shape description and matching using integral invariants on eccentricity transformed images matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision to keep track of changes inside the breast for example it is important for a computer aided detection system to establish correspondences between regions of interest shape transformations computed both with integral invariants ii and with geodesic distance yield signatures that are invariant to isometric deformations such as bending and articulations integral invariants describe the boundaries of planar shapes however they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure conversely eccentricity transforms ecc can match shapes by signatures of geodesic distance histograms based on information from inside the shape but they ignore the boundary information we describe a method that combines the boundary signature of a shape obtained from ii and structural information from the ecc to yield results that improve on them separately

on shape of plane elastic curves we study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending stretching or compressing line segments non uniformly along their extensions shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape preserving transformations the elastic properties of the curves are encoded in riemannian metrics on these spaces geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques the shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated

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

dali deformation and light invariant descriptor recent advances in 3d shape analysis and recognition have shown that heat diffusion theory can be effectively used to describe local features of deforming and scaling surfaces in this paper we show how this description can be used to characterize 2d image patches and introduce dali a novel feature point descriptor with high resilience to non rigid image transformations and illumination changes in order to build the descriptor 2d image patches are initially treated as 3d surfaces patches are then described in terms of a heat kernel signature which captures both local and global information and shows a high degree of invariance to non linear image warps in addition by further applying a logarithmic sampling and a fourier transform invariance to photometric changes is achieved finally the descriptor is compacted by mapping it onto a low dimensional subspace computed using principal component analysis allowing for an efficient matching a thorough experimental validation demonstrates that dali is significantly more discriminative and robust to illuminations changes and image transformations than state of the art descriptors even those specifically designed to describe non rigid deformations

the dynamical critical exponent of the two three and five dimensional kinetic ising model abstract we present monte carlo simulation results for the dynamical critical exponent z of the two three and five dimensional kinetic ising model we used glauber as well as metropolis dynamics both type of dynamics lead to the same z values in two and three dimensions the z values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at tc for very large systems up to 169984 2 3072 3 and 48 5 for the two dimensional case we obtain z 2 21 0 03 and for the three dimensional case z 2 08 0 03 for the five dimensional glauber case the requirement z 2 gives a critical point j kbtc 0 11391 from monte carlo simulations whereas new series expansions with four more terms give 0 113935 0 000015 for this ratio

efficient computation of isometry invariant distances between surfaces we present an efficient computational framework for isometry invariant comparison of smooth surfaces we formulate the gromov hausdorff distance as a multidimensional scaling like continuous optimization problem in order to construct an efficient optimization scheme we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples for isometry invariant comparison of surfaces in the case of partially missing data we present the partial embedding distance which is computed using a similar scheme the main idea is finding a minimum distortion mapping from one surface to another while considering only relevant geodesic distances we discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

hierarchical finite element analysis of the vibration of membranes abstract a hierachical finite element for the vibration of membranes is presented the element has the ability to be joined to neighbouring elements and the numbers of hierarchical terms are allowed to vary in both directions of the element co ordinate axes the element transverse displacement is described by four linear shape functions plus a variable number of hierarchical functions which are forms of legendre orthogonal polynomials the four nodal displacements and the amplitudes of the hierarchical functions on the edges and in the interior of the element are used as generalized co ordinates inter element compatibility is achieved by matching the generalized co ordinates at the nodes and edges shared by elements results are obtained for simply supported square and l shaped membranes comparisons are made with exact solutions for the square membrane and with highly accurate approximate and linear finite element solutions for the l shaped membrane the results for the square membrane confirm that the solutions always converge from above to the exact values as the numbers of hierarchical terms are increased and highly accurate answers are obtained depite the use of a very few hierarchical terms the results of the l shaped membrane show that the hierarchical finite element solutions are largely more accurate than the linear finite element solutions despite the use of fewer system degrees of freedom

three dimensional face recognition an expression invariant 3d face recognition approach is presented our basic assumption is that facial expressions can be modelled as isometries of the facial surface this allows to construct expression invariant representations of faces using the bending invariant canonical forms approach the result is an efficient and accurate face recognition algorithm robust to facial expressions that can distinguish between identical twins the first two authors we demonstrate a prototype system based on the proposed algorithm and compare its performance to classical face recognition methods the numerical methods employed by our approach do not require the facial surface explicitly the surface gradients field or the surface metric are sufficient for constructing the expression invariant representation of any given face it allows us to perform the 3d face recognition task while avoiding the surface reconstruction stage

approximating rate distortion graphs of individual data experiments in lossy compression and denoising classical rate distortion theory requires specifying a source distribution instead we analyze rate distortion properties of individual objects using the recently developed algorithmic rate distortion theory the latter is based on the noncomputable notion of kolmogorov complexity to apply the theory we approximate the kolmogorov complexity by standard data compression techniques and perform a number of experiments with lossy compression and denoising of objects from different domains we also introduce a natural generalization to lossy compression with side information to maintain full generality we need to address a difficult searching problem while our solutions are therefore not time efficient we do observe good denoising and compression performance

holographic representations of images we discuss a new type of holographic image representations that have advantages in a distributed world we call these representations holographic arbitrary portions of a holographic representation enable reconstruction of the whole image with distortions that decrease gradually with the increase in the size of the portions available holographic representations enable progressive refinement in image communication or retrieval tasks with no restrictions on the order in which the data fragments sections of the representation are accessed or become available

classification with nonmetric distances image retrieval and class representation a key problem in appearance based vision is understanding how to use a set of labeled images to classify new images systems that model human performance or that use robust image matching methods often use nonmetric similarity judgments but when the triangle inequality is not obeyed most pattern recognition techniques are not applicable exemplar based nearest neighbor methods can be applied to a wide class of nonmetric similarity functions the key issue however is to find methods for choosing good representatives of a class that accurately characterize it we show that existing condensing techniques are ill suited to deal with nonmetric dataspaces we develop techniques for solving this problem emphasizing two points first we show that the distance between images is not a good measure of how well one image can represent another in nonmetric spaces instead we use the vector correlation between the distances from each image to other previously seen images second we show that in nonmetric spaces boundary points are less significant for capturing the structure of a class than in euclidean spaces we suggest that atypical points may be more important in describing classes we demonstrate the importance of these ideas to learning that generalizes from experience by improving performance we also suggest ways of applying parametric techniques to supervised learning problems that involve a specific nonmetric distance functions showing how to generalize the idea of linear discriminant functions in a way that may be more useful in nonmetric spaces

representation and self similarity of shapes representing shapes in a compact and informative form is a significant problem for vision systems that must recognize or classify objects we describe a compact representation model for two dimensional 2d shapes by investigating their self similarities and constructing their shape axis trees sa trees our approach can be formulated as a variational one or equivalently as map estimation of a markov random field we start with a 2d shape its boundary contour and two different parameterizations for the contour one parameterization is oriented counterclockwise and the other clockwise to measure its self similarity the two parameterizations are matched to derive the best set of one to one point to point correspondences along the contour the cost functional used in the matching may vary and is determined by the adopted self similarity criteria e g cocircularity distance variation parallelism and region homogeneity the loci of middle points of the pairing contour points yield the shape axis and they can be grouped into a unique free tree structure the sa tree by implicitly encoding the local and global shape information into an sa tree a variety of vision tasks e g shape recognition comparison and retrieval can be performed in a more robust and efficient way via various tree based algorithms a dynamic programming algorithm gives the optimal solution in o n sup 1 where n is the size of the contour

multiscale distance matrix for fast plant leaf recognition in this brief we propose a novel contour based shape descriptor called the multiscale distance matrix to capture the shape geometry while being invariant to translation rotation scaling and bilateral symmetry the descriptor is further combined with a dimensionality reduction to improve its discriminative power the proposed method avoids the time consuming pointwise matching encountered in most of the previously used shape recognition algorithms it is therefore fast and suitable for real time applications we applied the proposed method to the task of plan leaf recognition with experiments on two data sets the swedish leaf data set and the icl leaf data set the experimental results clearly demonstrate the effectiveness and efficiency of the proposed descriptor

three dimensional free vibration analysis of plates using the h p version of the finite element method the h p version of the finite element method based on a pentahedral p element is applied to three dimensional free vibrations of plates the element s new hierarchical shape functions are expressed in terms of the shifted legendre orthogonal polynomials the accuracy of the solution can be improved by simultaneously refining the mesh and increasing the polynomial order the method is capable of providing a full frequency spectrum including both the in plane and the out of plane modes results of frequency calculations are first found for a skew plate on a soft edge support and a cantilevered right isosceles triangular plate and comparisons are made with other methods results are also found for a square plate on a hard edge support and comparisons are made with two dimensional plate theories furthermore highly accurate values for a free hexagonal plate are presented for the first time

generating and generalizing models of visual objects abstract we report on initial experiments with an implemented learning system whose inputs are images of two dimensional shapes the system first builds semantic network descriptions of shapes based on brady s smoothed local symmetry representation it learns shape models from them using a substantially modified version of winston s analogy program a generalization of gray coding enables the representation to be extended and also allows a single operation called ablation to achieve the effects of many standard induction heuristics the program can learn disjunctions and can learn concepts using only positive examples we discuss learnability and the pervasive importance of representational hierarchies

energy relaxation in ising models starting with all spins parallel simulations show the energy to relax at the critical point as t 1 z with z near 2 2 for 1699802 no logarithm and 2 1 for 28003

