region merging techniques using information theory statistical measures the purpose of the current work is to propose under a statistical framework a family of unsupervised region merging techniques providing a set of the most relevant region based explanations of an image at different levels of analysis these techniques are characterized by general and nonparametric region models with neither color nor texture homogeneity assumptions and a set of innovative merging criteria based on information theory statistical measures the scale consistency of the partitions is assured through i a size regularization term into the merging criteria and a classical merging order or ii using a novel scale based merging order to avoid the region size homogeneity imposed by the use of a size regularization term moreover a partition significance index is defined to automatically determine the subset of most representative partitions from the created hierarchy most significant automatically extracted partitions show the ability to represent the semantic content of the image from a human point of view finally a complete and exhaustive evaluation of the proposed techniques is performed using not only different databases for the two main addressed problems object oriented segmentation of generic images and texture image segmentation but also specific evaluation features in each case under and oversegmentation error and a large set of region based pixel based and error consistency indicators respectively results are promising outperforming in most indicators both object oriented and texture state of the art segmentation techniques

multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

modified numerov s method for inverse sturm liouville problems in this paper we propose a new modified numerov s method for recovering from eigenvalues a symmetric potential of a sturm liouville operator with dirichlet boundary conditions we use interpolation to refine the mesh sufficiently for numerov s method to be effective even without the asymptotic correction technique of andrew and paine accuracy and stability of the method are investigated convergence of the method is established our method is extended to deal with natural boundary conditions numerical experiments confirm its competitiveness

how many clusters are best an experiment this paper reports the results of a monte carlo study on the relative effectiveness of two internal indices in estimating the true number of clusters in multivariate data the two indices are the davies and bouldin 1 index and a new modification of the hubert statistic 2 data in d dimensions are clustered to create sequences of partitions estimates are based on plots of the indices as functions of the number of recovered clusters neither index uses a priori information the effects of sample size dimensionality cluster spread number of true clusters and sampling window are examined clustered data are generated to assure a given number of distinct clusters the degree of clustering in the data is verified by a separate monte carlo study based on the jaccard and corrected rand indices that exhibits the importance of correcting external indices for chance the modified hubert index proposed here for the first time is shown to perform better than the davies bouldin index under all experimental conditions recovery of the true number of clusters gets better as the number of true clusters decreases and as the number of dimensions increases no effect occurs due to sampling window the complete link clustering method and a square error clustering method recognize the true number of clusters consistently better than the single link method this study demonstrates the difficulty inherent in estimating the number of clusters

how many entries of a typical orthogonal matrix can be approximated by independent normals we solve an open problem of diaconis that asks what are the largest orders of p n and q n such that z n the p n x q n upper left block of a random matrix r n which is uniformly distributed on the orthogonal group o n can be approximated by independent standard normals this problem is solved by two different approximation methods first we show that the variation distance between the joint distribution of entries of z n and that of p n q n independent standard normals goes to zero provided p n o n and q n o n we also show that the above variation distance does not go to zero if p n x n and q n y n for any positive numbers x and y this says that the largest orders of p n and q n are o n 1 2 in the sense of the above approximation second suppose n ij n n is generated by performing the gram schmidt algorithm on the columns of y n y ij n n where y ij 1 i j n are i i d standard normals we show that e n m max 1 i n 1 j m n ij y ij goes to zero in probability as long as m m n o n log n we also prove that e n m n 2 in probability when m n n logn for any a 0 this says that m n o n log n is the largest order such that the entries of the first m n columns of n can be approximated simultaneously by independent standard normals

gaussian processes and almost spherical sections of convex bodies on presente une preuve simple avec des estimations pointues du theoreme de dvoretzky sur l existence des sections presque spheriques ayant une grande dimension dans des corps convexes arbitraires dans r n

weyl titchmarsh functions of vector valued sturm liouville operators on the unit interval the matrix valued weyl titchmarsh functions m of vector valued sturm liouville operators on the unit interval with the dirichlet boundary conditions are considered the collection of the eigenvalues i e poles of m and the residues of m is called the spectral data of the operator the complete characterization of spectral data or equivalently n n weyl titchmarsh functions corresponding to n n self adjoint square integrable matrix valued potentials is given if all n eigenvalues of the averaged potential are distinct

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

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

solution of the inverse spectral problem for an impedance with integrable derivative part ii the inverse eigenvalue problem for a sturm liouville equation in impedance form with dirichlet boundary conditions on a unit interval is solved the solution of this nonlinear problem requires the investigation of a combined map from the logarithmic derivative of the impedance assumed to be square integrable to two sequences of spectral data the first is the sequence of dirichlet eigenvalues shown to be locally bounded with square roots differing from the sequence of integral multiples of by a square summable sequence the second sequence has as first term the mean of the logarithmic derivative of the impedance each term in the remainder of the sequence is the logarithm of the product of the impedance and the derivative of an eigenfunction evaluated at an endpoint it is shown that this second sequence is a locally bounded square summable sequence the combined map is a real analytic isomorphism a uniqueness result follows from the asymptotics and analyticity shown in the first paper and properties of riesz bases the existence is shown by giving a closed form of the solution it is also shown that the same map solves the inverse sturm liouville problem in impedance form with neumann boundary conditions 1993 john wiley sons inc

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

binary partition tree analysis based on region evolution and its application to tree simplification pyramid image representations via tree structures are recognized methods for region based image analysis binary partition trees can be applied which document the merging process with small details found at the bottom levels and larger ones close to the root hindsight of the merging process is stored within the tree structure and provides the change histories of an image property from the leaf to the root node in this work the change histories are modelled by evolvement functions and their second order statistics are analyzed by using a knee function knee values show the reluctancy of each merge we have systematically formulated these findings to provide a novel framework for binary partition tree analysis where tree simplification is demonstrated based on an evolvement function for each upward path in a tree the tree node associated with the first reluctant merge is considered as a pruning candidate the result is a simplified version providing a reduced solution space and still complying with the definition of a binary tree the experiments show that image details are preserved whilst the number of nodes is dramatically reduced an image filtering tool also results which preserves object boundaries and has applications for segmentation

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

hyperspectral image representation and processing with binary partition trees the optimal exploitation of the information provided by hyperspectral images requires the development of advanced image processing tools this paper proposes the construction and the processing of a new region based hierarchical hyperspectral image representation relying on the binary partition tree bpt this hierarchical region based representation can be interpreted as a set of hierarchical regions stored in a tree structure hence the bpt succeeds in presenting 1 the decomposition of the image in terms of coherent regions and 2 the inclusion relations of the regions in the scene based on region merging techniques the bpt construction is investigated by studying the hyperspectral region models and the associated similarity metrics once the bpt is constructed the fixed tree structure allows implementing efficient and advanced application dependent techniques on it the application dependent processing of bpt is generally implemented through a specific pruning of the tree in this paper a pruning strategy is proposed and discussed in a classification context experimental results on various hyperspectral data sets demonstrate the interest and the good performances of the bpt representation

hierarchical segmentation using tree based shape spaces current trends in image segmentation are to compute a hierarchy of image segmentations from fine to coarse a classical approach to obtain a single meaningful image partition from a given hierarchy is to cut it in an optimal way following the seminal approach of the scale set theory while interesting in many cases the resulting segmentation being a non horizontal cut is limited by the structure of the hierarchy in this paper we propose a novel approach that acts by transforming an input hierarchy into a new saliency map it relies on the notion of shape space a graph representation of a set of regions extracted from the image each region is characterized with an attribute describing it we weigh the boundaries of a subset of meaningful regions local minima in the shape space by extinction values based on the attribute this extinction based saliency map represents a new hierarchy of segmentations highlighting regions having some specific characteristics each threshold of this map represents a segmentation which is generally different from any cut of the original hierarchy this new approach thus enlarges the set of possible partition results that can be extracted from a given hierarchy qualitative and quantitative illustrations demonstrate the usefulness of the proposed method

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

divergence estimation of continuous distributions based on data dependent partitions we present a universal estimator of the divergence d p spl par q for two arbitrary continuous distributions p and q satisfying certain regularity conditions this algorithm which observes independent and identically distributed i i d samples from both p and q is based on the estimation of the radon nikodym derivative dp dq via a data dependent partition of the observation space strong convergence of this estimator is proved with an empirically equivalent segmentation of the space this basic estimator is further improved by adaptive partitioning schemes and by bias correction the application of the algorithms to data with memory is also investigated in the simulations we compare our estimators with the direct plug in estimator and estimators based on other partitioning approaches experimental results show that our methods achieve the best convergence performance in most of the tested cases

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

hyperspectral image segmentation using a new spectral unmixing based binary partition tree representation the binary partition tree bpt is a hierarchical region based representation of an image in a tree structure the bpt allows users to explore the image at different segmentation scales often the tree is pruned to get a more compact representation and so the remaining nodes conform an optimal partition for some given task here we propose a novel bpt construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts linear spectral unmixing consists of finding the spectral signatures of the materials present in the image endmembers and their fractional abundances within each pixel the proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error results are presented on real hyperspectral data sets with different contexts and resolutions

antiextensive connected operators for image and sequence processing this paper deals with a class of morphological operators called connected operators these operators filter the signal by merging its flat zones as a result they do not create any new contours and are very attractive for filtering tasks where the contour information has to be preserved this paper shows that connected operators work implicitly on a structured representation of the image made of flat zones the max tree is proposed as a suitable and efficient structure to deal with the processing steps involved in antiextensive connected operators a formal definition of the various processing steps involved in the operator is proposed and as a result several lines of generalization are developed first the notion of connectivity and its definition are analyzed several modifications of the traditional approach are presented they lead to connected operators that are able to deal with texture they also allow the definition of connected operators with less leakage than the classical ones second a set of simplification criteria are proposed and discussed they lead to simplicity entropy and motion oriented operators the problem of using a nonincreasing criterion is analyzed its solution is formulated as an optimization problem that can be very efficiently solved by a viterbi 1979 algorithm finally several implementation issues are discussed showing that these operators can be very efficiently implemented

binary partition tree as an efficient representation for image processing segmentation and information retrieval this paper discusses the interest of binary partition trees as a region oriented image representation binary partition trees concentrate in a compact and structured representation a set of meaningful regions that can be extracted from an image they offer a multiscale representation of the image and define a translation invariant 2 connectivity rule among regions as shown in this paper this representation can be used for a large number of processing goals such as filtering segmentation information retrieval and visual browsing furthermore the processing of the tree representation leads to very efficient algorithms finally for some applications it may be interesting to compute the binary partition tree once and to store it for subsequent use for various applications in this context the paper shows that the amount of bits necessary to encode a binary partition tree remains moderate

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

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

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

a comparison principle for functions of a uniformly random subspace this note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the stiefel manifold in terms of the expected norm of a standard gaussian matrix with the same dimensions a related comparison holds for any convex function of a random matrix drawn from the stiefel manifold for certain norms a reversed inequality is also valid

the kullback leibler divergence rate between markov sources in this work we provide a computable expression for the kullback leibler divergence rate lim sub n spl rarr spl infin 1 nd p sup n spl par q sup n between two time invariant finite alphabet markov sources of arbitrary order and arbitrary initial distributions described by the probability distributions p sup n and q sup n respectively we illustrate it numerically and examine its rate of convergence the main tools used to obtain the kullback leibler divergence rate and its rate of convergence are the theory of nonnegative matrices and perron frobenius theory similarly we provide a formula for the shannon entropy rate lim sub n spl rarr spl infin 1 nh p sup n of markov sources and examine its rate of convergence

unsupervised simplification of image hierarchies via evolution analysis in scale sets framework region based hierarchical image representation is crucial in many computer vision applications however in practice an image hierarchy is usually dense and contains many less informative branches it is expected that a hierarchy should be accurate and simplified which is not only desirable for different applications but also saves considerable computational load for the further analysis to achieve this target this paper proposes a novel approach for unsupervised simplification of region based image hierarchies which employs the global and local evolution analyses of a hierarchy first we introduce a global evolution analysis in the scale sets framework which provides clues for eliminating less informative branches moreover a hybrid unsupervised simplification method is designed utilizing the information from global and local evolution functions a number of experiments on various images have shown that the proposed approach is effective and efficient in removing less informative nodes averagely about 90 of the whole nodes while preserving salient image details and retaining the accuracy

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

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

divergence measures based on the shannon entropy a novel class of information theoretic divergence measures based on the shannon entropy is introduced unlike the well known kullback divergences the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved more importantly their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds these bounds are crucial in many applications of divergence measures the measures are also well characterized by the properties of nonnegativity finiteness semiboundedness and boundedness

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

binary partition trees for object detection this paper discusses the use of binary partition trees bpts for object detection bpts are hierarchical region based representations of images they define a reduced set of regions that covers the image support and that spans various levels of resolution they are attractive for object detection as they tremendously reduce the search space in this paper several issues related to the use of bpt for object detection are studied concerning the tree construction we analyze the compromise between computational complexity reduction and accuracy this will lead us to define two parts in the bpt one providing accuracy and one representing the search space for the object detection task then we analyze and objectively compare various similarity measures for the tree construction we conclude that different similarity criteria should be used for the part providing accuracy in the bpt and for the part defining the search space and specific criteria are proposed for each case then we discuss the object detection strategy based on bpt the notion of node extension is proposed and discussed finally several object detection examples illustrating the generality of the approach and its efficiency are reported

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

the inverse sturn liouville problem iii on considere la theorie spectrale inverse du probleme de sturm liouville y q x y y 0 x 1 avec les conditions aux limites y 0 0 by 1 y 1 0 q l r 2 0 1 et b r

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time