segmentation of range images as the search for geometric parametric models segmentation of range images has long been considered in computer vision as an important but extremely difficult problem in this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces data aggregation is performed via model recovery in terms of variable order bi variate polynomials using iterative regression model recovery is initiated independently in regularly placed seed regions in the image all the recovered models are potential candidates for the final description of the data selection of the models is defined as a quadratic boolean problem and the solution is sought by the wta winner takes all technique which turns out to be a good compromise between the speed of computation and the accuracy of the solution the overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way partial recovery of the models is followed by the selection optimization procedure and only the best models are allowed to develop further

multiseeded segmentation using fuzzy connectedness fuzzy connectedness has been effectively used to segment out an object in a badly corrupted image we generalize the approach by providing a definition which is shown to always determine a simultaneous segmentation of multiple objects for any set of seed points the segmentation is uniquely determined by the definition an algorithm for finding this segmentation is presented and its output is illustrated the algorithm is fast as compared to other segmentation algorithms in current use we also report on an evaluation of the accuracy and robustness of the algorithm based on experiments in which several users were repeatedly asked to identify the seed points for the algorithm in a number of images

reasoning about noisy sensors and effectors in the situation calculus abstract agents interacting with an incompletely known world need to be able to reason about the effects of their actions and to gain further information about that world they need to use sensors of some sort unfortunately both the effects of actions and the information returned from sensors are subject to error to cope with such uncertainties the agent can maintain probabilistic beliefs about the state of the world with probabilistic beliefs the agent will be able to quantify the likelihood of the various outcomes of its actions and is better able to utilize the information gathered from its error prone actions and sensors in this paper we present a model in which we can reason about an agent s probabilistic degrees of belief and the manner in which these beliefs change as various actions are executed we build on a general logical theory of action developed by reiter and others formalized in the situation calculus we propose a simple axiomatization that captures an agent s state of belief and the manner in which these beliefs change when actions are executed our model displays a number of intuitively reasonable properties

robust active contours with insensitive parameters abstract active contours known as snakes have found wide applications since their first introduction in 1987 by kass et al int j comput vision 1 321 331 however one problem with the current models is that the performance depends on proper internal parameters and initial contour position which unfortunately cannot be determined a priori it is usually a hard job to tune internal parameters and initial contour position the problem comes from the fact that the internal normal force at each point of contour is also a function of contour shape to solve this problem we propose to compensate for this internal normal force so as to make it independent of shape as a result the new model works robustly with no necessity to fine tune internal parameters and can converge to high curvature points like corners

on detection of multiple object instances using hough transforms hough transform based methods for detecting multiple objects use nonmaxima suppression or mode seeking to locate and distinguish peaks in hough images such postprocessing requires the tuning of many parameters and is often fragile especially when objects are located spatially close to each other in this paper we develop a new probabilistic framework for object detection which is related to the hough transform it shares the simplicity and wide applicability of the hough transform but at the same time bypasses the problem of multiple peak identification in hough images and permits detection of multiple objects without invoking nonmaximum suppression heuristics our experiments demonstrate that this method results in a significant improvement in detection accuracy both for the classical task of straight line detection and for a more modern category level pedestrian detection problem

asymptotics for parametric garch in mean models abstract in this paper we develop an asymptotic theory for the quasi maximum likelihood estimator qmle of the parametric garch in mean model the asymptotics is based on a study of the volatility as a process of the model parameters the proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model nevertheless our theory does not yet treat all standard specifications of the mean function

robust image segmentation using resampling and shape constraints automated segmentation of images has been considered an important intermediate processing task to extract semantic meaning from pixels we propose an integrated approach for image segmentation based on a generative clustering model combined with coarse shape information and robust parameter estimation the sensitivity of segmentation solutions to image variations is measured by image resampling shape information is included in the inference process to guide ambiguous groupings of color and texture features shape and similarity based grouping information is combined into a semantic likelihood map in the framework of bayesian statistics experimental evidence shows that semantically meaningful segments are inferred even when image data alone gives rise to ambiguous segmentations

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

kalman filtering with random coefficients and contractions the riccati transformation of linear filtering control theory is shown to be a contraction on the space of positive symmetric matrices this is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters

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

quasi maximum likelihood estimation in conditionally heteroscedastic time series a stochastic recurrence equations approach this paper studies the quasi maximum likelihood estimator qmle in a general conditionally heteroscedastic time series model of multiplicative form xt t zt where the unobservable volatility t is a parametric function of xt 1 x t p t 1 t q for some p q 0 and zt is standardized i i d noise we assume that these models are solutions to stochastic recurrence equations which satisfy a contraction random lipschitz coefficient property these assumptions are satisfied for the popular garch asymmetric garch and exponential garch processes exploiting the contraction property we give conditions for the existence and uniqueness of a strictly stationary solution xt to the stochastic recurrence equation and establish consistency and asymptotic normality of the qmle we also discuss the problem of invertibility of such time series models 1 introduction gaussian quasi maximum likelihood estimation that is likelihood estimation under the hypothesis of gaussian innovations is a popular method which is widely used for inference in time series models however it is often a nontrivial task to establish the consistency and asymptotic normality of the quasi maximum likelihood estimator qmle applied to specific models and therefore an in depth analysis of the probabilistic structure generated by the model is called for a classical example of this kind is the seminal paper by hannan 18 on estimation in linear arma time series in this paper we study the qmle for a general class of conditionally heteroscedastic time series models which includes garch asymmetric garch and exponential garch recall that a garch p q generalized autoregressive conditionally heteroscedastic of order p q process 4 i s def ined by

bagging for path based clustering a resampling scheme for clustering with similarity to bootstrap aggregation bagging is presented bagging is used to improve the quality of path based clustering a data clustering method that can extract elongated structures from data in a noise robust way the results of an agglomerative optimization method are influenced by small fluctuations of the input data to increase the reliability of clustering solutions a stochastic resampling method is developed to infer consensus clusters a related reliability measure allows us to estimate the number of clusters based on the stability of an optimized cluster solution under resampling the quality of path based clustering with resampling is evaluated on a large image data set of human segmentations

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

stability based validation of clustering solutions data clustering describes a set of frequently employed techniques in exploratory data analysis to extract natural group structure in data such groupings need to be validated to separate the signal in the data from spurious structure in this context finding an appropriate number of clusters is a particularly important model selection question we introduce a measure of cluster stability to assess the validity of a cluster model this stability measure quantifies the reproducibility of clustering solutions on a second sample and it can be interpreted as a classification risk with regard to class labels produced by a clustering algorithm the preferred number of clusters is determined by minimizing this classification risk as a function of the number of clusters convincing results are achieved on simulated as well as gene expression data sets comparisons to other methods demonstrate the competitive performance of our method and its suitability as a general validation tool for clustering solutions in real world problems

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

local or global minima flexible dual front active contours most variational active contour models are designed to find local minima of data dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a desirable local minimum as opposed to an undesirable configuration due to noise or complex image structure as such there has been much research into the design of complex region based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge based energy functionals whose sensitivity to noise and texture is significantly worse unfortunately most of these more robust region based energy functionals are applicable to a much narrower class of imagery compared to typical edge based energies due to stronger global assumptions about the underlying image data devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima such implementations have been proposed for capturing global minima however sometimes the completely global minimum is just as undesirable as a minimum that is too local in this paper we propose a novel fast and flexible dual front implementation of active contours motivated by minimal path techniques and utilizing fast sweeping algorithms which is easily manipulated to yield minima with variable degrees of localness and globalness by simply adjusting the size of active regions the ability to gracefully move from capturing minima that are more local according to the initial placement of the active contour surface to minima that are more global allows this model to more easily obtain desirable minimizers which often are neither the most local nor the most global experiments on various 2d and 3d images and comparisons with some active contour models and region growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications

o log n bimodality analysis abstract the bimodality of a population p can be measured by dividing its range into two intervals so as to maximize the fisher distance between the resulting two subpopulations p 1 and p 2 if p is a mixture of two approximately gaussian subpopulations then p 1 and p 2 are good approximations to the original gaussians if their fisher distance is great enough moreover good approximations to p 1 and p 2 can be obtained by dividing p into small parts finding the maximum distance md subdivision of each part combining small groups of these subdivisions into approximate md subdivisions of larger parts and so on this divide and conquer approach yields an approximate md subdivision of p in o log n computational steps using o n processors where n is the size of p

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

knowledge action and the frame problem this paper proposes a method for handling the frame problem for knowledge producing actions an example of a knowledge producing action is a sensing operation performed by a robot to determine whether or not there is an object of a particular shape within its grasp the work is an extension of reiter s approach to the frame problem for ordinary actions and moore s work on knowledge and action the properties of our specification are that knowledge producing actions do not affect fluents other than the knowledge fluent and actions that are not knowledge producing only affect the knowledge fluent as appropriate in addition memory emerges as a side effect if something is known in a certain situation it remains known at successor situations unless something relevant has changed also it will be shown that a form of regression examined by reiter for reducing reasoning about future situations to reasoning about the initial situation now also applies to knowledge producing actions

a multiscale algorithm for image segmentation by variational method most segmentation algorithms are composed of several procedures split and merge small region elimination boundary smoothing each depending on several parameters the introduction of an energy to minimize leads to a drastic reduction of these parameters the authors prove that the most simple segmentation tool the region merging algorithm made according to the simplest energy is enough to compute a local energy minimum belonging to a compact class and to achieve the job of most of the tools mentioned above the authors explain why merging in a variational framework leads to a fast multiscale multichannel algorithm with a pyramidal structure the obtained algorithm is o n ln n where n is the number of pixels of the picture this fast algorithm is applied to make grey level and texture segmentation and experimental results are shown

stabilization of parametric active contours using a tangential redistribution term depending on implementation active contours have been classified as geometric or parametric active contours parametric contours irrespective of representation are known to suffer from the problem of irregular bunching and spacing out of curve points during the curve evolution in a spline based implementation of active contours this leads to occasional formation of loops locally and subsequently the curve blows up due to instabilities in this paper we analyze the reason for this problem and propose a solution to alleviate the same we propose an ordinary differential equation ode for controlling the curve parametrization during evolution by including a tangential force we show that the solution of the proposed ode is bounded we demonstrate the effectiveness of the proposed method for segmentation and tracking tasks on closed as well as open contours

semiparametric inference in a garch in mean model abstract a new semiparametric estimator for an empirical asset pricing model with general nonparametric risk return tradeoff and garch type underlying volatility is introduced based on the profile likelihood approach it does not rely on any initial parametric estimator of the conditional mean function and it is under stated conditions consistent asymptotically normal and efficient i e it achieves the semiparametric lower bound a sampling experiment provides finite sample comparisons with the parametric approach and the iterative semiparametric approach with parametric initial estimate of conrad and mammen 2008 an application to daily stock market returns suggests that the risk return relation is indeed nonlinear

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

bounded situation calculus action theories in this paper 1 we investigate bounded action theories in the situation calculus a bounded action theory is one which entails that in every situation the number of object tuples in the extension of fluents is bounded by a given constant although such extensions are in general different across the infinitely many situations we argue that such theories are common in applications either because facts do not persist indefinitely or because the agent eventually forgets some facts as new ones are learned we discuss various classes of bounded action theories then we show that verification of a powerful first order variant of the calculus is decidable for such theories notably this variant supports a controlled form of quantification across situations we also show that through verification we can actually check whether an arbitrary action theory maintains boundedness

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

superquadric segmentation in range images via fusion of region and boundary information the high potential of superquadrics as modeling elements for image segmentation tasks has been pointed out for years in the computer vision community in this work we employ superquadrics as modeling elements for multiple object segmentation in range images segmentation is executed in two stages first a hypothesis about the values of the segmentation parameters is generated second the hypothesis is refined locally in both stages object boundary and region information are considered boundary information is derived via model based edge detection in the input range image hypothesis generation uses boundary information to isolate image regions that can be accurately described by superquadrics within hypothesis refinement a game theoretic framework is used to fuse the two information sources by associating an objective function to each information source iterative optimization of the two objective functions in succession outputs a precise description of all image objects we demonstrate experimentally that this approach substantially improves the most established method in superquadric segmentation in terms of accuracy and computational efficiency we demonstrate the applicability of our segmentation framework in real world applications by constructing a novel robotic system for automatic unloading of jumbled box like objects from platforms

limit theory for the sample autocorrelations and extremes of a garch 1 1 process the asymptotic theory for the sample autocorrelations and extremes of a garch i 1 process is provided special attention is given to the case when the sum of the arch and garch parameters is close to 1 that is when one is close to an infinite variance marginal distribution this situation has been observed for various financial log return series and led to the introduction of the igarch model in such a situation the sample autocorrelations are unreliable estimators of their deterministic counterparts for the time series and its absolute values and the sample autocorrelations of the squared time series have nondegenerate limit distributions we discuss the consequences for a foreign exchange rate series

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

inference in arch and garch models with heavy tailed errors arch and garch models directly address the dependency of conditional second moments and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present these include financial time series which can be particularly heavy tailed however little is known about properties of arch or garch models in the heavy tailed setting and no methods are available for approximating the distributions of parameter estimators there in this paper we show that for heavy tailed errors the asymptotic distributions of quasi maximum likelihood parameter estimators in arch and garch models are nonnormal and are particularly difficult to estimate directly using standard parametric methods standard bootstrap methods also fail to produce consistent estimators to overcome these problems we develop percentile t subsample bootstrap approximations to estimator distributions studentizing is employed to approximate scale and the subsample bootstrap is used to estimate shape the good performance of this approach is demonstrated both theoretically and numerically

propositional knowledge base revision and minimal change abstract the semantics of revising knowledge bases represented by sets of propositional sentences is analyzed from a model theoretic point of view a characterization of all revision schemes that satisfy the gardenfors rationality postulates is given in terms of minimal change with respect to an ordering among interpretations revision methods proposed by various authors are surveyed and analyzed in this framework the correspondences between gardenfors like rationality postulates and minimal changes with respect to other orderings are also investigated

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

on the logic of iterated belief revision abstract we show in this paper that the agm postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision thus permitting improper responses to sequences of observations we remedy this weakness by proposing four additional postulates which are sound relative to a qualitative version of probabilistic conditioning contrary to the agm framework the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a belief set we also show that a simple modification to the agm framework can allow belief revision to be a function of epistemic states we establish a model based representation theorem which characterizes the proposed postulates and constrains in turn the way in which entrenchment orderings may be transformed under iterated belief revision

iterated belief change in the situation calculus john mccarthy s situation calculus has left an enduring mark on artificial intelligence research this simple yet elegant formalism for modelling and reasoning about dynamic systems is still in common use more than forty years since it was first proposed the ability to reason about action and change has long been considered a necessary component for any intelligent system the situation calculus and its numerous extensions as well as the many competing proposals that it has inspired deal with this problem to some extent in this paper we offer a new approach to belief change associated with performing actions that addresses some of the shortcomings of these approaches in particular our approach is based on a well developed theory of action in the situation calculus extended to deal with belief moreover by augmenting this approach with a notion of plausibility over situations our account handles nested belief belief introspection mistaken belief and handles belief revision and belief update together with iterated belief change

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

some contributions to the metatheory of the situation calculus we focus on a rich axiomatization for actions in the situation calculus that includes among other features a solution to the frame problem for deterministic actions our work is foundational in nature directed at simplifying the entailment problem for these axioms specifically we make four contributions to the metatheory of situation calculus axiomatizations of dynamical systems 1 we prove that the above mentioned axiomatization for actions has a relative satisfiability property the full axiomatization is satisfiable iff the axioms for the initial state are 2 we define the concept of regression relative to these axioms and prove a soundness and completeness theorem for a regression based approach to the entailment problem for a wide class of queries 3 our formalization of the situation calculus requires certain foundational axioms specifying the domain of situations these include an induction axiom whose presence complicates human and automated reasoning in the situation calculus we characterize various classes of sentences whose proofs do not require induction and in some cases some of the other foundational axioms 4 we prove that the logic programming language golog never requires any of the foundational axioms for the evaluation of programs

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

contour and texture analysis for image segmentation this paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture natural images contain both textured and untextured regions so the cues of contour and texture differences are exploited simultaneously contours are treated in the intervening contour framework while texture is analyzed using textons each of these cues has a domain of applicability so to facilitate cue combination we introduce a gating operator based on the texturedness of the neighborhood at a pixel having obtained a local measure of how likely two nearby pixels are to belong to the same region we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness experimental results on a wide range of images are shown

the uncertainty principle in image processing the uncertainty principle is recognized as one of the fundamental results in signal processing its role in inference is however less well known outside of quantum mechanics it is the aim of this paper to provide a unified approach to the problem of uncertainty in image processing it is shown that uncertainty can be derived from the fundamental constraints on the process of vision the requirements for class defining operations which are both shift invariant and insensitive to changes in illumination it is thus shown that uncertainty plays a key role in the language of vision since it affects the choice of both the alphabet the elementary signals and the syntax the inferential structure of vision the report is concluded with a number of practical illustrations of these ideas taken from such image processing tasks as enhancement data compression and segmentation

the contracting curve density algorithm fitting parametric curve models to images using local self adapting separation criteria the task of fitting parametric curve models to the boundaries of perceptually meaningful image regions is a key problem in computer vision with numerous applications such as image segmentation pose estimation object tracking and 3 d reconstruction in this article we propose the contracting curve density ccd algorithm as a solution to the curve fitting problem the ccd algorithm extends the state of the art in two important ways first it applies a novel likelihood function for the assessment of a fit between the curve model and the image data this likelihood function can cope with highly inhomogeneous image regions because it is formulated in terms of local image statistics the local image statistics are learned on the fly from the vicinity of the expected curve they provide therefore locally adapted criteria for separating the adjacent image regions these local criteria replace often used predefined fixed criteria that rely on homogeneous image regions or specific edge properties the second contribution is the use of blurred curve models as efficient means for iteratively optimizing the posterior density over possible model parameters these blurred curve models enable the algorithm to trade off two conflicting objectives namely heaving a large area of convergence and achieving high accuracy we apply the ccd algorithm to several challenging image segmentation and 3 d pose estimation problems our experiments with rgb images show that the ccd algorithm achieves a high level of robustness and sub pixel accuracy even in the presence of severe texture shading clutter partial occlusion and strong changes of illumination

belief revision and projection in the epistemic situation calculus abstract this article considers defeasible beliefs in dynamic settings in particular we examine the belief projection problem what is believed after performing an action and or receiving new information the approach is based on an epistemic variant of reiter s situation calculus where actions not only have physical effects but may also provide new information to the agent the preferential belief structure is initially determined using conditional statements new information is then incorporated using two popular belief revision schemes namely natural and lexicographic revision the projection problem is solved twofold in this formalism by goal regression and by knowledge base progression

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners