cortical surface based analysis ii inflation flattening and a surface based coordinate system the surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds as such it is a difficult domain for computational as well as visualization purposes we have therefore designed a set of procedures for modifying the representation of the cortical surface to i inflate it so that activity buried inside sulci may be visualized ii cut and flatten an entire hemisphere and iii transform a hemisphere into a simple parameterizable surface such as a sphere for the purpose of establishing a surface based coordinate system r 1999 academic press

rigorous results on the threshold network model we analyse the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold we prove some convergence theorems and central limit theorems on the vertex degree degree correlation and the number of prescribed subgraphs we also generalize some results in the spatially extended cases

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

freeform surface filtering using the diffusion equation the measurement of texture for geometric surfaces is well established for surfaces that are of a planar euclidean nature gaussian filtering is the fundamental base for scalelimited surfaces used in surface texture but cannot be applied to non euclidean surfaces without distortion of the results a link exists between gaussian filtering and solutions of the pde that models linear isotropic diffusion in particular an analytical solution of this diffusion equation over a planar region at a time t is given by the continuous convolution of the initial distribution of the diffused quantity with a gaussian function of standard deviation s 2t a practical implementation of the standard gaussian filter on sampled data can be viewed as a discretization of this process on a noneuclidean surface the diffusion equation is formulated by using the laplace beltrami operator using this generalization a method of gaussian filtering for freeform surface data is proposed by solving the diffusion equation for approximation residuals defined on a freeform least squares approximation of the measurement surface data results of the application of these methods to simulated and experimental data are presented

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

a multi resolution scheme for distortion minimizing mapping between human subcortical structures based on geodesic construction on riemannian manifolds in this paper we deal with a subcortical surface registration problem subcortical structures including hippocampi and caudates have a small number of salient features such as heads and tails unlike cortical surfaces therefore it is hard if not impossible to perform subcortical surface registration with only such features it is also non trivial for neuroanatomical experts to select landmarks consistently for subcortical surfaces of different subjects we therefore present a landmark free approach for subcortical surface registration by measuring the amount of mesh distortion between subcortical surfaces assuming that the surfaces are represented by meshes the input meshes can be constructed using any surface modeling tool available in the public domain since our registration method is independent of a surface modeling process given the source and target surfaces together with their representing meshes the vertex positions of the source mesh are iteratively displaced while preserving the underlying surface shape in order to minimize the distortion to the target mesh by representing each surface mesh as a point on a high dimensional riemannian manifold we define a distance metric on the manifold that measures the amount of distortion from a given source mesh to the target mesh based on the notion of isometry while penalizing triangle flipping under this metric we reduce the distortion minimization problem to the problem of constructing a geodesic curve from the moving source point to the fixed target point on the manifold while satisfying the shape preserving constraint we adopt a multi resolution framework to solve the problem for distortion minimizing mapping between the source and target meshes we validate our registration scheme through several experiments distance metric comparison visual validation using real data robustness test to mesh variations feature alignment using anatomic landmarks consistency with previous clinical findings and comparison with a surface based registration method lddmm surface

diffusion on a curved surface coupled to diffusion in the volume an algorithm is presented for solving a diffusion equation on a curved surface coupled to diffusion in the volume a problem often arising in cell biology it applies to pixilated surfaces obtained from experimental images and performs at low computational cost in the method the laplace beltrami operator is approximated locally by the laplacian on the tangential plane and then a finite volume discretization scheme based on a voronoi decomposition is applied convergence studies show that mass conservation built in the discretization scheme and cancellation of sampling error ensure convergence of the solution in space with an order between 1 and 2 the method is applied to a cell biological problem where a signaling molecule g protein rac cycles between the cytoplasm and cell membrane thus coupling its diffusion in the membrane to that in the cell interior simulations on realistic cell geometry are performed to validate and determine the accuracy of a recently proposed simplified quantitative analysis of fluorescence loss in photobleaching the method is implemented within the virtual cell computational framework freely accessible at www vcell org

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

analysis of scale free networks based on a threshold graph with intrinsic vertex weights many real networks are complex and have power law vertex degree distribution short diameter and high clustering we analyze the network model based on thresholding of the summed vertex weights which belongs to the class of networks proposed by caldarelli et al phys rev lett 89 258702 2002 power law degree distributions particularly with the dynamically stable scaling exponent 2 realistic clustering and short path lengths are produced for many types of weight distributions thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2 it contrasts with the class of growth models with preferential attachment which is marked by competitiveness and baseline scaling exponent 3

method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces a novel numerical scheme is proposed to solve the shallow water equations swes on arbitrary rotating curved surfaces based on the method of moving frames mmf in which the geometry is represented by orthonormal vectors the proposed scheme not only has the fewest dimensionality both in space and time but also does not require either of metric tensors composite meshes or the ambient space the mmf swe formulation is numerically discretized using the discontinuous galerkin method of arbitrary polynomial order pin space and an explicit runge kutta scheme in time the numerical model is validated against six standard tests on the sphere and the optimal order of convergence of p 1 is numerically demonstrated the mmf swe scheme is also demonstrated for its efficiency and stability on the general rotating surfaces such as ellipsoid irregular and non convex surfaces

convergence of discrete laplace beltrami operators over surfaces the convergence property of the discrete laplace beltrami operator is the foundationof convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator the aim of this paper is to review several already used discrete laplace beltrami operators over triangulated surface and study numerically as well as theoretically their convergent behavior we show that none of them is convergent in general but two of them proposed by desbrun et al and meyer et al are convergent in a special case we point out that this special case is very important in the numerical simulation of geometric partial differential equations

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

pattern formation in reaction diffusion systems on evolving surfaces abstract in this paper we propose an explicit time stepping scheme for the pattern formation in reaction diffusion systems on evolving surfaces the proposed numerical method is based on a simple discretization scheme of laplace beltrami operator over triangulated surface on the static and evolving domains we perform various numerical experiments for effect of domain growth and pattern formations the computational results demonstrate that our proposed method can simulate pattern formation in reaction diffusion systems on evolving surfaces the actual zebra skin pattern and computational results are compared in the computational results we can observe different pattern formations on the evolving surface with specific rotation speed

high order surface radiation conditions for time harmonic waves in exterior domains abstract we formulate a new family of high order on surface radiation conditions to approximate the outgoing solution to the helmholtz equation in exterior domains motivated by the pseudo differential expansion of the dirichlet to neumann operator developed by antoine et al 1999 we design a systematic procedure to apply pseudo differential symbols of arbitrarily high order numerical results are presented to illustrate the performance of the proposed method for solving both the dirichlet and the neumann boundary value problems possible improvements and extensions are also discussed

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

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

shape evolution with structural and topological changes using blending this paper describes a framework for the estimation of shape from sparse or incomplete range data it uses a shape representation called blending which allows for the geometric combination of shapes into a unified model selected regions of the component shapes are cut out and glued together estimation of shape by this representation is realized using a physics based framework and it also includes a process for deciding how to adapt the structure and topology of the model to improve the fit the blending representation helps avoid abrupt changes in model geometry during fitting by allowing the smooth evolution of the shape which improves the robustness of the technique we demonstrate this framework with a series of experiments showing its ability to automatically extract structured representations from range data given both structurally and topologically complex objects

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

a discrete scheme of laplace beltrami operator and its convergence over quadrilateral meshes laplace beltrami operator and its discretization play a central role in the fields of image processing computer graphics computer aided geometric design and so on in this paper a discrete scheme for laplace beltrami operator over quadrilateral meshes is constructed based on a bilinear interpolation of the quadrilateral convergence results for the proposed discrete scheme are established under some conditions numerical results which justify the theoretical analysis are also given

a spectral approach to learning structural variations in graphs this paper shows how to construct a linear deformable model for graph structure by performing principal components analysis pca on the vectorised adjacency matrix we commence by using correspondence information to place the nodes of each of a set of graphs in a standard reference order using the correspondences order we convert the adjacency matrices to long vectors and compute the long vector covariance matrix by projecting the vectorised adjacency matrices onto the leading eigenvectors of the covariance matrix we embed the graphs in a pattern space we illustrate the utility of the resulting method for shape analysis