature matrix into two matrices one consisting of the representative features and the other containing the weights of representative features at each pixel used for linear combination the factorization method is based on singular value decomposition and nonnegative matrix factorization the method uses local spectral histograms to discriminate region appearances in a computationally efficient way and at the same time accurately localizes region boundaries the experiments conducted on public segmentation data sets show the promise of this simple yet powerful approach

image segmentation using active contours driven by the bhattacharyya gradient flow this paper addresses the problem of image segmentation by means of active contours whose evolution is driven by the gradient flow derived from an energy functional that is based on the bhattacharyya distance in particular given the values of a photometric variable or of a set thereof which is to be used for classifying the image pixels the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours the above discrepancy is measured by means of the bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand the proposed methodology can be viewed as a generalization of the segmentation methods in which active contours maximize the difference between a finite number of empirical moments of the ldquoinsiderdquo and ldquooutsiderdquo distributions furthermore it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed as an additional contribution a method for automatically adjusting the smoothness properties of the empirical distributions is proposed such a procedure is crucial in situations when the number of data samples supporting a certain segmentation class varies considerably in the course of the evolution of the active contour in this case the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over or underestimation artifacts finally a number of relevant segmentation results are demonstrated and some further research directions are discussed

globally optimal regions and boundaries as minimum ratio weight cycles we describe a new form of energy functional for the modeling and identification of regions in images the energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modeling information both from the boundary intensity gradients etc and from the interior of the region texture homogeneity etc we describe two polynomial time digraph algorithms for finding the global minima of this energy one of the algorithms is completely general minimizing the functional for any choice of modeling information it runs in a few seconds on a 256 spl times 256 image the other algorithm applies to a subclass of functionals but has the advantage of being extremely parallelizable neither algorithm requires initialization

from binary temporal relations to non binary ones and back abstract in this paper a new approach towards temporal reasoning is presented that scales up from the temporal relations commonly used in allen s qualitative interval calculus and in quantitative temporal constraint satisfaction problems to include interval relations with distances temporal rules and other non binary relations into the reasoning scheme for this purpose we generalize well known methods for constraint propagation determination of consistency and computation of the minimal network from simpler schemes that only allow for binary relations thereby we find that levels of granularity play a major role for applying these techniques in our more expressive framework indeed the technical preliminaries we provide are especially apt to investigate the switching between different granularities of representation hence illucitating and exploiting the tradeoff between expressiveness and efficiency of temporal reasoning schemes on the one side and between expressiveness and understandability on the other side

robust real time pattern matching using bayesian sequential hypothesis testing this paper describes a method for robust real time pattern matching we first introduce a family of image distance measures the image hamming distance family members of this family are robust to occlusion small geometrical transforms light changes and nonrigid deformations we then present a novel bayesian framework for sequential hypothesis testing on finite populations based on this framework we design an optimal rejection acceptance sampling algorithm this algorithm quickly determines whether two images are similar with respect to a member of the image hamming distance family we also present a fast framework that designs a near optimal sampling algorithm extensive experimental results show that the sequential sampling algorithm s performance is excellent implemented on a pentium iv 3 ghz processor the detection of a pattern with 2 197 pixels in 640times480 pixel frames where in each frame the pattern rotated and was highly occluded proceeds at only 0 022 seconds per frame

reasoning about qualitative temporal information abstract representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks an interval based framework and a point based framework have been proposed for representing such temporal information in this paper we address two fundamental reasoning tasks that arise in applications of these frameworks given possibly indefinite and incomplete knowledge of the relationships between some intervals or points i find a scenario that is consistent with the information provided and ii find the feasible relations between all pairs of intervals or points for the point based framework and a restricted version of the interval based framework we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations our algorithms are marked improvements over the previously known algorithms in particular we develop an o n2 time algorithm for finding one consistent scenario that is an o n improvement over the previously known algorithm where n is the number of intervals or points and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm for the unrestricted version of the interval based framework finding a consistent scenario and finding the feasible relations have been shown to be np complete we show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems

robust shape tracking with multiple models in ultrasound images this paper addresses object tracking in ultrasound images using a robust multiple model tracker the proposed tracker has the following features 1 it uses multiple dynamic models to track the evolution of the object boundary and 2 it models invalid observations outliers reducing their influence on the shape estimates the problem considered in this paper is the tracking of the left ventricle which is known to be a challenging problem the heart motion presents two phases diastole and systole with different dynamics the multiple models used in this tracker try to solve this difficulty in addition ultrasound images are corrupted by strong multiplicative noise which prevents the use of standard deformable models robust estimation techniques are used to address this difficulty the multiple model data association mmda tracker proposed in this paper is based on a bank of nonlinear filters organized in a tree structure the algorithm determines which model is active at each instant of time and updates its state by propagating the probability distribution using robust estimation techniques

statistical modeling of 3 d natural scenes with application to bayesian stereopsis we studied the empirical distributions of luminance range and disparity wavelet coefficients using a coregistered database of luminance and range images the marginal distributions of range and disparity are observed to have high peaks and heavy tails similar to the well known properties of luminance wavelet coefficients however we found that the kurtosis of range and disparity coefficients is significantly larger than that of luminance coefficients we used generalized gaussian models to fit the empirical marginal distributions we found that the marginal distribution of luminance coefficients have a shape parameter p between 0 6 and 0 8 while range and disparity coefficients have much smaller parameters p 0 32 corresponding to a much higher peak we also examined the conditional distributions of luminance range and disparity coefficients the magnitudes of luminance and range disparity coefficients show a clear positive correlation which means at a location with larger luminance variation there is a higher probability of a larger range disparity variation we also used generalized gaussians to model the conditional distributions of luminance and range disparity coefficients the values of the two shape parameters p s reflect the observed luminance range disparity dependency as an example of the usefulness of luminance statistics conditioned on range statistics we modified a well known bayesian stereo ranging algorithm using our natural scene statistics models which improved its performance

automatic estimation and removal of noise from a single image image denoising algorithms often assume an additive white gaussian noise awgn process that is independent of the actual rgb values such approaches cannot effectively remove color noise produced by today s ccd digital camera in this paper we propose a unified framework for two tasks automatic estimation and removal of color noise from a single image using piecewise smooth image models we introduce the noise level function nlf which is a continuous function describing the noise level as a function of image brightness we then estimate an upper bound of the real nlf by fitting a lower envelope to the standard deviations of per segment image variances for denoising the chrominance of color noise is significantly removed by projecting pixel values onto a line fit to the rgb values in each segment then a gaussian conditional random field gcrf is constructed to obtain the underlying clean image from the noisy input extensive experiments are conducted to test the proposed algorithm which is shown to outperform state of the art denoising algorithms

modeling visual patterns by integrating descriptive and generative methods this paper presents a class of statistical models that integrate two statistical modeling paradigms in the literature i descriptive methods such as markov random fields and minimax entropy learning zhu s c wu y n and mumford d 1997 neural computation 9 8 and ii generative methods such as principal component analysis independent component analysis bell a j and sejnowski t j 1997 vision research 37 3327 3338 transformed component analysis frey b and jojic n 1999 iccv wavelet coding mallat s and zhang z 1993 ieee trans on signal processing 41 3397 3415 chen s donoho d and saunders m a 1999 journal on scientific computing 20 1 33 61 and sparse coding olshausen b a and field d j 1996 nature 381 607 609 lewicki m s and olshausen b a 1999 josa a 16 7 1587 1601 in this paper we demonstrate the integrated framework by constructing a class of hierarchical models for texton patterns the term texton was coined by psychologist julesz in the early 80s at the bottom level of the model we assume that an observed texture image is generated by multiple hidden texton maps and textons on each map are translated scaled stretched and oriented versions of a window function like mini templates or wavelet bases the texton maps generate the observed image by occlusion or linear superposition this bottom level of the model is generative in nature at the top level of the model the spatial arrangements of the textons in the texton maps are characterized by minimax entropy principle which leads to embellished versions of gibbs point process models stoyan d kendall w s and mecke j 1985 stochastic geometry and its applications the top level of the model is descriptive in nature we demonstrate the integrated model by a set of experiments

rigid shape matching by segmentation averaging we use segmentations to match images by shape the new matching technique does not require point to point edge correspondence and is robust to small shape variations and spatial shifts to address the unreliability of segmentations computed bottom up we give a closed form approximation to an average over all segmentations our method has many extension yielding new algorithms for tracking object detection segmentation and edge preserving smoothing for segmentation instead of a maximum a posteriori approach we compute the central segmentation minimizing the average distance to all segmentations of an image for smoothing instead of smoothing images based on local structures we smooth based on the global optimal image structures our methods for segmentation smoothing and object detection perform competitively and we also show promising results in shape based tracking

nonlocal center surround reconstruction based bottom up saliency estimation many saliency models consider the feature extraction as the algorithmic core and the performance of their methods relies on the selection of the features to a great extent however there can hardly be a set of features effective to pop out the salient regions under various visual environments moreover because saliency is not tuned to certain visual features a location winning the spatial competition in any feature space can be defined as salient instead of seeking for or learning the features to highlight the difference between the salient areas and the background we focus more on the sparsity and uniqueness carried by the original image itself the source of all the features to propose a nonlocal reconstruction based saliency model in the proposed approach the saliency is measured by the sparse reconstruction residual of representing the central patch with a linear combination of its surrounding patches sampled in a nonlocal manner in addition this is generalized to model the global aspect saliency which provides a complement to the nonlocal saliency and improves the performance further as a generalization of itti et al s classical center surround comparison scheme the proposed approach performs well on images where itti et al s method fails as well as on general natural images numerical experiments show the proposed approach produces better results compared with the state of the art algorithms on three public databases highlightsa nonlocal reconstruction based bottom up saliency estimation method is proposed nonlocal image processing is employed to provide a better treatment of textures sparsity pursuit is very effective for removing duplicated similar image regions reconstruction residual is inherently coherent with the bottom up saliency our method is stable under three public datasets and consistent with human fixations

