on the generation of skeletons from discrete euclidean distance maps the skeleton is an important representation for shape analysis a common approach for generating discrete skeletons takes three steps 1 computing the distance map 2 detecting maximal disks from the distance map and 3 linking the centers of maximal disks cmds into a connected skeleton algorithms using approximate distance metrics are abundant and their theory has been well established however the resulting skeletons may be inaccurate and sensitive to rotation in this paper we study methods for generating skeletons based on the exact euclidean metric we first show that no previous algorithms identify the exact set of discrete maximal disks under the euclidean metric we then propose new algorithms and show that they are correct to link cmds into connected skeletons we examine two prevalent approaches connected thinning and steepest ascent we point out that the connected thinning approach does not work properly for euclidean distance maps only the steepest ascent algorithm produces skeletons that are truly medially placed the resulting skeletons have all the desirable properties they have the same simple connectivity as the figure they are well centered they are insensitive to rotation and they allow exact reconstruction the effectiveness of our algorithms is demonstrated with numerous examples

skeletonization based on error reduction the accuracy of a non pixel based skeletonization method is largely dependent on the contour information chosen as input when using a constrained delaunay triangulation to construct an object s skeleton a number of contour pixels must be chosen as a basis for triangulation this paper presents a new method of selecting these contour pixels a new method for measuring skeletonization error is proposed which quantifies the deviation of a skeleton segment from the true medial axis of a stroke in an image the goal of the proposed algorithm is to reduce this error to an acceptable level whilst retaining the superior efficiencies of previous non pixel based techniques experimental results show that the proposed method is adept at following the medial axis of an image and is capable of producing a skeleton that is confirmed by a human s perception of the image it is also computationally efficient and robust against noise

an adaptive active contour model for highly irregular boundaries abstract snake is an active contour model for representing image contours in this paper we propose an efficient active contour model which can represent highly irregular boundaries the algorithm includes an adaptive force along the contour and adjusts the number of points for the snake according to the desired boundary a better stopping criterion based on the area of a closed contour is devised furthermore in this method a contour can break automatically to represent the contours of multiple objects experiments show that this method can extract object s boundaries accurately and efficiently

medial axis transformation of a planar shape the medial axis transformation is a means first proposed by blum to describe a shape in this paper we present a 0 n log n algorithm for computing the medial axis of a planar shape represented by an n edge simple polygon the algorithm is an improvement over most previously known results interms of both efficiency and exactness and has been implemented in fortran some computer plotted output of the program are also shown in the paper

fourth rank tensors of the thirty two crystal classes multiplication tables the fourth rank tensors that embody the elastic or other properties of crystalline anisotropic substances can be partitioned into a number of sets in order that each shall acknowledge the symmetry of one or more of the crystal classes and moreover shall make up a closed linear associative algebra of hypercomplex numbers for the purpose of calculating the sums products and inverses of its constituent tensors to which end coordinate invariant expressions of the tensors are adopted the calculations are simplified immensely and ensuing physical analyses are well prepared for once the structure of every algebra is unravelled completely in terms of a number of separate subalgebras isomorphic to familiar algebras such as the binary one of the complex numbers the quaternary one of the 2x2 matrices and the octonary one of the complex quaternions the fourth rank tensors do not seem to have been submitted previously to the present algebraic point of view and nor do those of any other rank a parallel but less intricate development can be provided for the second rank ones

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

skeleton based morphological coding of binary images this paper presents new properties of the discrete morphological skeleton representation of binary images along with a novel coding scheme for lossless binary image compression that is based on these properties following a short review of the theoretical background two sets of new properties of the discrete morphological skeleton representation of binary images are proved the first one leads to the conclusion that only the radii of skeleton points belonging to a subset of the ultimate erosions are needed for perfect reconstruction this corresponds to a lossless sampling of the quench function the second set of new properties is related to deterministic prediction of skeletonal information in a progressive transmission scheme based on the new properties a novel coding scheme for binary images is presented the proposed scheme is suitable for progressive transmission and fast implementation computer simulations also presented show that the proposed coding scheme substantially improves the results obtained by previous skeleton based coders and performs better than classical coders including run length huffman quadtree and chain coders for facsimile images its performance can be placed between the modified read mr method k 4 and modified modified read mmr method

separators and structure prediction in sparse orthogonal factorization abstract in the factorization a qr of a sparse matrix a the orthogonal matrix q can be represented either explicitly as a matrix or implicitly as a sequence of householder vectors a folk theorem states that the householder vectors are much sparser than q in practice in this paper we make this folk theorem precise we prove tight upper and lower bounds on the nonzero counts of the two representations in terms of the quality of separators in the column intersection graph of a we conclude that the folk theorem is true when a is nearly square but not when a has many more rows than columns

optimum design of chamfer distance transforms the distance transform has found many applications in image analysis chamfer distance transforms are a class of discrete algorithms that offer a good approximation to the desired euclidean distance transform at a lower computational cost they can also give integer valued distances that are more suitable for several digital image processing tasks the local distances used to compute a chamfer distance transform are selected to minimize an approximation error a new geometric approach is developed to find optimal local distances this new approach is easier to visualize than the approaches found in previous work and can be easily extended to chamfer metrics that use large neighborhoods a new concept of critical local distances is presented which reduces the computational complexity of the chamfer distance transform without increasing the maximum approximation error

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

detection of 3 d simple points for topology preserving transformations with application to thinning the problems of 3 d digital topology preservation under binary transformations and 3 d object thinning are considered in this correspondence first the authors establish the conditions under which transformation of an object voxel to a non object voxel or its inverse does not affect the image topology an efficient algorithm to detect a simple point has been proposed on the basis of those conditions in this connection some other interesting properties of 3 d digital geometry are also discussed using these properties and the simple point detection algorithm the authors have proposed an algorithm to generate a surface skeleton so that the topology of the original image is preserved the shape of the image is maintained as much as possible and the results are less affected by noise

object matching with hierarchical skeletons the skeleton of an object provides an intuitive and effective abstraction which facilitates object matching and recognition however without any human interaction traditional skeleton based descriptors and matching algorithms are not stable for deformable objects specifically some fine grained topological and geometrical features would be discarded if the skeleton was incomplete or only represented significant visual parts of an object moreover the performance of skeleton based matching highly depends on the quality and completeness of skeletons in this paper we propose a novel object representation and matching algorithm based on hierarchical skeletons which capture the shape topology and geometry through multiple levels of skeletons for object representation we reuse the pruned skeleton branches to represent the coarse and fine grained shape topological and geometrical features moreover this can improve the stability of skeleton pruning without human interaction we also propose an object matching method which considers both global shape properties and fine grained deformations by defining singleton and pairwise potentials for similarity computation between hierarchical skeletons our experiments attest our hierarchical skeleton based method a significantly better performance than most existing shape based object matching methods on six datasets achieving a 99 21 bulls eye score on the mpeg7 shape dataset highlightsit represents the coarse and fine grained shape topological and geometrical features it improves the stability of skeleton pruning without human interaction it considers both global and fine shape properties by different potential functions it achieves a better performance than most existing methods on six datasets experiments attest our method a better performance than most related approaches we achieve a 99 21 bulls eye score on the mpeg7 shape dataset

a minimal integrity basis for the elasticity tensor we definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth order elasticity tensor c decomposing c into its so 3 irreducible components we reduce this problem to finding joint invariants of a triplet a b d where a and b are second order harmonic tensors and d is a fourth order harmonic tensor combining theorems of classical invariant theory and formal computations a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time

derivation of anisotropic matrix for bi dimensional strain gradient elasticity behavior the different forms of second order elasticity operators in mindlin s strain gradient elasticity are given for a bi dimensional physical space these different forms are obtained according to the different symmetry classes of a material media dimensional aspects are discussed together with observations made on the physical behavior of such a media

why finite element discretizations can be factored by triangular hierarchical matrices although the asymptotic complexity of direct methods for the solution of large sparse finite element systems arising from second order elliptic partial differential operators is far from being optimal these methods are often preferred over modern iterative methods this is mainly due to their robustness in this article it is shown that an approximate lu decomposition exists which can be computed in the algebra of hierarchical matrices with almost linear complexity and with the same robustness as the classical lu decomposition low precision approximations may be used for preconditioning iterative solvers as a byproduct we prove that schur complements of stiffness matrices can be approximated with almost linear complexity

block computation and representation of a sparse nullspace basis of a rectangular matrix abstract in this paper we propose a new method to efficiently compute a representation of an orthogonal basis of the nullspace of a sparse matrix operator b t with b r n m n m we assume that b has full rank i e rank b m it is well known that the last n m columns of the orthogonal matrix q in a qr factorization b qr form such a desired null basis the orthogonal matrix q can be represented either explicitly as a matrix or implicitly as a matrix h of householder vectors typically the matrix h represents the orthogonal factor much more compactly than q we will employ this observation to design an efficient block algorithm that computes a sparse representation of the nullspace basis in almost optimal complexity this new algorithm may e g be used to construct a null space basis of the discrete divergence operator in the finite element context and we will provide numerical results for this particular application

a topology preserving parallel 3d thinning algorithm for extracting the curve skeleton we introduce a new topology preserving 3d thinning procedure for deriving the curve voxel skeleton from 3d binary digital images based on a rigorously defined classification procedure the algorithm consists of sequential thinning iterations each characterized by six parallel directional sub iterations followed by a set of sequential sub iterations the algorithm is shown to produce concise and geometrically accurate 3d curve skeletons the thinning algorithm is also insensitive to object rotation and only moderately sensitive to noise although this thinning procedure is valid for curve skeleton extraction of general elongated objects in this paper we specifically discuss its application to the orientation modeling of trabecular biological tissues

a skeleton family generator via physics based deformable models this paper presents a novel approach for object skeleton family extraction the introduced technique utilizes a 2 d physics based deformable model that parameterizes the objects shape deformation equations are solved exploiting modal analysis and proportional to model physical characteristics a different skeleton is produced every time generating in this way a family of skeletons the theoretical properties and the experiments presented demonstrate that obtained skeletons match to hand labeled skeletons provided by human subjects even in the presence of significant noise and shape variations cuts and tears and have the same topology as the original skeletons in particular the proposed approach produces no spurious branches without the need of any known skeleton pruning method

invariant based reconstruction of bidimensional elasticity tensors in the present paper a method to reconstruct the 2d elasticity tensor from observations is proposed the novelty of the method compared to other ones is that this approach is based on the identification of the invariants rather than the components of the elasticity tensor the main advantage is that all the information concerning the material such as its symmetry class and the orientation of the tested sample are obtained during the reconstruction process we believe that such an approach based on intrinsic quantities may find interesting applications for the identification of mechanical parameters based on full field measurements

how to overcome indetermination and interpenetration in granular systems via nonsmooth contact dynamics an exploratory investigation abstract the present paper is an exploratory investigation to overcome difficulties encountered in the simulation of dense granulates when a nscd approach is used some simple examples permit identification of impulse indetermination as the main cause of the failure or the slowdown of the numerical algorithm we propose to deal directly with the space of impulses with null resulting momentum a prediction correction scheme is detailed and enriched to restrict at best the interpenetration finally sophisticated tools are developed to preserve the sparsity of the matrices and consequently to ensure an efficient implementation of an adapted nonsmooth solver

hierarchic voronoi skeletons abstract robust and time efficient skeletonization of a planar shape which is connectivity preserving and based on euclidean metrics can be achieved by first regularizing the voronoi diagram vd of a shape s boundary points i e by removal of noise sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents each component of the vd is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise the second processing step a hierarchic clustering of skeleton branches leads to a multiresolution representation of the skeleton termed skeleton pyramid

flux maximizing geometric flows several geometric active contour models have been proposed for segmentation in computer vision and image analysis the essential idea is to evolve a curve in 2d or a surface in 3d under constraints from image forces so that it clings to features of interest in an intensity image recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented however it is still unclear how to apply these techniques to images of narrow elongated structures such as blood vessels where intensity contrast may be low and reliable region statistics cannot be computed to address this problem we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve in 2d or a surface in 3d the key idea is to exploit the direction of the vector field along with its magnitude the calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions we illustrate its advantages with several level set based segmentations of 2d and 3d angiography images of blood vessels

overlapping cell nuclei segmentation using a spatially adaptive active physical model a method for the segmentation of overlapping nuclei is presented which combines local characteristics of the nuclei boundary and a priori knowledge about the expected shape of the nuclei a deformable model whose behavior is driven by physical principles is trained on images containing a single nuclei and attributes of the shapes of the nuclei are expressed in terms of modal analysis based on the estimated modal distribution and driven by the image characteristics we develop a framework to detect and describe the unknown nuclei boundaries in images containing two overlapping nuclei the problem of the estimation of an accurate nucleus boundary in the overlapping areas is successfully addressed with the use of appropriate weight parameters that control the contribution of the image force in the total energy of the deformable model the proposed method was evaluated using 152 images of conventional pap smears each containing two overlapping nuclei comparisons with other segmentation methods indicate that our method produces more accurate nuclei boundaries which are closer to the ground truth

high order accurate solution of the incompressible navier stokes equations on massively parallel computers the emergence of petascale supercomputers requires us to develop today s simulation codes for incompressible flows by codes which are using numerical schemes and methods that are better able to exploit the offered computational power in that spirit we present a massively parallel high order navier stokes solver for large incompressible flow problems in three dimensions the governing equations are discretized with finite differences in space and a semi implicit time integration scheme this discretization leads to a large linear system of equations which is solved with a cascade of iterative solvers the iterative solver for the pressure uses a highly efficient commutation based preconditioner which is robust with respect to grid stretching the efficiency of the implementation is further enhanced by carefully setting the adaptive termination criteria for the different iterative solvers the computational work is distributed to different processing units by a geometric data decomposition in all three dimensions this decomposition scheme ensures a low communication overhead and excellent scaling capabilities the discretization is thoroughly validated first we verify the convergence orders of the spatial and temporal discretizations for a forced channel flow second we analyze the iterative solution technique by investigating the absolute accuracy of the implementation with respect to the different termination criteria third orr sommerfeld and squire eigenmodes for plane poiseuille flow are simulated and compared to analytical results fourth the practical applicability of the implementation is tested for transitional and turbulent channel flow the results are compared to solutions from a pseudospectral solver subsequently the performance of the commutation based preconditioner for the pressure iteration is demonstrated finally the excellent parallel scalability of the proposed method is demonstrated with a weak and a strong scaling test on up to o 10 4 processing units and o 10 1 1 grid points

existence of ℋ matrix approximants to the inverse fe matrix of elliptic operators with l coefficients this article deals with the existence of blockwise low rank approximants so called matrices to inverses of fem matrices in the case of uniformly elliptic operators with l coefficients unlike operators arising from boundary element methods for which the matrix theory has been extensively developed the inverses of these operators do not benefit from the smoothness of the kernel function however it will be shown that the corresponding green functions can be approximated by degenerate functions giving rise to the existence of blockwise low rank approximants of fem inverses numerical examples confirm the correctness of our estimates as a side product we analyse the matrix property of the inverse of the fe mass matrix

multiple instance subspace learning via partial random projection tree for local reflection symmetry in natural images local reflection symmetry detection in nature images is a quite important but challenging task in computer vision the main obstacle is both the scales and the orientations of symmetric structure are unknown the multiple instance learning mil framework sheds lights onto this task owing to its capability to well accommodate the unknown scales and orientations of the symmetric structures however to differentiate symmetry vs non symmetry remains to face extreme confusions caused by clutters scenes and ambiguous object structures in this paper we propose a novel multiple instance learning framework for local reflection symmetry detection named multiple instance subspace learning misl which instead learns a group of models respectively on well partitioned subspaces to obtain such subspaces we propose an efficient dividing strategy under mil setting named partial random projection tree prpt by taking advantage of the fact that each sample bag is represented by the proposed symmetry features computed at specific scale and orientation combinations instances encouraging experimental results on two datasets demonstrate that the proposed local reflection symmetry detection method outperforms current state of the arts highlightswe perform clustering on samples represented by multiple instances we learn a group of mil classifiers on subspaces we report state of the arts results on the symmetry detection benchmark

fast homotopy preserving skeletons using mathematical morphology two algorithms for skeletonization of 2 d binary images each of which explicitly separates the two major aspects of skeletonization are described the identification of points critical to shape representation and the identification of further points necessary to preserve homotopy sets of points critical to shape representation are found by eroding the original image i with a nested sequence of structuring elements e sub i by choosing appropriate e sub i and d a structuring element either algorithm is capable of producing a variety of skeletons corresponding to different distance functions a sufficient condition is given for the original image to be reconstructed from the skeleton in the case of the first algorithm there are few restrictions on the set of structuring elements it uses a simple search strategy to find points whose removal would alter homotopy the second faster algorithm has a more constructional approach to finding points necessary for preserving homotopy which limits it to a more restricted set of structuring elements than the first algorithm however it may still be used with a variety of distance functions

determination of the symmetries of an experimentally determined stiffness tensor application to acoustic measurements abstract for most materials the symmetry group is known a priori and deduced from the realization process this allows many simplifications for the measurements of the stiffness tensor we deal here with the case where the symmetry is a priori unknown as for biological or geological materials or when the process makes the material symmetry axis uncertain some composites monocrystals the measurements are then more complicated and the raw stiffness tensor obtained does not exhibit any symmetry in the voigt s matrical form as it is expressed in the arbitrarily chosen specimen s base a complete ultrasonic measurement of this stiffness tensor from redundant measurements is proposed in a second time we show how to make a plane symmetry pole figure able to give visual information about the quasi symmetries of a raw stiffness tensor determined by any measurement method finally we introduce the concept of distance from a raw stiffness tensor to one of the eight symmetry classes available for a stiffness tensor the method provides the nearest tensor to the raw stiffness tensor possessing a chosen symmetry class with its associated natural symmetry base

elasticity and symmetry of triangular lattice materials the elastic tensor of any triangular 2d lattice material is given with re spect to the geometry and the mechanical properties of the links between the nodes the links can bear central forces tensional material for example with hinged joints momentums flexural materials or a combination of the two the symmetry class of the stiffness tensor is detailed in any case by using the invariants of forte and vianello a distinction is made between the trivial cases where the elasticity symmetry group corresponds to the mi crostructure s symmetry group and the non trivial cases in the opposite case interesting examples of isotropic auxetic materials with negative poisson s ratio and non trivial materials with isotropic elasticity but anisotropic frac turation weak direction are shown the proposed set of equations can be used in a engineering process to create a 2d triangular lattice material of the desired elasticity

extraction of the euclidean skeleton based on a connectivity criterion abstract the skeleton is essential for general shape representation the commonly required properties of a skeletonization algorithm are that the extracted skeleton should be accurate robust to noise position and rotation able to reconstruct the original object and able to produce a connected skeleton in order to preserve its topological and hierarchical properties however the use of a discrete image presents a lot of problems that may influence the extraction of the skeleton moreover most of the methods are memory intensive and computationally intensive and require a complex data structure in this paper we propose a fast efficient and accurate skeletonization method for the extraction of a well connected euclidean skeleton based on a signed sequential euclidean distance map a connectivity criterion is proposed which can be used to determine whether a given pixel is a skeleton point independently the criterion is based on a set of point pairs along the object boundary which are the nearest contour points to the pixel under consideration and its 8 neighbors our proposed method generates a connected euclidean skeleton with a single pixel width without requiring a linking algorithm or iteration process experiments show that the runtime of our algorithm is faster than the distance transformation and is linearly proportional to the number of pixels of an image

simulating the grassfire transform using an active contour model a method for shape description of planar objects that integrates both region and boundary features is presented the method is an implementation of a 2d dynamic grassfire that relies on a distance surface on which elastic contours minimize an energy function the method is based on an active contour model numerous implementation aspects of the shape description method were optimized a euclidean metric was used for optimal accuracy and the active contour model permits bypassing some of the discretization limitations inherent in using a digital grid noise filtering was performed on the basis of both contour feature measures and region measures that is curvature extremum significance and ridge support respectively to obtain robust shape descriptors other improvements and variations of the algorithmic implementation are proposed

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

skeleton pruning by contour partitioning with discrete curve evolution in this paper we introduce a new skeleton pruning method based on contour partitioning any contour partition can be used but the partitions obtained by discrete curve evolution dce yield excellent results the theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable even in the presence of significant noise and shape variations and have the same topology as the original skeletons in particular we have proven that the proposed approach never produces spurious branches which are common when using the known skeleton pruning methods moreover the proposed pruning method does not displace the skeleton points consequently all skeleton points are centers of maximal disks again many existing methods displace skeleton points in order to produces pruned skeletons

binary shape recognition using the morphological skeleton transform abstract binary image representation by its morphological skeleton transform has been proposed in the past as an information preserving representation in this paper this skeleton representation is adopted as the start point for the development of a binary shape recognition scheme a skeleton matching algorithm is presented that efficiently characterizes the similarity between two skeletons as a distance measure this skeleton matching algorithm resembles the well known from speech processing elastic matching technique

on row and column orderings for sparse least squares problems let p 1 and p 2 be respectively m times m and n times n permutation matrices with m geqq n suppose the m times n sparse matrix bar a p 1 ap 2 is reduced to upper trapezoidal form left begin array 20 c r 0 end array right through the application of givens rotations sequentially to the rows of bar a it is well known that the sparsity of r depends only on the choice of p 2 but the choice of p 1 can drastically affect the arithmetic required to compute r in this paper we provide a mechanism for studying the connection between good row and good column orderings along with a modified nested dissection algorithm for finding a good p 2 which automatically induces a good p 1 an analysis for a model problem is given along with some experimental results