elastically adaptive deformable models we present a technique for the automatic adaptation of a deformable model s elastic parameters within a kalman filter framework for shape estimation applications the novelty of the technique is that the model s elastic parameters are not constant but spatio temporally varying the variation of the elastic parameters depends on the distance of the model from the data and the rate of change of this distance each pass of the algorithm uses physics based modeling techniques to iteratively adjust both the geometric and the elastic degrees of freedom of the model in response to forces that are computed from the discrepancy between the model and the data by augmenting the state equations of an extended kalman filter to incorporate these additional variables we are able to significantly improve the quality of the shape estimation therefore the model s elastic parameters are always initialized to the same value and they are subsequently modified depending on the data and the noise distribution we present results demonstrating the effectiveness of our method for both two dimensional and three dimensional data

a maximum likelihood surface estimator for dense range data describes how to estimate 3d surface models from dense sets of noisy range data taken from different points of view i e multiple range maps the proposed method uses a sensor model to develop an expression for the likelihood of a 3d surface conditional on a set of noisy range measurements optimizing this likelihood with respect to the model parameters provides an unbiased and efficient estimator the proposed numerical algorithms make this estimation computationally practical for a wide variety of circumstances the results from this method compare favorably with state of the art approaches that rely on the closest point or perpendicular distance metric a convenient heuristic that produces biased solutions and fails completely when surfaces are not sufficiently smooth as in the case of complex scenes or noisy range measurements empirical results on both simulated and real ladar data demonstrate the effectiveness of the proposed method for several different types of problems furthermore the proposed method offers a general framework that can accommodate extensions to include surface priors more sophisticated noise models and other sensing modalities such as sonar or synthetic aperture radar

learning shape correspondence for n d curves we present a learning method that introduces explicit knowledge into the shape correspondence problem given two input curves to be matched our approach establishes a dense correspondence field between them where the characteristics of the matching field closely resemble those in an a priori learning set we build a shape distance matrix from the values of a shape descriptor computed at every point along the curves this matrix embeds the correspondence problem in a highly expressive and redundant construct and provides the basis for a pattern matching strategy for curve matching we selected the previously introduced observed transport measure as a shape descriptor as its properties make it particularly amenable to the matching problem synthetic and real examples are presented along with discussions of the robustness and applications of the technique

power stable aggregation functions we discuss and exemplify binary power stable aggregation functions on the interval 0 1 i e log ratio invariant aggregation functions for continuous power stable aggregation functions we introduce several methods of constructing dependence functions we also study dependence functions yielding symmetry idempotency and some other properties finally continuous associative power stable aggregation functions are completely characterized

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

multi level shape representation using global deformations andlocally adaptive finite elements we present a model based method for the multi level shape pose estimation and abstraction of an object s surface from range data the surface shape is estimated based on the parameters of a superquadric that is subjected to global deformations tapering and bending and a varying number of levels of local deformations local deformations are implemented using locally adaptive finite elements whose shape functions are piecewise cubic functions with c 1 continuity the surface pose is estimated based on the model s translational and rotational degrees of freedom the algorithm first does a coarse fit solving for a first approximation to the translation rotation and global deformation parameters and then does several passes of mesh refinement by locally subdividing triangles based on the distance between the given datapoints and the model the adaptive finite element algorithm ensures that during subdivision the desirable finite element mesh generation properties of conformity non degeneracy and smoothness are maintained each pass of the algorithm uses physics based modeling techniques to iteratively adjust the global and local parameters of the model in response to forces that are computed from approximation errors between the model and the data we present results demonstrating the multi level shape representation for both sparse and dense range data

a sequential stochastic assignment problem in a partially observable markov chain a sequential stochastic assignment problem in a stationary markov chain where the states are not known explicitly is considered this is an optimization problem in a partially observable markov chain and an optimal policy and the total expected reward under this policy are obtained here we specify the learning procedure by the bayes theorem and the optimal policy is not always a critical number policy as a special case of this problem a problem of optimal selections is considered and a relation to former results of a sequential stochastic assignment problem is observed

properties of a job search problem on a partially observable markov chain in a dynamic economy this paper observes a job search problem on a partially observable markov chain which can be considered as an extension of a job search in a dynamic economy in 1 this problem is formulated as the state changes according to a partially observable markov chain i e the current state cannot be observed but there exists some information regarding what a present state is all information about the unobservable state are summarized by the probability distributions on the state space and we employ the bayes theorem as a learning procedure the total positivity of order two or simply tp 2 is a fundamental property to investigate sequential decision problems and it also plays an important role in the bayesian learning procedure for a partially observable markov process by using this property we consider some relationships among prior and posterior information and the optimal policy we will also observe the probabilities to make a transition into each state after some additional transitions by empolying the optimal policy in the stock market suppose that the states correspond to the business situation of one company and if there is a state designating the default then the problem is what time the stocks are sold off before bankrupt and the probability to become bankrupt will be also observed

constraints on deformable models recovering 3d shape and nongrid motion abstract inferring the 3d structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision our approach makes use of dynamic elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real world visual constraints we specialize these models to include intrinsic forces inducing a preference for axisymmetry image based constraints are applied as extrinsic forces that mold the symmetry seeking model into shapes consistent with image data we describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects we generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data for time varying images the force becomes dynamic and the model is able to infer not only depth but nonrigid motion as well we demonstrate the recovery of 3d shape and nonrigid motion from natural imagery

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

estimating optical flow in segmented images using variable order parametric models with local deformations this paper presents a new model for estimating optical flow based on the motion of planar regions plus local deformations the approach exploits brightness information to organize and constrain the interpretation of the motion by using segmented regions of piecewise smooth brightness to hypothesize planar regions in the scene parametric flow models are estimated in these regions in a two step process which first computes a coarse fit and then estimates the appropriate parametrization of the motion of the region the initial fit is refined using a generalization of the standard area based regression approaches since the assumption of planarity is likely to be violated we allow local deformations from the planar assumption in the same spirit as physically based approaches which model shape using coarse parametric models plus local deformations this parametric plus deformation model exploits the strong constraints of parametric approaches while retaining the adaptive nature of regularization approaches experimental results on a variety of images model produces accurate flow estimates while the incorporation of brightness segmentation boundaries

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

efficient model based quantification of left ventricular function in 3 d echocardiography quantitative functional analysis of the left ventricle plays a very important role in the diagnosis of heart diseases while in standard two dimensional echocardiography this quantification is limited to rather crude volume estimation three dimensional 3 d echocardiography not only significantly improves its accuracy but also makes it possible to derive valuable additional information like various wall motion measurements in this paper we present a new efficient method for the functional evaluation of the left ventricle from 3 d echographic sequences it comprises a segmentation step that is based on the integration of 3 d deformable surfaces and a four dimensional statistical heart motion model the segmentation results in an accurate 3 d time left ventricle discrete representation functional descriptors like local wall motion indexes are automatically derived from this representation the method has been successfully tested both on electrocardiography gated and real time 3 d data it has proven to be fast accurate and robust

minimal surfaces based object segmentation a geometric approach for 3d object segmentation and representation is presented the segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3d image the model is based on curvature motion and the computation of surfaces with minimal areas better known as minimal surfaces the space where the surfaces are computed is induced from the 3d image volumetric data in which the objects are to be detected the model links between classical deformable surfaces obtained via energy minimization and intrinsic ones derived from curvature based flows the new approach is stable robust and automatically handles changes in the surface topology during the deformation

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

discrete active models and applications abstract optimization processes based on active models play central roles in many areas of computational vision as well as computational geometry unfortunately current models usually require highly complex and sophisticated mathematical machinery and at the same time they suffer from a number of limitations which impose restrictions on their applicability in this paper a simple class of discrete active models called migration processes mps is presented the processes are based on iterated averaging over neighborhoods defined by constant geodesic distance it is demonstrated that the mp model a system of self organizing active particles has a number of advantages over previous models both parametric active models snakes and implicit contour evolution models due to the generality of the mp model the process can be applied to derive natural solutions to a variety of optimization problems including defining minimal surface patches given their boundary curves finding shortest paths joining sets of points and decomposing objects into primitive parts

hierarchical vibrations for part based recognition of complex objects we propose a technique for the recognition and segmentation of complex shapes in 2d images using a hierarchy of finite element vibration modes in an evolutionary shape search the different levels of the shape hierarchy can influence each other which can be exploited in top down part based image analysis our method overcomes drawbacks of existing structural approaches which cannot uniformly encode shape variation and co variation or rely on training we present results demonstrating that by utilizing a quality of fit function the model explicitly recognizes missing parts of a complex shape thus allowing for categorization between shape classes

geodesic deformable models for medical image analysis in this paper implicit representations of deformable models for medical image enhancement and segmentation are considered the advantage of implicit models over classical explicit models is that their topology can be naturally adapted to objects in the scene a geodesic formulation of implicit deformable models is especially attractive since it has the energy minimizing properties of classical models the aim of this paper is twofold first a modification to the customary geodesic deformable model approach is introduced by considering all the level sets in the image as energy minimizing contours this approach is used to segment multiple objects simultaneously and for enhancing and segmenting cardiac computed tomography ct and magnetic resonance images second the approach is used to effectively compare implicit and explicit models for specific tasks this shows the complementary character of implicit models since in case of poor contrast boundaries or gaps in boundaries e g due to partial volume effects noise or motion artifacts they do not perform well since the approach is completely data driven

3 d shape recovery using distributed aspect matching an approach to the recovery of 3 d volumetric primitives from a single 2 d image is presented the approach first takes a set of 3 d volumetric modeling primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives conditional probabilities capture the ambiguity of mappings between levels of the hierarchy from a region segmentation of the input image the authors present a formulation of the recovery problem based on the grouping of the regions into aspects no domain independent heuristics are used only the probabilities inherent in the aspect hierarchy are exploited once the aspects are recovered the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity as a front end to an object recognition system the approach provides the indexing power of complex 3 d object centered primitives while exploiting the convenience of 2 d viewer centered aspect matching aspects are used to represent a finite vocabulary of 3 d parts from which objects can be constructed

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

design and recovery of 2 d and 3 d shapes using rational gaussian curves and surfaces a new representation for parametric curves and surfaces is introduced here it is in rational form and uses rational gaussian bases this representation allows design of 2 d and 3 d shapes and makes recovery of shapes from noisy image data possible the standard deviations of gaussians in a curve or surface control the smoothness of a recovered shape the control points of a surface in this representation are not required to form a regular grid and a scattered set of control points is sufficient to reconstruct a surface examples of shape design shape recovery and image segmentation using the proposed representation are given

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

inference of integrated surface curve and junction descriptions from sparse 3d data we address the problem of inferring integrated high level descriptions such as surfaces 3d curves and junctions from a sparse point set for precise localization we propose a noniterative cooperative algorithm in which surfaces curves and junctions work together initial estimates are computed based on the work by guy and medioni 1997 where each point in the given sparse and possibly noisy point set is convolved with a predefined vector mask to produce dense saliency maps these maps serve as input to our novel extremal surface and curve algorithms for initial surface and curve extraction these initial features are refined and integrated by using excitatory and inhibitory fields consequently intersecting surfaces resp curves are fused precisely at their intersection curves resp junctions results on several synthetic as well as real data sets are presented

the medial scaffold of 3d unorganized point clouds we introduce the notion of the medial scaffold a hierarchical organization of the medial axis of a 3d shape in the form of a graph constructed from special medial curves connecting special medial points a key advantage of the scaffold is that it captures the qualitative aspects of shape in a hierarchical and tightly condensed representation we propose an efficient and exact method for computing the medial scaffold based on a notion of propagation along the scaffold itself starting from initial sources of the flow and constructing the scaffold during the propagation we examine this method specifically in the context of an unorganized cloud of points in 3d e g as obtained from laser range finders which typically involve hundreds of thousands of points but the ideas are generalizable to data arising from geometrically described surface patches the computational bottleneck in the propagation based scheme is in finding the initial sources of the flow we thus present several ideas to avoid the unnecessary consideration of pairs of points which cannot possibly form a medial point source such as the visibility of a point from another given a third point and the interaction of clusters of points an application of using the medial scaffold for the representation of point samplings of real life objects is also illustrated

flexible multibody dynamics and adaptive finite element techniques for model synthesis and estimation abstract this paper develops a general approach for the efficient modeling and animation of non rigid multibody objects we develop a new family of physics based modeling primitives that can undergo free motions as well as parameterized and free form deformations starting with parameterized geometric primitives and adding global geometric deformations local finite element deformations mass distributions and elasticities we create deformable models that display correct physical behaviors in order to further enhance the accuracy of our shape representation we develop adaptive finite element techniques our algorithm ensures that during element subdivision the desirable finite element mesh properties of conformity non degeneracy and smoothness are maintained in this way not only can we represent more accurately an object surface but also more efficiently because new model nodes are added only when necessary in a local fashion furthermore in the paper we adapt and implement efficient constraint methods for connecting physical primitives together to make articulated multibody objects we demonstrate the computationally efficient performance of our algorithms for the synthesis and visualization of deformable models as well as for estimating the shapes and motions of deformable objects

from multiple stereo views to multiple 3 d surfaces we present a framework for 3 dimensional surface reconstruction that can be used to model fully 3 d scenes from an arbitrary number of stereo views taken from vastly different viewpoints this is a key step toward producing 3 d world descriptions of complex scenes using stereo and is a very challenging problem real world scenes tend to contain many 3 d objects they do not usually conform to the 2 1 2 d assumption made by traditional algorithms and one cannot take it for granted that the computed 3 d points can easily be clustered into separate groups furthermore stereo data is often incomplete and sometimes erroneous which makes the problem even more difficult by combining a particle based representation robust fitting and optimization of an image based objective function we have been able to reconstruct surfaces without any a priori knowledge of their topology and in spite of the noisiness of the stereo data our current implementation goes through three steps initializing a set of particles from the input 3 d data optimizing their location and finally grouping them into global surfaces using several complex scenes containing multiple objects we demonstrate the competence of this method and its ability to merge information and thus to go beyond what can be done with conventional stereo alone

on deformable models for visual pattern recognition this paper reviews model based methods for non rigid shape recognition these methods model match and classify non rigid shapes which are generally problematic for conventational algorithms using rigid models issues including model representation optimization criteria formulation model matching and classification are examined in detail with the objective to provide interested researchers a roadmap for exploring the field this paper emphasizes on 2d deformable models their potential applications and future research directions particularly on deformable pattern classification are discussed

3 d to 2 d pose determination with regions this paper presents a novel approach to parts based object recognition in the presence of occlusion we focus on the problem of determining the pose of a 3 d object from a single 2 d image when convex parts of the object have been matched to corresponding regions in the image we consider three types of occlusions self occlusion occlusions whose locus is identified in the image and completely arbitrary occlusions we show that in the first two cases this is a convex optimization problem derive efficient algorithms and characterize their performance for the last case we prove that the problem of finding valid poses is computationally hard but provide an efficient approximate algorithm this work generalizes our previous work on region based object recognition which focused on the case of planar models

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

robust shape recovery from occluding contours using a linear smoother recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent for three or more views shape recovery is possible and several algorithms have recently been developed for this purpose we present a new approach to the multiframe stereo problem that does not depend on differential measurements in the image which may be noise sensitive instead we use a linear smoother to optimally combine all of the measurements available at the contours and other edges in all of the images this allows us to extract a robust and reasonably dense estimate of surface shape and to integrate shape information from both surface markings and occluding contours results are presented which empirically show that in the presence of noise smoothing over more than three views reduces the error even when the epipolar curve is nonplanar

surface deformation models for nonrigid 3d shape recovery three dimensional detection and shape recovery of a nonrigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data here we introduce an approach to creating such models for deformable 3d surfaces we exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets we use this set of angles to create a representative set of potential shapes which we feed to a simple dimensionality reduction technique to produce low dimensional 3d deformation models we show that these models can be used to accurately model a wide range of deforming 3d surfaces from video sequences acquired under realistic conditions

matching 3 d anatomical surfaces with non rigid deformations using octree splines presents a new method for determining the minimal nonrigid deformation between two 3d surfaces such as those which describe anatomical structures in 3d medical images although the authors match surfaces they represent the deformation as a volumetric transformation their method performs a least squares minimization of the distance between the two surfaces of interest to quickly and accurately compute distances between points on the two surfaces the authors use a precomputed distance map represented using an octree spline whose resolution increases near the surface to quickly and robustly compute the deformation the authors use a second octree spline to model the deformation function the coarsest level of the deformation encodes the global e g affine transformation between the two surfaces while finer levels encode smooth local displacements which bring the two surfaces into closer registration the authors present experimental results on both synthetic and real 3d surfaces

adaptive reproducing kernel particle method for extraction of the cortical surface we propose a novel adaptive approach based on the reproducing kernel particle method rkpm to extract the cortical surfaces of the brain from three dimensional 3 d magnetic resonance images mris to formulate the discrete equations of the deformable model a flexible particle shape function is employed in the galerkin approximation of the weak form of the equilibrium equations the proposed support generation method ensures that support of all particles cover the entire computational domains the deformable model is adaptively adjusted by dilating the shape function and by inserting or merging particles in the high curvature regions or regions stopped by the target boundary the shape function of the particle with a dilation parameter is adaptively constructed in response to particle insertion or merging the proposed method offers flexibility in representing highly convolved structures and in refining the deformable models self intersection of the surface during evolution is prevented by tracing backward along gradient descent direction from the crest interface of the distance field which is computed by fast marching these operations involve a significant computational cost the initial model for the deformable surface is simple and requires no prior knowledge of the segmented structure no specific template is required e g an average cortical surface obtained from many subjects the extracted cortical surface efficiently localizes the depths of the cerebral sulci unlike some other active surface approaches that penalize regions of high curvature comparisons with manually segmented landmark data are provided to demonstrate the high accuracy of the proposed method we also compare the proposed method to the finite element method and to a commonly used cortical surface extraction approach the cruise method we also show that the independence of the shape functions of the rkpm from the underlying mesh enhances the convergence speed of the deformable model

multiscale 3 d shape representation and segmentation using spherical wavelets this paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform this work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures such as the caudate nucleus or the hippocampus our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations enabling the construction of more descriptive nonglobal nonuniform shape probability priors to be included in the segmentation and shape analysis framework in particular this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine local variations in a population of shapes in the presence of a limited dataset specifically our technique defines a multiscale parametric model of surfaces belonging to the same population using a compact set of spherical wavelets targeted to that population we further refine the shape representation by separating into groups wavelet coefficients that describe independent global and or local biological variations in the population using spectral graph partitioning we then learn a prior probability distribution induced over each group to explicitly encode these variations at different scales and spatial locations based on this representation we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior for segmentation additionally the optimization method can be applied in a coarse to fine manner we apply our algorithm to two different brain structures the caudate nucleus and the hippocampus of interest in the study of schizophrenia we show 1 a reconstruction task of a test set to validate the expressiveness of our multiscale prior and 2 a segmentation task in the reconstruction task our results show that for a given training set size our algorithm significantly improves the approximation of shapes in a testing set over the point distribution model which tends to oversmooth data in the segmentation task our validation shows our algorithm is computationally efficient and outperforms the active shape model algorithm by capturing finer shape details

recovery of parametric models from range images the case for superquadrics with global deformations a method for recovery of compact volumetric models for shape representation of single part objects in computer vision is introduced the models are superquadrics with parametric deformations bending tapering and cavity deformation the input for the model recovery is three dimensional range points model recovery is formulated as a least squares minimization of a cost function for all range points belonging to a single part during an iterative gradient descent minimization process all model parameters are adjusted simultaneously recovery position orientation size and shape of the model such that most of the given range points lie close to the model s surface a specific solution among several acceptable solutions where are all minima in the parameter space can be reached by constraining the search to a part of the parameter space the many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization results using real range data show that the recovered models are stable and that the recovery procedure is fast

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

what is the best causal scale space for three dimensional images we study the unique affine invariant morphological scale space in three dimensions we discuss its properties and show that it improves the dynamic shape model we explain the algorithms and display the first numerical experiments

learning to track the visual motion of contours abstract a development of a method for tracking visual contours is described given an untrained tracker a training motion of an object can be observed over some extended time and stored as an image sequence the image sequence is used to learn parameters in a stochastic differential equation model these are used in turn to build a tracker whose predictor imitates the motion in the training set tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions

hierarchical active shape models using the wavelet transform active shape models asms are often limited by the inability of relatively few eigenvectors to capture the full range of biological shape variability this paper presents a method that overcomes this limitation by using a hierarchical formulation of active shape models using the wavelet transform the statistical properties of the wavelet transform of a deformable contour are analyzed via principal component analysis and used as priors in the contour s deformation some of these priors reflect relatively global shape characteristics of the object boundaries whereas some of them capture local and high frequency shape characteristics and thus serve as local smoothness constraints this formulation achieves two objectives first it is robust when only a limited number of training samples is available second by using local statistics as smoothness constraints it eliminates the need for adopting ad hoc physical models such as elasticity or other smoothness models which do not necessarily reflect true biological variability examples on magnetic resonance images of the corpus callosum and hand contours demonstrate that good and fully automated segmentations can be achieved even with as few as five training samples

technical note stochastic sequential decision making with a random number of jobs this paper addresses a class of problems in which available resources need to be optimally allocated to a random number of jobs with stochastic parameters optimal policies are presented for variations of the sequential stochastic assignment problem and the dynamic stochastic knapsack problem in which the number of arriving jobs is unknown until after the final arrival and the job parameters are assumed to be independent but not identically distributed random variables

1 lipschitz power stable aggregation functions in this paper we study the structure of the class of all binary 1 lipschitz power stable aggregation functions a special attention is devoted to the characterization of power stable quasi copulas moreover the relations between copulas and quasi copulas as 1 lipschitz aggregation functions with neutral element e 1 sup and inf closures of copulas and track defined functions based on copulas in the framework of binary power stable aggregation functions are characterized

the dynamic and stochastic knapsack problem the dynamic and stochastic knapsack problem dskp is defined as follows items arrive according to a poisson process in time each item has a demand size for a limited resource the knapsack and an associated reward the resource requirements and rewards are jointly distributed according to a known probability distribution and become known at the time of the item s arrival items can be either accepted or rejected if an item is accepted the item s reward is received and if an item is rejected a penalty is paid the problem can be stopped at any time at which time a terminal value is received which may depend on the amount of resource remaining given the waiting cost and the time horizon of the problem the objective is to determine the optim al policy that maximizes the expected value rewards minus costs accumulated assuming that all items have equal sizes but random rewards optimal solutions are derived for a variety of cost structures and time horizons and recursive algorithms for computing them are developed optimal closed form solutions are obtained for special cases the dskp has applications in freight transportation in scheduling of batch processors in selling of assets and in selection of investment projects

the dynamic and stochastic knapsack problem with deadlines in this paper a dynamic and stochastic model of the well known knapsack problem is developed and analyzed the problem is motivated by a wide variety of real world applications objects of random weight and reward arrive according to a stochastic process in time the weights and rewards associated with the objects are distributed according to a known probability distribution each object can either be accepted to be loaded into the knapsack of known weight capacity or be rejected the objective is to determine the optimal policy for loading the knapsack within a fixed time horizon so as to maximize the expected accumulated reward the optimal decision rules are derived and are shown to exhibit surprising behavior in some cases it is also shown that if the distribution of the weights is concave then the decision rules behave according to intuition

detection of object wings in fused range and intensity imagery abstract we present methods for detecting primitives in scenes containing objects whose surfaces are approximately piecewise quadric using a sensor that yields fused range and intensity the primitives detected in a fused image are viewpoint dependent and are called object wings which consist of adjacent fragments of object contour and surface wings are small enough so that some object parts can be sensed despite significant occlusion yet rich enough to be of use in indexing to candidate models in constraining object pose and in aggregation methods which combine primitives into larger structures or objects fitting procedures are defined for specific wing primitives experiments with both synthetic and real data show that classification within the wing types of planar spherical conical cylindrical can be achieved with over 90 accuracy contour information available in fitting fused data improves fitting relative to use of surface data alone moreover it is shown that only a small number of contour and surface samples are needed for extraction of primitives oc 1997 pattern recognition society

a bayesian framework for noise covariance estimation using the facet model in image processing literature thus far researchers have assumed the perturbation in the data to be white or uncorrelated having a covariance matrix spl sigma sup 2 i i e assumption of equal variance for all the data samples and that no correlation exists between the data samples however there have been very few attempts to estimate noise characteristics under the assumption that there is a correlation between data samples in this work we propose a new and a novel approach for the simultaneous bayesian estimation of the unknown colored or correlated noise population covariance matrix and the hyperparameters of the covariance model using the well known facet model we also estimate the facet model coefficients we use the facet model because of its simple yet elegant mathematical formulation we use the generalized inverted wishart density as the prior model for the noise covariance matrix we place a structure on the covariance matrix using the parameters of a correlation filter these hyperparameters are estimated by a new extension of the expectation maximization algorithm called the generalized constrained expectation maximization algorithm that we developed

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

point tracked quantitative analysis of left ventricular surface motion from 3 d image sequences proposes and validates the hypothesis that one can use differential shape properties of the myocardial surfaces to recover dense field motion from standard three dimensional 3 d image sequences mri and ct quantitative measures of left ventricular regional function can be further inferred from the point correspondence maps the noninvasive algorithm derived results are validated on two levels first the motion trajectories are compared to those of implanted imaging opaque markers of a canine model in two imaging modalities where subpixel accuracy is achieved second the validity of using motion parameters path length and thickness changes for detecting myocardial injury area is tested by comparing algorithms derived results to postmortem analysis ttc staining of myocardial tissue where the achieved pearson product moment correlation value is 0 968