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

full and partial symmetries of non rigid shapes symmetry and self similarity are the cornerstone of nature exhibiting themselves through the shapes of natural creations and ubiquitous laws of physics since many natural objects are symmetric the absence of symmetry can often be an indication of some anomaly or abnormal behavior therefore detection of asymmetries is important in numerous practical applications including crystallography medical imaging and face recognition to mention a few conversely the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis traditionally symmetries are described as extrinsic geometric properties of the shape while being adequate for rigid shapes such a description is inappropriate for non rigid ones extrinsic symmetry can be broken as a result of shape deformations while its intrinsic symmetry is preserved in this paper we present a generalization of symmetries for non rigid shapes and a numerical framework for their analysis addressing the problems of full and partial exact and approximate symmetry detection and classification

wesd weighted spectral distance for measuring shape dissimilarity this paper presents a new distance for measuring shape dissimilarity between objects recent publications introduced the use of eigenvalues of the laplace operator as compact shape descriptors here we revisit the eigenvalues to define a proper distance called weighted spectral distance wesd for quantifying shape dissimilarity the definition of wesd is derived through analyzing the heat trace this analysis provides the proposed distance with an intuitive meaning and mathematically links it to the intrinsic geometry of objects we analyze the resulting distance definition present and prove its important theoretical properties some of these properties include 1 wesd is defined over the entire sequence of eigenvalues yet it is guaranteed to converge 2 it is a pseudometric 3 it is accurately approximated with a finite number of eigenvalues and 4 it can be mapped to the 0 1 interval last experiments conducted on synthetic and real objects are presented these experiments highlight the practical benefits of wesd for applications in vision and medical image analysis

partial similarity of objects or how to compare a centaur to a horse similarity is one of the most important abstract concepts in human perception of the world in computer vision numerous applications deal with comparing objects observed in a scene with some a priori known patterns often it happens that while two objects are not similar they have large similar parts that is they are partially similar here we present a novel approach to quantify partial similarity using the notion of pareto optimality we exemplify our approach on the problems of recognizing non rigid geometric objects images and analyzing text sequences

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

analysis of two dimensional non rigid shapes analysis of deformable two dimensional shapes is an important problem encountered in numerous pattern recognition computer vision and computer graphics applications in this paper we address three major problems in the analysis of non rigid shapes similarity partial similarity and correspondence we present an axiomatic construction of similarity criteria for deformation invariant shape comparison based on intrinsic geometric properties of the shapes and show that such criteria are related to the gromov hausdorff distance next we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole and present a construction of set valued distances based on the notion of pareto optimality finally we show that the correspondence between non rigid shapes can be obtained as a byproduct of the non rigid similarity problem as a numerical framework we use the generalized multidimensional scaling gmds method which is the numerical core of the three problems addressed in this paper

generalized gradients priors on minimization flows this paper tackles an important aspect of the variational problem underlying active contours optimization by gradient flows classically the definition of a gradient depends directly on the choice of an inner product structure this consideration is largely absent from the active contours literature most authors explicitely or implicitely assume that the space of admissible deformations is ruled by the canonical l 2 inner product the classical gradient flows reported in the literature are relative to this particular choice here we investigate the relevance of using i other inner products yielding other gradient descents and ii other minimizing flows not deriving from any inner product in particular we show how to induce different degrees of spatial consistency into the minimizing flow in order to decrease the probability of getting trapped into irrelevant local minima we report numerical experiments indicating that the sensitivity of the active contours method to initial conditions which seriously limits its applicability and efficiency is alleviated by our application specific spatially coherent minimizing flows we show that the choice of the inner product can be seen as a prior on the deformation fields and we present an extension of the definition of the gradient toward more general priors

representation and detection of deformable shapes we describe some techniques that can be used to represent and detect deformable shapes in images the main difficulty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates this makes the problem of finding an optimal match of a deformable template to an image incredibly hard using a new representation for deformable shapes we show how to efficiently find a global optimal solution to the nonrigid matching problem the representation is based on the description of objects using triangulated polygons our matching algorithm can minimize a large class of energy functions making it applicable to a wide range of problems we present experimental results of detecting shapes in medical images and images of natural scenes we also consider the problem of learning a nonrigid shape model for a class of objects from examples we show how to learn good models while constraining them to be in the form required by the matching algorithm

efficient parallelization of the 2d swendsen wang algorithm we established a fast swendsen wang algorithm for the two dimensional ising model on parallel computers with a high efficiency on an intel paragon with 140 processors we reached spin update times of only 14 ns with an efficiency of 89 this algorithm was used to examine the non equilibrium relaxation of magnetization and energy in large ising systems of a size up to 17920 17920 spins nevertheless we observed still a strong finite size effect for the magnetization we assume both magnetization and energy decay to behave like t e bt in an infinitely large system thus for long times magnetization and energy show an exponential asymtotic time dependence implying a critical dynamic exponent z of zero

the farthest point strategy for progressive image sampling a new method of farthest point strategy fps for progressive image acquisition an acquisition process that enables an approximation of the whole image at each sampling stage is presented its main advantage is in retaining its uniformity with the increased density providing efficient means for sparse image sampling and display in contrast to previously presented stochastic approaches the fps guarantees the uniformity in a deterministic min max sense within this uniformity criterion the sampling points are irregularly spaced exhibiting anti aliasing properties comparable to those characteristic of the best available method poisson disk a straightforward modification of the fps yields an image dependent adaptive sampling scheme an efficient o n log n algorithm for both versions is introduced and several applications of the fps are discussed

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

shape similarity measure based on correspondence of visual parts a cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2d objects to reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a novel process of digital curve evolution to compute our similarity measure we first establish the best possible correspondence of visual parts without explicitly computing the visual parts then the similarity between corresponding parts is computed and aggregated we applied our similarity measure to shape matching of object contours in various image databases and compared it to well known approaches in the literature the experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions

nonlinear shape registration without correspondences in this paper we propose a novel framework to estimate the parameters of a diffeomorphism that aligns a known shape and its distorted observation classical registration methods first establish correspondences between the shapes and then compute the transformation parameters from these landmarks herein we trace back the problem to the solution of a system of nonlinear equations which directly gives the parameters of the aligning transformation the proposed method provides a generic framework to recover any diffeomorphic deformation without established correspondences it is easy to implement not sensitive to the strength of the deformation and robust against segmentation errors the method has been applied to several commonly used transformation models the performance of the proposed framework has been demonstrated on large synthetic data sets as well as in the context of various applications

free vibration analysis of membranes using the h p version of the finite element method abstract the h p version of the finite element method is applied to the vibration of membranes this is accomplished using a polynomially enriched triangular element new simple expressions of hierarchical c 0 shape functions for triangles are given in terms of the shifted legendre orthogonal polynomials the h p version of the finite element method marries both the concepts of the conventional h version and the p version the accuracy of the solution is sought by simultaneously refining the mesh and increasing the polynomial order in each element results of frequency calculations are found for triangular and l shaped membranes using a number of meshes and polynomial orders it is shown that the h p version of the finite element method is always convergent from above and produces a high accuracy with few degrees of freedom

deformation based curved shape representation in this paper we introduce a deformation based representation space for curved shapes in mathbb r n given an ordered set of points sampled from a curved shape the proposed method represents the set as an element of a finite dimensional matrix lie group variation due to scale and location are filtered in a preprocessing stage while shapes that vary only in rotation are identified by an equivalence relationship the use of a finite dimensional matrix lie group leads to a similarity metric with an explicit geodesic solution subsequently we discuss some of the properties of the metric and its relationship with a deformation by least action furthermore invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function thereafter two possible approaches are presented to solve the point correspondence estimation problem finally we propose an adaptation of k means clustering for shape analysis in the proposed representation space experimental results show that the proposed representation is robust to uninformative cues e g local shape perturbation and displacement in comparison to state of the art methods it achieves a high precision on the swedish and the flavia leaf datasets and a comparable result on mpeg 7 kimia99 and kimia216 datasets

non equilibrium critical relaxation of the wolff dynamics of the ising model abstract the non equilibrium critical relaxation of the single cluster dynamics is studied for the ferromagnetic ising model on the square and cubic lattices power law behavior is observed in the energy relaxation process starting from an all up spin configuration from this power decay the dynamical exponent z is estimated to be 0 50 0 05 and 1 3 0 1 for the square and cubic lattices respectively where the time is defined by the number of cluster flip trials if the time scale is normalized by cluster mass they are 0 25 0 05 and 0 3 0 1 respectively