backtracking algorithms for disjunctions of temporal constraints abstract we extend the framework of simple temporal problems studied originally by dechter meiri and pearl to consider constraints of the form x 1 y 1 r 1 x n y n r n where x 1 x n y 1 y n are variables ranging over the real numbers r 1 r n are real constants and n 1 this is a wide class of temporal constraints that can be used to model a variety of problems in temporal reasoning scheduling planning and temporal constraint databases we have implemented several progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints backtracking backjumping three variations of forward checking and forward checking with backjumping we have partially ordered the above algorithms according to the number of visited search nodes and the number of performed consistency checks although our problem is non binary our results agree with the results of kondrak and van beek who consider only binary constraints we have also studied the performance of the above algorithms experimentally using randomly generated sets of data and job shop scheduling problems the experiments with random instances allowed us to locate the hard region for this class of problems the results show that hard problems occur at a critical value of the ratio of disjunctions to variables

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

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

new solutions for solving problem of particle trajectories in linear deep water waves via lie group method the nonlinear equations of the two dimensional inviscid incompressible fluid in a constant gravitational field describing the wave propagation on the water surface are considered the lie group method has been applied for determining symmetry reductions of the system of partial differential equations lie group method starts out with a general infinitesimal group of transformations under which the given partial differential equations are invariant the determining equations are a set of linear differential equations the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables after the group has been determined a solution to the given partial differential equations may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables of the system effects of the wavelength l and time t on the particle path have been studied and the results are plotted

affinity learning with diffusion on tensor product graph in many applications we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples often the pairwise similarities which are also called affinities are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples as observed in several recent approaches more reliable similarities can be obtained if the original similarities are diffused in the context of other data points where the context of each point is a set of points most similar to it compared to the existing methods our approach differs in two main aspects first instead of diffusing the similarity information on the original graph we propose to utilize the tensor product graph tpg obtained by the tensor product of the original graph with itself since tpg takes into account higher order information it is not a surprise that we obtain more reliable similarities however it comes at the price of higher order computational complexity and storage requirement the key contribution of the proposed approach is that the information propagation on tpg can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph we prove that a graph diffusion process on tpg is equivalent to a novel iterative algorithm on the original graph which is guaranteed to converge after its convergence we obtain new edge weights that can be interpreted as new learned affinities we stress that the affinities are learned in an unsupervised setting we illustrate the benefits of the proposed approach for data manifolds composed of shapes images and image patches on two very different tasks of image retrieval and image segmentation with learned affinities we achieve the bull s eye retrieval score of 99 99 percent on the mpeg 7 shape dataset which is much higher than the state of the art algorithms when the data points are image patches the ncut with the learned affinities not only significantly outperforms the ncut with the original affinities but it also outperforms state of the art image segmentation methods

from local to global consistency abstract in reasoning tasks involving the maintenance of consistent databases so called qqconstraint networks q q it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data in this paper we present a relationship between the sizes of the variables domains the constraints arity and the level of local consistency sufficient to ensure global consistency based on these parameters a new tractability classification of constraint networks is presented we also show based on this relationship that any relation on bi valued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables

fuzzy constraint networks for signal pattern recognition this paper deals with representation and reasoning on information concerning the evolution of a physical parameter by means of a model based on the fuzzy constraint satisfaction problem formalism and with which it is possible to define what we call fuzzy temporal profiles ftp based on fundamentally linguistic information this model allows the integration of knowledge on the evolution of a set of parameters into a knowledge representation scheme in which time plays a fundamental role the ftp model describes the behaviour of a physical parameter on the basis of a set of signal events and which allows the evolution of the parameter between each pair of events to be modelled as signal episodes given the fundamentally linguistic nature of the information represented the consistency analysis of this information is an essential task nevertheless the obtention of the minimal representation of the network that defines an ftp is an np hard problem in spite of this we supply algorithms guaranteeing local levels of consistency that allow to correct a large proportion of the errors committed by a human expert in the linguistic description of the profile furthermore we propose a new topology whose consistency can be guaranteed in polynomial time we also study the applicability of this model in the recognition of signal patterns

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed