the role of network topology on extremism propagation with the relative agreement opinion dynamics abstract in deffuant et al j artif soc soc simulation 5 2002 4 we proposed a simple model of opinion dynamics which we used to simulate the influence of extremists in a population simulations were run without any specific interaction structure and varying the simulation parameters we observed different attractors such as predominance of centrism or of extremism we even observed in certain conditions that the whole population drifts to one extreme of the opinion even if initially there are an equal number of extremists at each extreme of the opinion axis in the present paper we study the influence of the social networks on the presence of such a dynamical behavior in particular we use small world networks with variable connectivity and randomness of the connections we find that the drift to a single extreme appears only beyond a critical level of connectivity which decreases when the randomness increases

a level set approach to 3d reconstruction from range data this paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3d objects from range data the strategy is to formulate 3d reconstruction as a statistical problem find that surface which is mostly likely given the data and some prior knowledge about the application domain the resulting optimization problem is solved by an incremental process of deformation we represent a deformable surface as the level set of a discretely sampled scalar function of three dimensions i e a volume such level set models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume the result is a voxel based modeling technology that offers several advantages over conventional parametric models including flexible topology no need for reparameterization concise descriptions of differential structure and a natural scale space for hierarchical representations this paper builds on previous work in both 3d reconstruction and level set modeling it presents a fundamental result in surface estimation from range data an analytical characterization of the surface that maximizes the posterior probability it also presents a novel computational technique for level set modeling called the sparse field algorithm which combines the advantages of a level set approach with the computational efficiency and accuracy of a parametric representation the sparse field algorithm is more efficient than other approaches and because it assigns the level set to a specific set of grid points it positions the level set model more accurately than the grid itself these properties computational efficiency and subcell accuracy are essential when trying to reconstruct the shapes of 3d objects results are shown for the reconstruction objects from sets of noisy and overlapping range maps

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

asymptotic evolution of smooth curves under geodesic flow on hyperbolic manifolds extending the earlier results for analytic curve segments in this article we describe the asymptotic behaviour of evolution of a finite segment of a c n smooth curve under the geodesic flow on the unit tangent bundle of a finite volume hyperbolic n manifold in particular we show that if the curve satisfies certain natural geometric conditions the pushforward of the parameter measure on the curve under the ge odesic flow converges to the normalized canonical riemannian measure on the tangent bundle in the limit we also study the limits of geodesic evolution of shrinking segments we use ratner s classification of ergodic invariant measures for unipo tent flows on homogeneous spaces of so n 1 and an observation re lating local growth properties of smooth curves and dynamics of linear sl 2 r actions

equidistribution of expanding translates of curves and dirichlet s theorem on diophantine approximation we show that for almost all points on any analytic curve on k which is not contained in a proper affine subspace the dirichlet s theorem on simultaneous approximation as well as its dual result for simultaneous approximation of linear forms cannot be improved the result is obtained by proving asymptotic equidistribution of evolution of a curve on a strongly unstable leaf under certain partially hyperbolic flow on the space of unimodular lattices in k 1 the proof involves ratner s theorem on ergodic properties of unipotent flows on homogeneous spaces

mosaic decomposition an electronic cleansing method for inhomogeneously tagged regions in noncathartic ct colonography electronic cleansing ec is a method that segments fecal material tagged by an x ray opaque oral contrast agent in computed tomographic colonography ctc images and effectively removes the material for digitally cleansing the colon in this study we developed a novel ec method called mosaic decomposition md for reduction of the artifacts due to incomplete cleansing of inhomogeneously tagged fecal material in ctc images especially in noncathartic ctc images in our approach the entire colonic region including the residual fecal regions was first decomposed into a set of local homogeneous regions called tiles after application of a 3 d watershed transform to the ctc images each tile was then subjected to a single class support vector machine svm classifier for soft tissue discrimination the feature set of the soft tissue svm classifier was selected by a genetic algorithm ga a scalar index called a soft tissue likelihood is formulated for differentiation of the soft tissue tiles from those of other materials then ec based on md called md cleansing is performed by first initializing of the level set front with the classified tagged regions the front is then evolved by use of a speed function that was designed based on the soft tissue index to reserve the submerged soft tissue structures while suppressing the residual fecal regions the performance of the md cleansing method was evaluated by use of a phantom and of clinical cases in the phantom evaluation our md cleansing was trained with the supine prone scan and tested on the prone supine scan respectively in both cases the sensitivity and specificity of classification were 100 the average cleansing ratio was 90 6 and the soft tissue preservation ratio was 97 6 in the clinical evaluation 10 noncathartic ctc cases 20 scans were collected and the ground truth of a total of 2095 tiles was established by manual assignment of a material class to each tile five cases were randomly selected for training ga svm and the remaining five cases were used for testing the overall sensitivity and specificity of the proposed classification scheme were 97 1 and 85 3 respectively and the accuracy was 94 6 the area under the roc curve az was 0 96 our results indicated that the use of md cleansing substantially improved the effectiveness of our ec method in the reduction of incomplete cleansing artifacts

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

segmentation of intra retinal layers from optical coherence tomography images using an active contour approach optical coherence tomography oct is a noninvasive depth resolved imaging modality that has become a prominent ophthalmic diagnostic technique we present a semi automated segmentation algorithm to detect intra retinal layers in oct images acquired from rodent models of retinal degeneration we adapt chan vese s energy minimizing active contours without edges for the oct images which suffer from low contrast and are highly corrupted by noise a multiphase framework with a circular shape prior is adopted in order to model the boundaries of retinal layers and estimate the shape parameters using least squares we use a contextual scheme to balance the weight of different terms in the energy functional the results from various synthetic experiments and segmentation results on oct images of rats are presented demonstrating the strength of our method to detect the desired retinal layers with sufficient accuracy even in the presence of intensity inhomogeneity resulting from blood vessels our algorithm achieved an average dice similarity coefficient of 0 84 over all segmented retinal layers and of 0 94 for the combined nerve fiber layer ganglion cell layer and inner plexiform layer which are the critical layers for glaucomatous degeneration

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

finite element methods on very large dynamic tubular grid encoded implicit surfaces the simulation of physical processes on interfaces and a variety of applications in geometry processing and geometric modeling are based on the solution of partial differential equations on curved and evolving surfaces frequently an implicit level set type representation of these surfaces is the most effective and computationally advantageous approach this paper addresses the computational problem of how to solve partial differential equations on highly resolved level sets with an underlying very high resolution discrete grid these high resolution grids are represented in a very efficient dynamic tubular grid encoding format for a narrow band a reaction diffusion model on a fixed surface and surface evolution driven by a nonlinear geometric diffusion approach by isotropic or truly anisotropic curvature motion are investigated as characteristic model problems the proposed methods are based on semi implicit finite element discretizations directly on these narrow bands require only standard numerical quadrature and allow for large time steps to combine large time steps with a very thin and thus storage inexpensive narrow band suitable transparent boundary conditions on the boundary of the narrow band and a nested iteration scheme in each time step are investigated this nested iteration scheme enables the discrete interfaces to move in a single time step significantly beyond the domain of the narrow band of the previous time step furthermore algorithmic tools are provided to assemble finite element matrices and to apply matrix vector operators via fast cache coherent access to the dynamic tubular grid encoded data structure the consistency of the presented approach is evaluated and various numerical examples show its application potential

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

improving level set method for fast auroral oval segmentation auroral oval segmentation from ultraviolet imager images is of significance in the field of spatial physics compared with various existing image segmentation methods level set is a promising auroral oval segmentation method with satisfactory precision however the traditional level set methods are time consuming which is not suitable for the processing of large aurora image database for this purpose an improving level set method is proposed for fast auroral oval segmentation the proposed algorithm combines four strategies to solve the four problems leading to the high time complexity the first two strategies including our shape knowledge based initial evolving curve and neighbor embedded level set formulation can not only accelerate the segmentation process but also improve the segmentation accuracy and then the latter two strategies including the universal lattice boltzmann method and sparse field method can further reduce the time cost with an unlimited time step and narrow band computation experimental results illustrate that the proposed algorithm achieves satisfactory performance for auroral oval segmentation within a very short processing time

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

computational geometry for patient specific reconstruction and meshing of blood vessels from mr and ct angiography investigation of three dimensional 3 d geometry and fluid dynamics in human arteries is an important issue in vascular disease characterization and assessment thanks to recent advances in magnetic resonance mr and computed tomography ct it is now possible to address the problem of patient specific modeling of blood vessels in order to take into account interindividual anatomic variability of vasculature generation of models suitable for computational fluid dynamics is still commonly performed by semiautomatic procedures in general based on operator dependent tasks which cannot be easily extended to a significant number of clinical cases in this paper we overcome these limitations making use of computational geometry techniques in particular 3 d modeling was carried out by means of 3 d level sets approach model editing was also implemented ensuring harmonic mean curvature vectors distribution on the surface and model geometric analysis was performed with a novel approach based on solving eikonal equation on voronoi diagram this approach provides calculation of central paths maximum inscribed sphere estimation and geometric characterization of the surface generation of adaptive thickness boundary layer finite elements is finally presented the use of the techniques presented here makes it possible to introduce patient specific modeling of blood vessels at clinical level

growth motion and 1 parameter families of symmetry sets associated to every plane curve there is the locus of centres of circles bitangent to that curve the so called symmetry set of the curve we can view this set as the spine of our curve which can be recovered by taking the envelope of circles of varying radii along this spine varying the symmetry set in some isotopy while keeping the radius function fixed may be viewed as crudely modelling motion of the original curve viewed as a biological object fixing the symmetry set and varying the radius function can be considered to model growth crudely in this paper we shall describe the generic changes in the curves which take place in the process of growth and motion and outline the corresponding results for spheres centred on a space curve we also use the idea of a stratified morse function to describe the generic changes which occur in one parameter families of full bifurcation sets in the plane applying this to the bifurcation set of distance squared functions we find all the transitions of a symmetry set and evolute which occur in a generic isotopy of a plane curve

exponential mixing for the geodesic flow on hyperbolic three manifolds we give a short and direct proof of exponential mixing of geodesic flows on compact hyperbolic three manifolds with respect to the liouville measure this complements earlier results of collet epstein gallovotti moore and ratner for hyperbolic surfaces furthermore since the analysis is even easier in three dimensions than in two dimensions because of the absence of discrete series and the simplicity of the zonal spherical functions in this case this apparently gives the simplest example of a flow with exponential mixing

disjunctive normal parametric level set with application to image segmentation level set methods are widely used for image segmentation because of their convenient shape representation for numerical computations and capability to handle topological changes however in spite of the numerous works in the literature the use of level set methods in image segmentation still has several drawbacks these shortcomings include formation of irregularities of the signed distance function sensitivity to initialization lack of locality and expensive computational cost which increases dramatically as the number of objects to be simultaneously segmented grows in this paper we propose a novel parametric level set method called disjunctive normal level set dnls and apply it to both two phase single object and multiphase multiobject image segmentations dnls is a differentiable model formed by the union of polytopes which themselves are created by intersections of half spaces we formulate the segmentation algorithm in a bayesian framework and use a variational approach to minimize the energy with respect to the parameters of the model the proposed dnls can be considered as an open framework that allows the use of different appearance models and shape priors compared with the conventional level sets available in the literature the proposed dnls has the following major advantages it requires significantly less computational time and memory it naturally keeps the level set function regular during the evolution it is more suitable for multiphase and local region based image segmentations and it is less sensitive to noise and initialization the experimental results show the potential of the proposed method

gradient flows for optimizing triangular mesh based surfaces applications to 3d reconstruction problems dealing with visibility this article tackles the problem of using variational methods for evolving 3d deformable surfaces we give an overview of gradient descent flows when the shape is represented by a triangular mesh based surface and we detail the gradients of two generic energy functionals which embody a number of energies used in mesh processing and computer vision in particular we show how to rigorously account for visibility in the surface optimization process we present different applications including 3d reconstruction from multiple views for which the visibility is fundamental the gradient correctly takes into account the visibility changes that occur when a surface moves this forces the contours generated by the reconstructed surface to match with the apparent contours in the input images

image relaxation restoration and feature extraction the techniques of a posteriori image restoration and iterative image feature extraction are described and compared image feature extraction methods known as graduated nonconvexity gnc variable conductance diffusion vcd anisotropic diffusion and biased anisotropic diffusion bad which extract edges from noisy images are compared with a restoration feature extraction method known as mean field annealing mfa all are shown to be performing the same basic operation image relaxation this equivalence shows the relationship between energy minimization methods and spatial analysis methods and between their respective parameters of temperature and scale as a result of the equivalence vcd is demonstrated to minimize a cost function and that cost is specified explicitly furthermore operations over scale space are shown to be a method of avoiding local minima

on the reconstruction of height functions and terrain maps from dense range data this paper describes a method for combining multiple dense range images to create surface reconstructions of height functions height functions are a special class of three dimensional 3 d surfaces where one 3 d coordinate is a function of the other two they are relevant for application domains such as terrain modeling or two and half dimensional surface reconstruction dense range maps are produced by either a range measuring device combined with a scanning mechanism or a triangulation scheme such as active or passive stereo the proposed method follows from a statistical formulation that characterizes the optimal surface estimate as the one that maximizes the posterior probability conditional on the input data and prior information about the application domain because the domain of the reconstruction is a two dimensional 2 d scalar function the optimal surface can be expressed as an image and the variational form of that optimization produces a 2 d partial differential equation pde the pde consists of two parts a first order data term and a second order smoothing term thus optimal surface reconstruction is formulated as the solution to a second order nonlinear pde on an image which is related to the family of pde based image processing algorithms in the literature this paper presents the theory for reconstruction and some particular aspects of the numerical implementation it also analyzes results on both synthetic and real data sets which show a 75 95 reduction of the rms sensor error

variational b spline level set a linear filtering approach for fast deformable model evolution in the field of image segmentation most level set based active contour approaches take advantage of a discrete representation of the associated implicit function we present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a b spline basis starting from the active contour energy functional we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the b splines as a consequence the minimization of the functional is directly obtained in terms of the b spline coefficients we also show that each step of this minimization may be expressed through a convolution operation because the b spline functions are separable this convolution may in turn be performed as a sequence of simple 1 d convolutions which yields an efficient algorithm as a further consequence each step of the level set evolution may be interpreted as a filtering operation with a b spline kernel such filtering induces an intrinsic smoothing in the algorithm which can be controlled explicitly via the degree and the scale of the chosen b spline kernel we illustrate the behavior of this approach on simulated as well as experimental images from various fields

graduated nonconvexity by functional focusing reconstruction of noise corrupted surfaces may be stated as a in general nonconvex functional minimization problem for functionals with quadratic data term this paper addresses the criteria for such functionals to be convex and the variational approach for minimization i present two automatic and general methods of approximation with convex functionals based on gaussian convolution they are compared to the blake zisserman graduated nonconvexity gnc method 1987 and bilbro et al 1992 and geiger and girosi s 1991 mean field annealing mfa of a weak membrane

on raghunathan s measure conjecture this paper represents the last in our three part series on raghunathan s measure conjecture see r1 r2 for parts i and ii more specifically let g be a real lie group all groups in this paper are assumed to be second countable with the lie algebra r a discrete subgroup of g and ir g r g the projection lwg rg the group g acts by right translations on r g x x g x e r g g e g let gt be a borel probability measure on r g define

a real time algorithm for the approximation of level set based curve evolution in this paper we present a complete and practical algorithm for the approximation of level set based curve evolution suitable for real time implementation in particular we propose a two cycle algorithm to approximate level set based curve evolution without the need of solving partial differential equations pdes our algorithm is applicable to a broad class of evolution speeds that can be viewed as composed of a data dependent term and a curve smoothness regularization term we achieve curve evolution corresponding to such evolution speeds by separating the evolution process into two different cycles one cycle for the data dependent term and a second cycle for the smoothness regularization the smoothing term is derived from a gaussian filtering process in both cycles the evolution is realized through a simple element switching mechanism between two linked lists that implicitly represents the curve using an integer valued level set function by careful construction all the key evolution steps require only integer operations a consequence is that we obtain significant computation speedups compared to exact pde based approaches while obtaining excellent agreement with these methods for problems of practical engineering interest in particular the resulting algorithm is fast enough for use in real time video processing applications which we demonstrate through several image segmentation and video tracking experiments

a new multiscale representation for shapes and its application to blood vessel recovery in this paper we will first introduce a novel multiscale representation msr for shapes via level set motions and pdes based on the msr we will then design a surface inpainting algorithm to recover three dimensional geometry of blood vessels because of the nature of irregular morphology in vessels and organs both phantom and real inpainting scenarios were tested using our new algorithm successful vessel recoveries are demonstrated with numerical estimation of the degree of arteriosclerosis and vessel occlusion

simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension we introduce simplex free adaptive tree numerical methods for solving static and time dependent hamilton jacobi equations arising in level set problems in arbitrary dimension the data structure upon which our method is built in a generalized n dimensional binary tree but it does not require the complicated splitting of cubes into simplices aka generalized n dimensional triangles or hypertetrahedrons that current tree based methods require it has enough simplicity that minor variants of standard numerical hamiltonians developed for uniform grids can be applied yielding consistent monotone convergent schemes combined with the fast sweeping strategy the resulting tree based methods are highly efficient and accurate thus without changing more than a few lines of code when changing dimension we have obtained results for calculations in up to n 7 dimensions

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

adaptively merging large scale range data with reflectance properties in this paper we tackle the problem of geometric and photometric modeling of large intricately shaped objects typical target objects we consider are cultural heritage objects when constructing models of such objects we are faced with several important issues that have not been addressed in the past issues that mainly arise due to the large amount of data that has to be handled we propose two novel approaches to efficiently handle such large amounts of data a highly adaptive algorithm for merging range images and an adaptive nearest neighbor search to be used with the algorithm we construct an integrated mesh model of the target object in adaptive resolution taking into account the geometric and or photometric attributes associated with the range images we use surface curvature for the geometric attributes and laser reflectance values for the photometric attributes this adaptive merging framework leads to a significant reduction in the necessary amount of computational resources furthermore the resulting adaptive mesh models can be of great use for applications such as texture mapping as we will briefly demonstrate additionally we propose an additional test for the k d tree nearest neighbor search algorithm our approach successfully omits back tracking which is controlled adaptively depending on the distance to the nearest neighbor since the main consumption of computational cost lies in the nearest neighbor search the proposed algorithm leads to a significant speed up of the whole merging process in this paper we present the theories and algorithms of our approaches with pseudo code and apply them to several real objects including large scale cultural assets

phase transitions as a persistent feature of groups with leaders in models of opinion formation a class of models of opinion formation based on the concept of cellular automata and the theory of social impact is studied in particular the case when a strong leader and external impact are present the rapid changes of the opinion distribution with a continuous change of a system parameter which was previously observed for the model with geometric structure prove to be present also for much larger class of mutual interaction architectures we study random connections with dierent probability distributions the theoretical results obtained in the framework of mean eld approximation are conrmed by the numerical simulations of the model c 2000 elsevier science b v all rights reserved

a quasi dense approach to surface reconstruction from uncalibrated images this paper proposes a quasi dense approach to 3d surface model acquisition from uncalibrated images first correspondence information and geometry are computed based on new quasi dense point features that are resampled subpixel points from a disparity map the quasi dense approach gives more robust and accurate geometry estimations than the standard sparse approach the robustness is measured as the success rate of full automatic geometry estimation with all involved parameters fixed the accuracy is measured by a fast gauge free uncertainty estimation algorithm the quasi dense approach also works for more largely separated images than the sparse approach therefore it requires fewer images for modeling more importantly the quasi dense approach delivers a high density of reconstructed 3d points on which a surface representation can be reconstructed this fills the gap of insufficiency of the sparse approach for surface reconstruction essential for modeling and visualization applications second surface reconstruction methods from the given quasi dense geometry are also developed the algorithm optimizes new unified functionals integrating both 3d quasi dense points and 2d image information including silhouettes combining both 3d data and 2d images is more robust than the existing methods using only 2d information or only 3d data an efficient bounded regularization method is proposed to implement the surface evolution by level set methods its properties are discussed and proven for some cases as a whole a complete automatic and practical system of 3d modeling from raw images captured by hand held cameras to surface representation is proposed extensive experiments demonstrate the superior performance of the quasi dense approach with respect to the standard sparse approach in robustness accuracy and applicability

on the modelling and simulation of the competition for a secession under media influence by active particles methods and functional subsystems decomposition this paper deals with the development of a mathematical model for complex socio economical systems where external actions play a key role the aim of the paper is to show the emergence of collective behaviors or macroscopic trends from individual based interactions where agents are identified by functional subsystems the approach is based on the methods of the mathematical kinetic theory for active particles which describes the evolution of large systems of interacting entities which are carriers of specific functions in our specific application socio political activities subjected to the influence of the media

invariant distributions and time averages for horocycle flows there are infinitely many obstructions to existence of smooth solutions of the cohomological equation uu f where u is the vector field generating the horocycle flow on the unit tangent bundle sm of a riemann m surface of finite area and f is a given function on sm we study the sobolev regularity of these obstructions construct smooth solutions of the cohomological equation and derive asymptotics for the ergodic averages of horocycle flows

integral points on symmetric varieties and satake compatifications let v be an affine symmetric variety defined over q we compute the asymptotic distribution of the angular components of the integral points in v this distribution is described by a family of invariant measures concentrated on the satake boundary of v in the course of the proof we describe the structure of the satake compactifications for general affine symmetric varieties and compute the asymptotic of the volumes of norm balls

on the uniform equidistribution of long closed horocycles it is well known that on any given hyperbolic surface of finite area a closed horocycle of length becomes asymptotically equidistributed as in this paper we prove that any subsegment of length greater than 1 2 e of such a closed horocycle also becomes equidistributed as the exponent 1 2 e is the best possible and improves upon a recent result by hejhal he3 we give two proofs of the above result our second proof leads to explicit information on the rate of convergence we also prove a result on the asymptotic joint equidistribution of a finite number of distinct subsegments having equal length proportional to

3 d b spline wavelet based local standard deviation bwlsd its application to edge detection and vascular segmentation in magnetic resonance angiography extracting reliable image edge information is crucial for active contour models as well as vascular segmentation in magnetic resonance angiography mra however conventional edge detection techniques such as gradient based methods and wavelet based methods are incapable of returning reliable detection responses from low contrast edges in the images in this paper we propose a novel edge detection method by combining b spline wavelet magnitude with standard deviation inside local region it is proved theoretically and demonstrated experimentally in this paper that the new edge detection method namely bwlsd is able to give consistent and reliable strengths for edges with different image contrasts moreover the relationship between the size of local region with non zero wavelet magnitudes and the scale of wavelet function is established this relationship indicates that if the scale of the adopted wavelet function is s then the size of a local region from which the standard deviation is estimated should be 2s 1 the proposed edge detection technique is embedded in flux namely bwlsd flux for vascular segmentation in mra image volumes experimental results on clinical images show that as compared with the conventional flux bwlsd flux can achieve better segmentations of vasculatures in mra images under same initial conditions

hole filling of a 3d model by flipping signs of a signed distance field in adaptive resolution when we use range finders to observe the shape of an object many occluded areas may occur these become holes and gaps in the model and make it undesirable for various applications we propose a novel method to fill holes and gaps to complete this incomplete model as an intermediate representation we use a signed distance field sdf which stores euclidean signed distances from a voxel to the nearest point of the mesh model by using an sdf we can obtain interpolating surfaces for holes and gaps the proposed method generates an interpolating surface that becomes smoothly continuous with real surfaces by minimizing the area of the interpolating surface since the isosurface of an sdf can be identified as being a real or interpolating surface from the magnitude of signed distances our method computes the area of an interpolating surface in the neighborhood of a voxel both before and after flipping the sign of the signed distance of the voxel if the area is reduced by flipping the sign then our method changes the sign for the voxel therefore we minimize the area of the interpolating surface by iterating this computation until convergence unlike methods based on partial differential equations pdes our method does not require any boundary condition and the initial state that we use is automatically obtained by computing the distance to the closest point of the real surface moreover because our method can be applied to an sdf of adaptive resolution our method efficiently interpolates large holes and gaps of high curvature we tested the proposed method with both synthesized and real objects and evaluated the interpolating surfaces

on the uniform equidistribution of closed horospheres in hyperbolic manifolds we prove equidistribution results for pieces of closed horospheres in cofinite hyperbolic manifolds of dimension n 1 using spectral methods this extends earlier results by hejhal hej2 and str

higher order nonlinear priors for surface reconstruction for surface reconstruction problems with noisy and incomplete range data a bayesian estimation approach can improve the overall quality of the surfaces the bayesian approach to surface estimation relies on a likelihood term which ties the surface estimate to the input data and the prior which ensures surface smoothness or continuity this paper introduces a new high order nonlinear prior for surface reconstruction the proposed prior can smooth complex noisy surfaces while preserving sharp geometric features and it is a natural generalization of edge preserving methods in image processing such as anisotropic diffusion an exact solution would require solving a fourth order partial differential equation pde which can be difficult with conventional numerical techniques our approach is to solve a cascade system of two second order pdes which resembles the original fourth order system this strategy is based on the observation that the generalization of image processing to surfaces entails filtering the surface normals we solve one pde for processing the normals and one for refitting the surface to the normals furthermore we implement the associated surface deformations using level sets hence the algorithm can accommodate very complex shapes with arbitrary and changing topologies this paper gives the mathematical formulation and describes the numerical algorithms we also show results using range and medical data

weighted local variance based edge detection and its application to vascular segmentation in magnetic resonance angiography accurate detection of vessel boundaries is particularly important for a precise extraction of vasculatures in magnetic resonance angiography mra in this paper we propose the use of weighted local variance wlv based edge detection scheme for vessel boundary detection in mra the proposed method is robust against changes of intensity contrast of edges and capable of giving high detection responses on low contrast edges these robustness and capabilities are essential for detecting the boundaries of vessels in low contrast regions of images which can contain intensity inhomogeneity such as bias field interferences induced from other tissues or fluctuation of the speed related vessel intensity the performance of the wlv based edge detection scheme is studied and shown to be able to return strong and consistent detection responses on low contrast edges in the experiments the proposed edge detection scheme can be embedded naturally in the active contour models for vascular segmentation the wlv based vascular segmentation method is tested using mra image volumes it is experimentally shown that the wlv based edge detection approach can achieve high quality segmentation of vasculatures in mra images

the behavior under projection of dilating sets in a covering space let m be a compact riemannian manifold with covering space s and suppose dcur o r oo is a family of borel probability measures on s all of which arise from some fixed measure by r homotheties of s about some point followed by renormalization of the resulting measure in this paper we study the ergodic properties as a function of r of the corresponding family of projected measures on m in the euclidean and hyperbolic cases a typical example arises by considering the behavior of a dilating family of spheres under projection suppose tn is the n dimensional integral torus regarded as the quotient of rn by the lattice r of integral translations and suppose d1i is a borel probability measure on rn i e d1i is a real nonnegative borel measure on rn having total mass 1 by projection d i gives rise to a borel probability measure dm on tn if we define the measure of a set in tn to be the measure with respect to d i of its total preimage in rn with respect to the projection map from rn to tn for various types of f invariant functions f on rn or what is the same thing functions on tn it is natural to study the difference 1 fn f x dx f x dm x tn tn where dx is normalized lebesgue measure this quantity arises for example in the study of equidistribution of sequences and in the study of ergodic properties of irrational lines in tn in order to study 1 suppose for the moment that f is coo with fourier series e cn e27i n x and suppose d y f e20i xy dc4 x is the fourier transform of d u then it is easily checked that the nth fourier coefficient of dm x is d n and since f is smooth the parseval equality can be applied to conclude that j f x dm x cn t n co ezcn n tn where the prime indicates that the origin is omitted from the summation but co ftn f x dx so 2 f x dx f x dm x s cn n tn tn i e from our point of view the study of 1 is equivalent to the study of the asymptotic behavior of it is the purpose of this paper to illustrate this principle received by the editors october 21 1983 1980 mathmatics suject czassification primary 22d40 x 1984 american mathematical society 0002 9947 84 1 00 25 per page 855 this content downloaded from 207 46 13 149 on mon 03 oct 2016 06 26 09 utc all use subject to http about jstor org terms

flows on homogeneous spaces and diophantine approximation on manifolds we present a new approach to metric diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain flows on homogeneous spaces this approach yields a new proof of a conjecture of mahler originally settled by v g sprindzuk in 1964 we also prove several related hypotheses of baker and sprindzuk formulated in 1970s the core of the proof is a theorem which generalizes and sharpens earlier results on nondivergence of unipotent flows on the space of lattices

limiting distributions of curves under geodesic flow on hyperbolic manifolds we consider the evolution of a compact segment of an analytic curve on the unit tangent bundle of a finite volume hyperbolic n manifold under the geodesic flow suppose that the curve is not contained in a stable leaf of the flow it is shown that under the geodesic flow the normalized parameter measure on the curve gets asymptotically equidistributed with respect to the normalized natural riemannian measure on the unit tangent bundle of a closed totally geodesically immersed submanifold moreover if this immersed submanifold is a proper subset then a lift of the curve to the universal covering space t 1 h n is mapped into a proper subsphere of the ideal boundary sphere h n under the visual map this proper subsphere can be realized as the ideal boundary of an isometrically embedded hyperbolic subspace in h n covering the closed immersed submanifold in particular if the visual map does not send a lift of the curve into a proper subsphere of h n then under the geodesic flow the curve gets asymptotically equidistributed on the unit tangent bun dle of the manifold with respect to the normalized natural rie mannian measure the proof uses dynamical properties of unipotent flows on finite volume homogeneous spaces of so n 1

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality