comments on nonparametric segmentation of curves into various representations with reply the author points out the existence of a theoretical difficulty that underlies the curve segmentation problem studied in the work of rosin and west ibid vol 17 no 12 p 1140 53 1995 and present a possible solution to it the problem arises because curves are segmented into low and high order features and the former are a subset of the latter in reply rosin and west discuss the advantages and disadvantages of two approaches to model selection their original heuristic sequential method and the information theoretic method suggested by kanatani and others

application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

a symmetry measure for damage detection with mode shapes abstract this paper introduces a feature for detecting damage or changes in structures the continuous symmetry measure which can quantify the amount of a particular rotational mirror or translational symmetry in a mode shape of a structure many structures in the built environment have geometries that are either symmetric or almost symmetric however damage typically occurs in a local manner causing asymmetric changes in the structure s geometry or material properties and alters its mode shapes the continuous symmetry measure can quantify these changes in symmetry as a novel indicator of damage for data based structural health monitoring approaches this paper describes the concept as a basis for detecting changes in mode shapes and detecting structural damage application of the method is demonstrated in various structures with different symmetrical properties a pipe cross section with a finite element model and experimental study the nasa 8 bay truss model and the simulated iasc asce structural health monitoring benchmark structure the applicability and limitations of the feature in applying it to structures of varying geometries is discussed

a modified version of the k means algorithm with a distance based on cluster symmetry we propose a modified version of the k means algorithm to cluster data the proposed algorithm adopts a novel nonmetric distance measure based on the idea of point symmetry this kind of point symmetry distance can be applied in data clustering and human face detection several data sets are used to illustrate its effectiveness

an unstructured finite elements method for solving the compressible rans equations and the spalart allmaras turbulence model this paper deals with a stabilized finite element method for solving the compressible navier stokes equations combined with the spalart allmaras turbulence model the aim is to assess the ability of this formulation to solve high reynolds number turbulent flows over anisotropic meshes this formulation lies in the framework of the stream line upwind petrove galerkin method we propose a simple and efficient formulation for the stabilization matrix and develop a shock capturing operator numerical tests on the 3d boundary layer over a flat plate and on the onera m6 wing show the stability and robustness of the proposed method

aeroelastic dynamic analysis of a full f 16 configuration for various flight conditions an overview is given of recent advances in a three field methodology for modeling and solving nonlinear fluid structure interaction problems and its application to the prediction of the aeroelastic frequencies and damping coefficients of a full f 16 configuration in various subsonic transonic and supersonic airstreams is reported in this three field methodology the flow is described by the arbitrary lagrangian eulerian form of the euler equations the structure is represented by a detailed finite element model and the fluid mesh is unstructured dynamic and updated by a robust torsional spring analogy method simulation results are presented for stabilized accelerated low g and high g flight conditions and correlated with flight test data consequently the practical feasibility and potential of the described computational fluid dynamics based computational method for the flutter analysis of high performance aircraft particularly in the transonic regime are discussed

a multi scale formulation for compressible turbulent flows suitable for general variational discretization techniques based on the recently introduced variational multi scale vms approach to large eddy simulation les as introduced in t j r hughes l mazzei k e jansen large eddy simulation and the variational multiscale method comput visual sci 3 2001 47 59 s s collis monitoring unresolved scales in multiscale turbulence modeling phys fluids 13 6 2001 1800 1806 we present a vms formulation which can be used in the simulation of compressible flows special attention is given to obtain a vms formulation which is suitable for complex flow domains and general variational discretization techniques a generalization of the favre averaging procedure is introduced such that the formulation resembles the favre filtered navier stokes equations traditionally used in les of compressible flow and no explicit subgrid terms arise in the continuity equation also we show that with the use of discretization methods other than fourier spectral methods the vms projection no longer commutes with differentiation this results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to les

stationary turbulent closure via the hopf functional equation exact closed form solutions are exhibited for the hopf equation for stationary incompressible 3d navier stokes flow for the cases of homogeneous forced flow including a solution with depleted nonlinearity and inhomogeneous flow with arbitrary boundary conditions this provides an exact method for computing two and higher point moments given the mean flow

line drawing interpretation bilateral symmetry results previously derived by the author are used to investigate the implication of bilateral symmetry in line drawings it is shown that the line drawing of an orthographically protected surface of revolution exhibits bilateral symmetry about the projection of its axis of revolution irrespective of the viewing direction barring one exception a bilaterally symmetric line drawing is necessarily the orthographic projection of a local surface of revolution whenever its symmetry axis continues to be the projection of a fixed line in space under perturbation of viewpoint the axis of revolution is the invariant preimage of the symmetry axis various line drawing causes are detailed which facilitate the deduction of invariant preimages of symmetry axes and consequently of local surfaces of revolution

comments on symmetry as a continuous feature we point out the existence of a theoretical difficulty that underlies the symmetry detection studied by zabrodsky et al 1995 and present a possible solution to it

3d symmetry detection using the extended gaussian image symmetry detection is important in the area of computer vision a 3d symmetry detection algorithm is presented in this paper the symmetry detection problem is converted to the correlation of the gaussian image once the gaussian image of the object has been obtained the algorithm is independent of the input format the algorithm can handle different kinds of images or objects simulated and real images have been tested in a variety of formats and the results show that the symmetry can be determined using the gaussian image

variational multiscale turbulence modelling in a high order spectral element method in the variational multiscale vms approach to large eddy simulation les the governing equations are projected onto an a priori scale partitioning of the solution space this gives an alternative framework for designing and analyzing turbulence models we describe the implementation of the vms les methodology in a high order spectral element method with a nodal basis and discuss the properties of the proposed scale partitioning the spectral element code is first validated by doing a direct numerical simulation of fully developed plane channel flow the performance of the turbulence model is then assessed by several coarse grid simulations of channel flow at different reynolds numbers

analyzing skewed symmetries symmetry is pervasive in both man made objects and nature since symmetries project to skew symmetries finding axes of skew symmetry is an important vision task this paper presents a linear time algorithm for finding the axes of skew symmetry where the degree of symmetry is known first we present a review and critique of current methods for finding the axes of skew symmetry next we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a shear symmetry and recovering the shear parameter of a reflexive symmetry using this approach the authors derive a direct non heuristic moment based technique for finding the axes of skew symmetry for skew symmetric figures with degree of symmetry less than five we obtain a closed form solution the method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour s degree of symmetry it is the first algorithm to find the axes of skew symmetry ino n time where n is the number of contour points the method is especially suited to industrial applications where the degree of symmetry is often knowna priori examples of the method are presented for both real and synthetic images and an error analysis of the method is given

chiral coefficient a measure of the amount of structural chirality a new concept of quantitative measurement of chiral structure is introduced and labelled as chiral coefficient chi a distinction is made between geometric and physical chiralities and chi is defined for various physical cases few general geometrical features are discussed and it is shown that for every chiral body there exists a natural z direction depending on the physical property treated possible practical applications of this concept are discussed a few simple examples of the chiral coefficient of mass chi m for chiral molecules are treated

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

dealiasing techniques for high order spectral element methods on regular and irregular grids high order methods are becoming increasingly attractive in both academia and industry especially in the context of computational fluid dynamics however before they can be more widely adopted issues such as lack of robustness in terms of numerical stability need to be addressed particularly when treating industrial type problems where challenging geometries and a wide range of physical scales typically due to high reynolds numbers need to be taken into account one source of instability is aliasing effects which arise from the nonlinearity of the underlying problem in this work we detail two dealiasing strategies based on the concept of consistent integration the first uses a localised approach which is useful when the nonlinearities only arise in parts of the problem the second is based on the more traditional approach of using a higher quadrature the main goal of both dealiasing techniques is to improve the robustness of high order spectral element methods thereby reducing aliasing driven instabilities we demonstrate how these two strategies can be effectively applied to both continuous and discontinuous discretisations where in the latter both volumetric and interface approximations must be considered we show the key features of each dealiasing technique applied to the scalar conservation law with numerical examples and we highlight the main differences in terms of implementation between continuous and discontinuous spatial discretisations

a variational germano approach for stabilized finite element methods in this paper the recently introduced variational germano procedure is revisited the procedure is explained using commutativity diagrams a general germano identity for all types of discretizations is derived this relation is similar to the variational germano identity but is not restricted to variational numerical methods based on the general germano identity an alternative algorithm in the context of stabilized methods is proposed this partitioned algorithm consists of distinct building blocks several options for these building blocks are presented and analyzed and their performance is tested using a stabilized finite element formulation for the convection diffusion equation non homogenous boundary conditions are shown to pose a serious problem for the dissipation method this is not the case for the least squares method although here the issue of basis dependence occurs the latter can be circumvented by minimizing a dual norm of the weak relation instead of the euclidean norm of the discrete residual

on symmetry detection a straight line is an axis ofsymmetry of a planar figure if the figure is invariant to reflection with respect to that line the purpose of this correspondence is to describe an o n log n time algorithm for enumerating all the axes of symmetry of a planar figure which is made up of possibly intersecting segments circles points etc the solution involves a reduction of the problem to a combinatorial question on words our algorithm is optimal since we can establish an n log n time lower bound for this problem

spectral symmetry analysis we present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n dimensions our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points irn and its extension to image analysis by way of local features each object is represented by a set of points s irn where the symmetry is manifested by the multiple self alignments of s the alignment problem is formulated as a quadratic binary optimization problem with an efficient solution via spectral relaxation for symmetric objects this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry we improve the scheme s robustness by incorporating geometrical constraints into the spectral analysis our approach is experimentally verified by applying it to 2d and 3d synthetic objects as well as real images

a variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes application to vortex shedding the variational multiscale formulation of large eddy simulations developed by hughes and his co workers for incompressible turbulent flows is first extended to the case of compressible turbulent flows next a finite volume element discretization on tetrahedral meshes of this method is proposed this discretization features an economical procedure based on agglomeration for separating a priori the scales a corresponding projector for eliminating the small scales from the system of equations and an effective control of the numerical dissipation induced by upwinding the resulting les method is validated with the three dimensional numerical simulation of a low speed flow past a square cylinder at m 0 1 and re 22 000 and various comparisons with experimental data

a dynamic approach for evaluating parameters in a numerical method a new methodology for evaluating unknown parameters in a numerical method for solving a partial differential equation is developed the main result is the identification of a functional form for the parameters which is derived by requiring the numerical method to yield optimal solutions over a set of finite dimensional function spaces the functional depends upon the numerical solution the forcing function the set of function spaces and the definition of the optimal solution it does not require exact or approximate analytical solutions of the continuous problem and is derived from an extension of the variational germano identity this methodology is applied to the one dimensional linear advection diffusion problem to yield a non linear dynamic diffusivity method it is found that this method yields results that are commensurate to the supg method the same methodology is then used to evaluate the smagorinsky eddy viscosity for the large eddy simulation of the decay of homogeneous isotropic turbulence in three dimensions in this case the resulting method is found to be more accurate than the constant coefficient and the traditional dynamic versions of the smagorinsky model copyright 2004 john wiley sons ltd

ellipsoidal decision regions for motif based patterned fabric defect detection this paper presents a study of using ellipsoidal decision regions for motif based patterned fabric defect detection the result of which is found to improve the original detection success using max min decision region of the energy variance values in our previous research max min decision region was found to be effective in distinct cases but ill detect the ambiguous false positive and false negative cases to alleviate this problem we first assume that the energy variance values can be described by a gaussian mixture model second we apply k means clustering to roughly identify the various clusters that make up the entire data population third convex hull of each cluster is employed as a basis for fitting an ellipsoidal decision region over it defect detection is then based on these ellipsoidal regions to validate the method three wallpaper groups are evaluated using the new ellipsoidal regions and compared with those results obtained using the max min decision region for the p2 group success rate improves from 93 43 to 100 for the pmm group success rate improves from 95 9 to 96 72 while the p4m group records the same success rate at 90 77 this demonstrates the superiority of using ellipsoidal decision regions in motif based defect detection

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

finding defects in texture using regularity and local orientation abstract we address basic aspects of detection of structural defects in regular and flow like patterns textures humans are able to find such defects without prior knowledge of the defect free pattern this capability to perceive local disorder has not attracted proper attention in machine vision despite its obvious relation to various application areas e g industrial texture inspection instead numerous ad hoc techniques have been developed to locate particular sorts of defects for particular tasks although useful these techniques do not help us understand the nature of structural defects which is the primary goal of our study in no attempt to compete with the existing dedicated algorithms we approach texture defects based on two fundamental structural properties regularity and local orientation anisotropy the two properties belong to a hierarchy of structural descriptions with the former being a higher level one than the latter both properties have great perceptual value in this study they are assumed to underlie recognition of structural defects defects are viewed as inhomogeneities in regularity and orientation fields two distinct but conceptually related approaches are presented the first one defines structural defects as regions of abruptly falling regularity the second one as perturbations in the dominant orientation both methods are general in the sense that each of them is applicable to a variety of patterns and defects however they are better suited to different kinds of patterns two tests are presented to assess and compare the two methods in the first test diverse textures are processed individually and defects are searched in each pattern in the second test classified defects in groups of textiles are considered conclusions concerning the scopes of the two approaches are drawn

3 d reconstruction using mirror images based on a plane symmetry recovering method three dimensional reconstruction from a perspective 2d image using mirrors is addressed the mirrors are used to form symmetrical relations between the direct image and mirror images by finding correspondences between them the 3d shape can be reconstructed by means of plane symmetry recovering method using the vanishing point two constraints are used in determining the correspondence in the case where only one mirror is used invisible parts both in the direct image and in the mirror image may still remain using multiple mirrors however occluded parts will decrease or disappear and occlusion free object reconstruction becomes possible

faster and more robust point symmetry based k means algorithm based on the recently published point symmetry distance psd measure this paper presents a novel psd measure namely symmetry similarity level ssl operator for k means algorithm our proposed modified point symmetry based k means mpsk algorithm is more robust than the previous psk algorithm by su and chou not only the proposed mpsk algorithm is suitable for the symmetrical intra clusters as the psk algorithm does the proposed mpsk algorithm is also suitable for the symmetrical inter clusters in addition two speedup strategies are presented to reduce the time required in the proposed mpsk algorithm experimental results demonstrate the significant execution time improvement and the extension to the symmetrical inter clusters of the proposed mpsk algorithm when compared to the previous psk algorithm

a three level finite element method for the instationary incompressible navier stokes equations we present a two and a three level finite element method for the numerical simulation of incompressible flow governed by the navier stokes equations within the theoretical framework of the variational multiscale method and exploiting the concept of residual free bubbles we propose a separation of three different scale groups namely large resolved scales small resolved scales and unresolved scales the resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches the dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of our algorithm the proposed algorithm is tested for various laminar flow situations and compared to the results obtained via an unusual stabilized finite element method it is supposed to be the basic scheme also for turbulent flow in a subsequent study

exact theory for the self similarity and decay of homogeneous turbulence it is shown that space time dilatation invariance x 1x t 2t with concomitant transformations for dependent variables and linearity of the equation engender an exact time explicit generic form for the solution applicable to freely decaying homogeneous incompressible fluid turbulence this solution features a summation over mutually independent dynamical modes labeled by the dilatation scaling index n 1 without the assumption of isotropy nor introduction of a closure approximation procedure the theory provides an explanation for the experimentally observed self similarity of the correlation tensors and the decay laws u x t 2 t n for the different types and decay stages of homogeneous turbulence

a dynamic variational multiscale method for large eddy simulations on unstructured meshes abstract a dynamic version of the variational multiscale vms method for large eddy simulation les on unstructured meshes of turbulent compressible flows is presented its key features include two variational analogues of germano s algebraic identity and a computationally efficient agglomeration based numerical procedure agglomeration is used both for separating a priori the scales and computing dynamically a smagorinsky parameter and the turbulent prandtl number on unstructured finite volume or finite element meshes numerical predictions of low speed 20 angle of attack turbulent flows past a 6 1 prolate spheroid and a forward swept scaled wing are presented they are contrasted with counterpart results obtained using similar implementations on unstructured meshes of the vms les traditional les and traditional dynamic les methods they are also compared to experimental data when available

globally optimal grouping for symmetric closed boundaries by combining boundary and region information many natural and man made structures have a boundary that shows a certain level of bilateral symmetry a property that plays an important role in both human and computer vision in this paper we present a new grouping method for detecting closed boundaries with symmetry we first construct a new type of grouping token in the form of symmetric trapezoids by pairing line segments detected from the image a closed boundary can then be achieved by connecting some trapezoids with a sequence of gap filling quadrilaterals for such a closed boundary we define a unified grouping cost function in a ratio form the numerator reflects the boundary information of proximity and symmetry and the denominator reflects the region information of the enclosed area the introduction of the region area information in the denominator is able to avoid a bias toward shorter boundaries we then develop a new graph model to represent the grouping tokens in this new graph model the grouping cost function can be encoded by carefully designed edge weights and the desired optimal boundary corresponds to a special cycle with a minimum ratio form cost we finally show that such a cycle can be found in polynomial time using a previous graph algorithm we implement this symmetry grouping method and test it on a set of synthetic data and real images the performance is compared to two previous grouping methods that do not consider symmetry in their grouping cost functions

similarity and symmetry measures for convex shapes using minkowski addition this paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on minkowski addition and the brunn minkowski inequality this means in particular that these measures are region based in contrast to most of the literature where one considers contour based measures all measures considered in this paper are invariant under translations furthermore they can be chosen to be invariant under rotations multiplications reflections or the class of affine transformations it is shown that the mixed volume of a convex polygon and a rotation of another convex polygon over an angle spl theta is a piecewise concave function of spl theta this and other results of a similar nature form the basis for the development of efficient algorithms for the computation of the given measures various results obtained in this paper are illustrated by experimental data although the paper deals exclusively with the two dimensional case many of the theoretical results carry over almost directly to higher dimensional spaces

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

nonlinear operator for oriented texture texture is an important part of the visual world of animals and humans and their visual systems successfully detect discriminate and segment texture relatively recently progress was made concerning structures in the brain that are presumably responsible for texture processing neurophysiologists reported on the discovery of a new type of orientation selective neuron in areas v1 and v2 of the visual cortex of monkeys which they called grating cells such cells respond vigorously to a grating of bars of appropriate orientation position and periodicity in contrast to other orientation selective cells grating cells respond very weakly or not at all to single bars which do not make part of a grating elsewhere we proposed a nonlinear model of this type of cell and demonstrated the advantages of grating cells with respect to the separation of texture and form information in this paper we use grating cell operators to obtain features and compare these operators in texture analysis tasks with commonly used feature extracting operators such as gabor energy and co occurrence matrix operators for a quantitative comparison of the discrimination properties of the concerned operators a new method is proposed which is based on the fisher 1923 linear discriminant and the fisher criterion the operators are also qualitatively compared with respect to their ability to separate texture from form information and their suitability for texture segmentation

study of the hopf functional equation for turbulence duhamel principle and dynamical scaling we consider a formulation for the hopf functional differential equation which governs statistical solutions of the navier stokes equations by introducing an exponential operator with a functional derivative we recast the hopf equation as an integro differential functional equation by the duhamel principle on this basis we introduce a successive approximation to the hopf equation as an illustration we take the burgers equation and carry out the approximations to the leading order scale invariance of the statistical navier stokes equations in d dimensions is formulated and contrasted with that of the deterministic navier stokes equations for the statistical navier stokes equations critical scale invariance is achieved for the characteristic functional of the d th derivative of the vector potential in d dimensions the deterministic equations corresponding to this choice of the dependent variable acquire the linear fokker planck operator under dynamic scaling in three dimensions it is the vorticity gradient that behaves like a fundamental solution more precisely source type solution of deterministic navier stokes equations in the long time limit physical applications of these ideas include study of a self similar decaying profile of fluid flows moreover we reveal typical physical properties in the late stage evolution by combining statistical scale invariance and the source type solution this yields an asymptotic form of the hopf functional in the long time limit improving the well known hopf titt solution in particular we present analyses for the burgers equations to illustrate the main ideas and indicate a similar analysis for the navier stokes equations

invariant and adaptive geometrical texture features for defect detection and classification automatic texture defect detection is highly important for many fields of visual inspection we introduce novel geometrical texture features for this task which are euclidean motion invariant and texture adaptive an algebraic function rational pade or polynomial is integrated over intensities in local circular neighborhoods on the image including an anisotropical texture analysis adaptiveness is achieved through the optimization of this feature kernel and further coefficients based on a simplex energy minimization constrained by a measure of texture discrimination fisher criterion a backpropagation trained multilayer perceptron network classifies the textures locally our approach contains new properties usually not common in feature theories theoretically implicit multiple invariances and an automatic and specific adaptation of the features to the texture images experiments with a fabric data set and brodatz textures reveal up to 98 6 recognition accuracy

radial symmetries based decomposition of cell clusters in binary and gray level images the segmentation of structures of complex cytological and histological images is a necessary intermediate step for image analysis that give rise to binary images in many cases these binary images can be rather far away from a subsequent object specific quantification because biological structures digitized by optoelectronic devices may situated close together so that they appear as one fused object in the projective image such fusions of objects may become complex so that large clusters of biological structures emerge to quantify individual objects of a cluster they must be separated the shape size and intensity variation of cells in complex organs like the brain may breed planar configurations that can be splitted only inadequate by common techniques e g watershed separation or basic morphological processing of images considering iteratively object contours suitable features of saliency can be accumulated that give rise to markers of singular objects such significant markers may drive a separation process more effective than common approaches the determination of markers by an iterative method should be scale translation and rotation invariant and robust with regard to noise due to the variability of biological specimen we realize a technique that splits cell clumps consisting of different cell sizes and shapes into meaningful parts the multiscale method applied here is based on the analysis of the contour shape and the object area by iterative voting using oriented kernels these cone shaped kernels vote iteratively for the local center of mass of the components of an aggregation the voting is performed along the gradient of the distance transformation of the binarized image of aggregates iterative voting is initialized by voting along the gradient direction where at each iteration the voting direction and shape of the kernel is refined resp the kernel topography is refined and reoriented iteratively it turned out that the kernel topography is unique because it votes for the most likely set of grid points where the gravity center of an individual cluster component may be located furthermore a new procedure is realized to use the local intensities of aggregations for kernel voting the last voted iteration provides gravitation centers resp centers of mass of the clumped cells these are extracted and used as markers to determine individual cell boundaries by a marker based watershed postprocessing the subject of this paper is to highlight the basic algorithm of iterative kernel voting and expanding it to process intensities within clusters as well as contour information the approach is applied to synthetic images that were modified systematically with regard to object topology natural aggregates of cells at the light microscopic level and cell clusters derived from high resolution flat bed scanning were splitted in addition to these examples images from a benchmark databases were investigated the splittings generated by the iterative voting approach were compared with expected splittings of test persons and with results of the watershed method especially the gray level based iterative voting method provides superior results for cell cluster separation in comparison to the watershed procedure

local preconditioning and variational multiscale stabilization for euler compressible steady flow abstract this paper introduces a preconditioned variational multiscale stabilization p vms method for compressible flows in this introductory paper we focus on inviscid flow and steady state problems the euler equations are solved on fully unstructured grids and discretized using the finite element method the p vms method can be decomposed into three parts first a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of mach numbers then the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations in this paper the solution is advanced in time using a fully explicit time discretization although p vms is general and can be applied to fully implicit solvers the proposed method is assessed by comparing convergence and accuracy of the solutions between the non preconditioned and preconditioned cases in particular for van leer lee roe s 1991 and choi merkle s 1993 preconditioners in some selected examples covering a large range of mach numbers

residual based variational multiscale turbulence models for unstructured tetrahedral meshes abstract this paper presents three level residual based turbulence models for the incompressible navier stokes equations employing the variational multiscale vms framework the velocity and pressure fields are decomposed into two overlapping hierarchical scales thereby leading to a system of coupled mixed field problems the mixed problem at the fine scales is stabilized via a subsequent vms application that results in a further decomposition of the fine scale velocity field into level i and level ii scales the level ii scales are modeled using higher order bubble functions that are then variationally embedded in the level i formulation to stabilize it the level i problem is modeled via a second set of bubble functions that are linearly independent of the bubbles employed at level ii finally the resulting level i fine scales are variationally embedded in the coarse scale formulation this yields a residual based turbulence model for the larger or coarser scales a significant feature of the proposed method is that it results in a concurrent top down and bottom up two way nesting of the scales in addition the resulting turbulence model does not possess any embedded tunable parameters another attribute of the formulation is that the fine scales at every level are driven by the residuals of the euler lagrange equations of the coarser scales at the preceding levels thereby resulting in a method that is variationally consistent various algorithmic generalizations of the method are presented that lead to computationally economic residual based turbulence models the proposed telescopic depth in scales approach helps make these models accurate for low order tetrahedral and hexahedral elements a feature that is facilitated by the higher order bubble functions over element interiors and it results in an enhanced representation of the fine scale terms modeling the fine viscous effects from a computational perspective this method results in easy to implement equal order pressure velocity elements and possesses the desirable p refinement feature numerical performance of the method is assessed on turbulent channel flow problems at re 395 and re 590 also presented are the results for turbulent sd 7003 airfoil at re 60 000 and comparison is made with the published experimental data and numerical results

subpixel detection of the center of an object using a spectral phase algorithm on the image this paper presents an algorithm designed for detecting the center of an object with central symmetry in an image it is well known that the spectral phase of such an object is a plane whose orientation depends on the object position in the image our algorithm applies weighting of the moduli to determine the slope and the orientation of this wrapped phase plane in the image spectrum a comparison is made with other conventional methods and shows the advantages of this algorithm subpixel resolution computing speed ease of implementation

motif based defect detection for patterned fabric this paper proposes a generalized motif based method for detecting defects in 16 out of 17 wallpaper groups in 2d patterned texture it assumes that most patterned texture can be decomposed into lattices and their constituents motifs it then utilizes the symmetry property of motifs to calculate the energy of moving subtraction and its variance among different motifs by learning the distribution of these values over a number of defect free patterns boundary conditions for discerning defective and defect free patterns can be determined this paper presents the theoretical foundation of the method and defines the relations between motifs and lattice from which a new concept called energy of moving subtraction is derived using norm metric measurement between a collection of circular shift matrices of motif and itself it has been shown in this paper that the energy of moving subtraction amplifies the defect information of the defective motif together with its variance an energy variance space is further defined where decision boundaries are drawn for classifying defective and defect free motifs as the 16 wallpaper groups of patterned fabric can be transformed into three major groups the proposed method is evaluated over these three major groups from which 160 defect free lattices samples are used for defining the decision boundaries with 140 defect free and 113 defective samples used for testing an overall detection success rate of 93 32 is achieved for the proposed method no other generalized approach can achieve this success rate has been reported before and hence this result outperforms all other previously published approaches

on the detection of the axes of symmetry of symmetric and almost symmetric planar images a simple algorithm is presented for finding all the axes of symmetry of symmetric and almost symmetric planar images having nonuniform gray level intensity images the technique which can also be used in conjunction with planar curves is based on the identification of the centroids of the given image and other related sets of points followed by a maximization of a specially defined coefficient of symmetry owing to the nature of the required procedures which are strictly based on the computation of mean values the method is not particularly affected by the presence of noise and is especially suited for application in conjunction with digitized figures

on symmetry and multiple view geometry structure pose and calibration from a single image in this paper we provide a principled explanation of how knowledge in global 3 d structural invariants typically captured by a group action on a symmetric structure can dramatically facilitate the task of reconstructing a 3 d scene from one or more images more importantly since every symmetric structure admits a canonical coordinate frame with respect to which the group action can be naturally represented the canonical pose between the viewer and this canonical frame can be recovered too which explains why symmetric objects e g buildings provide us overwhelming clues to their orientation and position we give the necessary and sufficient conditions in terms of the symmetry group admitted by a structure under which this pose can be uniquely determined we also characterize when such conditions are not satisfied to what extent this pose can be recovered we show how algorithms from conventional multiple view geometry after properly modified and extended can be directly applied to perform such recovery from all hidden images of one image of the symmetric structure we also apply our results to a wide range of applications in computer vision and image processing such as camera self calibration image segmentation and global orientation large baseline feature matching image rendering and photo editing as well as visual illusions caused by symmetry if incorrectly assumed

an exact representation of the space time characteristic functional of turbulent navier stokes flows with prescribed random initial states and driving forces by adopting a formal operator viewpoint the space time characteristic functional associated with navier stokes turbulence is expressed in terms of a linear operator acting on the space of functionals obtained by a simple similarity transformation of the local translation operator generated by the nonlinear terms in the navier stokes equation this operator is unitary with respect to the formal scalar product of functionals the equivalence of this operator representation to the functional integral representation of rosen is shown and for gaussian initial velocity and external force fields some consequences of this representation are presented

curved glide reflection symmetry detection we generalize the concept of bilateral reflection symmetry to curved glide reflection symmetry in 2d euclidean space such that classic reflection symmetry becomes one of its six special cases we propose a local feature based approach for curved glide reflection symmetry detection from real unsegmented 2d images furthermore we apply curved glide reflection axis detection for curved reflection surface detection in 3d images our method discovers groups and connects statistically dominant local glide reflection axes in an axis parameter space aps without preassumptions on the types of reflection symmetries quantitative evaluations and comparisons against state of the art algorithms on a diverse 64 test image set and 1 125 swedish leaf data images show a promising average detection rate of the proposed algorithm at 80 and 40 percent respectively and superior performance over existing reflection symmetry detection algorithms potential applications in computer vision particularly biomedical imaging include saliency detection from unsegmented images and quantification of deviations from normality we make our 64 test image set publicly available

the s kernel a measure of symmetry of objects in this paper we introduce a new symmetry feature named symmetry kernel sk to support a measure of symmetry given any symmetry transform s sk of a pattern p is the maximal included symmetric sub set of p for all directions and shifts we provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass then we prove that in any direction the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version that leads to a second algorithm the associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel a series of experiments supports the actual algorithm validation

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

numerical studies of finite element variational multiscale methods for turbulent flow simulations different realizations of variational multiscale vms methods within the framework of finite element methods are studied in turbulent channel flow simulations one class of vms methods uses bubble functions to model resolved small scales whereas the other class contains the definition of the resolved small scales by an explicit projection in its set of equations all methods are employed with eddy viscosity models of smagorinsky type the simulations are performed on grids for which a direct numerical simulation blows up in finite time

time dependent subgrid scales in residual based large eddy simulation of turbulent channel flow the present study investigates the effect of taking into account the time dependency of the fine subgrid scales in a residual based variational multiscale approach for large eddy simulation the residual based variational multiscale method with time dependent dynamic subgrid scales is presented and the impact of the time dependency is studied for the well known test case of turbulent channel flow results are presented from computations for various values of the reynolds number namely ret 180 ret 395 and ret 590 and several time step sizes a generalized a time integration scheme is employed results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time dependency of the subgrid scales into account for all re t values and time step sizes under consideration results for resolved quantities computed by both approaches are very similar this statement applies to both mean streamwise velocity and root mean square velocity fluctuations however it provides a model for the subgrid scales not depend ing on the time step size and enabling a more robust representation of unresolved scales thus we conclude that the time dependent subgrid scale approximation is not capable of producing more accurate results for this type of flow if the time step size is chosen within an optimal range however we expect it to be more advantageous for more complex problems since our results indicate that it provides a more reliable representation of unresolved scales

focus of attention from local color symmetries in this paper a continuous valued measure for local color symmetry is introduced the new algorithm is an extension of the successful gray value based symmetry map proposed by reisfeld et al the use of color facilitates the detection of focus points fps on objects that are difficult to detect using gray value contrast only the detection of fps is aimed at guiding the attention of an object recognition system therefore fps have to fulfill three major requirements stability distinctiveness and usability the proposed algorithm is evaluated for these criteria and compared with the gray value based symmetry measure and two other methods from the literature stability is tested against noise object rotation and variations of lighting as a measure for the distinctiveness of fps the principal components of fp centered windows are compared with those of windows at randomly chosen points on a large database of natural images finally usability is evaluated in the context of an object recognition task

irregular shape symmetry analysis theory and application to quantitative galaxy classification this paper presents a set of imperfectly symmetric measures based on a series of geometric transformation operations for quantitatively measuring the amount of symmetry of arbitrary shapes the definitions of both bilateral symmetricity and rotational symmetricity give new insight into analyzing the geometrical property of a shape and enable characterizing arbitrary shapes in a new way we developed a set of criteria for quantitative galaxy classification using our proposed irregular shape symmetry measures our study has demonstrated the effectiveness of the proposed method for the characterization of the shape of the celestial bodies the concepts described in the paper are applicable to many fields such as mathematics artificial intelligence digital image processing robotics biomedicine etc

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed

a variational multiscale method for incompressible turbulent flows bubble functions and fine scale fields this paper presents a residual based turbulence model for the incompressible navier stokes equations the method is derived employing the variational multiscale vms framework a multiscale decomposition of the continuous solution and a priori unique decomposition of the admissible spaces of functions lead to two coupled nonlinear problems termed as the coarse scale and the fine scale sub problems the fine scale velocity field is assumed to be nonlinear and time dependent and is modeled via the bubble functions approach applied directly to the fine scale sub problem a significant contribution in this paper is a systematic and consistent derivation of the fine scale variational operator commonly termed as the stabilization tensor that possesses the right order in the advective and diffusive limits and variationally projects the fine scale solution onto the coarse scale space a direct treatment of the fine scale problem via bubble functions offers several fine scale approximation options with varying degrees of mathematical sophistication that are investigated via benchmark problems numerical accuracy of the proposed method is shown on a forced isotropic turbulence problem statistically stationary turbulent channel flow problems at ret 395 and 590 and non equilibrium turbulent flow around a cylinder at re 3 900