generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

the multifrontal method for sparse matrix solution theory and practice this paper presents an overview of the multifrontal method for the solution of large sparse symmetric positive definite linear systems the method is formulated in terms of frontal matrices update matrices and an assembly tree formal definitions of these notions are given based on the sparse matrix structure various advances to the basic method are surveyed they include the role of matrix reorderings the use of supernodes and other implementatjon techniques the use of the method in different computational environments is also described

coupling biot and navier stokes equations for modelling fluid poroelastic media interaction the interaction between a fluid and a poroelastic structure is a complex problem that couples the navier stokes equations with the biot system the finite element approximation of this problem is involved due to the fact that both subproblems are indefinite in this work we first design residual based stabilization techniques for the biot system motivated by the variational multiscale approach then we state the monolithic navier stokes biot system with the appropriate transmission conditions at the interface for the solution of the coupled system we adopt both monolithic solvers and heterogeneous domain decomposition strategies different domain decomposition methods are considered and their convergence is analyzed for a simplified problem we compare the efficiency of all the methods on a test problem that exhibits a large added mass effect as it happens in hemodynamics applications

efficient structured multifrontal factorization for general large sparse matrices rank structures provide an opportunity to develop new efficient numerical methods for practical problems when the off diagonal blocks of certain dense intermediate matrices have small numerical

local registration and deformation of a road cartographic database on a spot satellite image abstract herein we propose a new method to locally register cartographic road networks on spot satellite images this approach is based on markov random fields mrf on graphs since the cartographic and image data are obtained from different sources the noises degrading these data are of different nature cartographers also introduce in the generalization process distortions in the road map in order to emphasize some details of the road this can create important differences between the map data and the ground truth the proposed algorithm aims at correcting the error due to noise and generalization hence increasing the accuracy of the road map the first step of the method is to translate the road network into a graph where the nodes are characteristic points of the roads e g crossroads the random variable or descriptors are defined by the nodes position the edges are defined by the roads joining these points then local registration is performed by defining a model in a bayesian framework the solution is obtained by computing the maximum a posteriori map the posterior probability is assumed to be a product of two probabilities the prior of the network and the likelihood of the map each depending on the image data both are markov random field probabilities the likelihood of the registered map is the probability of a network configuration given the map data it is a measure of a global resemblance between the two we use geometrical measures euclidean distances and angles to build this probability the prior consists of two terms both depending on the image data the dependance exists through the fact that between two connected nodes we compute a best path thanks to a dynamic programing algorithm minimizing a cost function based on image gray levels curvature and gradient information the first term of the prior penalizes configurations for which different roads overlap each other and the second term depends on gray level statistics along these paths we run a simulated annealing algorithm to optimize the proposed model the tests are done on one real image data extracted from spot satellite images and artificially noisy cartographic data translated rotated or randomly deformed network we present some results showing a good global registration but also accurate correction of local distortions

efficient preconditioning of hp fem matrix sequences with slowly varying coefficients an application to topology optimization abstract we previously introduced a preconditioner that has proven effective for h p fem discretizations of various challenging elliptic and hyperbolic problems the construction is inspired by standard nested dissection and relies on the assumption that the schur complements can be approximated to high precision by hierarchically semi separable matrices the preconditioner is built as an approximate l d m t factorization through a divide and conquer approach this implies an enhanced flexibility which allows to handle unstructured geometric meshes anisotropies and discontinuities we build on our previous numerical experiments and develop a preconditioner update strategy that allows us to handle matrix sequences arising from problems with slowly varying coefficients we investigate the performance of the preconditioner along with the update strategy in context of topology optimization of an acoustic cavity

analysis of mixed finite elements methods for the stokes problem a unified approach we develop a method for the analysis of mixed finite element methods for the stokes problem in the velocity pressure formulation a technical macroelement condition which is sufficient for the classical babuska brezzi inequality to be valid is introduced using this condition we are able to verify the stability and optimal order of convergence of several known mixed finite element methods

three dimensional finite element methods for the stokes problem the tetrahedral finite element approximation of the stokes problem is analyzed by means of polynomials piecewise of degree k 1 for the velocity and continuous piecewise of degree k for the pressure a stability result is given for every k ge 1

a theory of pseudoskeleton approximations abstract let an m n matrix a be approximated by a rank r matrix with an accuracy e we prove that it is possible to choose r columns and r rows of a forming a so called pseudoskeleton component which approximates a with o e r m n accuracy in the sense of the 2 norm on the way to this estimate we study the interconnection between the volume i e the determinant in the absolute value and the minimal singular value r of r r submatrices of an n r matrix with orthogonal columns we propose a lower bound better than one given by chandrasekaran and ipsen and by hong and pan for the maximum of r over all these submatrices and formulate a hypothesis on a tighter bound

comutations underlying the measuremnt of visual motion abstract the organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects their motion in space and their three dimensional structure a description of this movement is not provided to our visual system directly however it must be inferred from the pattern of changing intensity that reaches the eye this paper examines the problem of motion measurement which we formulate as the computation of an instantaneous two dimensional velocity field initial motion measurements occur at the location of significant intensity changes as suggested by marr and ullman 1 these measurements provide only one component of velocity and must be integrated to compute the two dimensional velocity field a fundamental problem for this integration is that motion is not determined uniquely from the changing image an additional constraint of smoothness of the velocity field is formulated based on the physical assumption that surfaces are generally smooth allowing the computation of a unique solution a theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible empirical studies show the results to be consistent with human motion perception

fast monte carlo algorithms for finding low rank approximations we consider the problem of approximating a given m n matrix a by another matrix of specified rank k which is smaller than m and n the singular value decomposition svd can be used to find the best such approximation however it takes time polynomial in m n which is prohibitive for some modern applications in this article we develop an algorithm that is qualitatively faster provided we may sample the entries of the matrix in accordance with a natural probability distribution in many applications such sampling can be done efficiently our main result is a randomized algorithm to find the description of a matrix d of rank at most k so that holds with probability at least 1 where v vf is the frobenius norm the algorithm takes time polynomial in k 1 e log 1 only and is independent of m and n in particular this implies that in constant time it can be determined if a given matrix of arbitrary size has a good low rank approximation

using angular dispersion of gradient direction for detecting edge ribbons edges in a scene generally project to smooth continuous curves nearly everywhere in the image which results in low angular deviation of the intensity gradients in small neighborhoods straddling edges angular deviation is shown to be a measure of snr a theoretical analysis of angular deviation arising due to independent and identically distributed n 0 sigma sup 2 random noise is presented angular deviation thresholds for neighborhood sizes from 3 3 to 11 11 pixels are determined both from this analysis and numerical examples the proposed gradient angular dispersion detection algorithm detects edge elements by comparing the measured angular deviation with values computed for the minimum acceptable snr low values of deviation violate the no edge hypothesis the algorithm is shown to make good use of the limited dynamic range of the imaging system the sensitivity and selectivity of the strategy are both shown to be high

stochastic completion fields a neural model of illusory contour shape and salience we describe an algorithm and representation level theory of illusory contour shape and salience unlike previous theories our model is derived from a single assumption that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane i e the space that one can reasonably assume is represented by neurons of the mammalian visual cortex our model does not employ numerical relaxation or other explicit minimization but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector field convolutions we show that for the random walk we define the maximum likelihood paths are curves of least energy that is on average random walks follow paths commonly assumed to model the shape of illusory contours a computer model is demonstrated on numerous illusory contour stimuli from the literature

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

improving multifrontal methods by means of block low rank representations matrices coming from elliptic partial differential equations pdes have been shown to have a low rank property well defined off diagonal blocks of their schur complements can be approximated by low rank products given a suitable ordering of the matrix which gives to the blocks a geometrical meaning such approximations can be computed using an svd or a rank revealing qr factorization the resulting representation offers a substantial reduction of the memory requirement and gives efficient ways to perform many of the basic dense algebra operations several strategies have been proposed to exploit this property we propose a low rank format called block low rank blr and explain how it can be used to reduce the memory footprint and the complexity of direct solvers for sparse matrices based on the multifrontal method we present experimental results that show how the blr format delivers gains that are comparable to those obtained with hierarchical formats such as hierarchical matrices h matrices and hierarchically semi separable hss matrices but provides much greater flexibility and ease of use which are essential in the context of a general purpose algebraic solver

finding structure with randomness probabilistic algorithms for constructing approximate matrix decompositions low rank matrix approximations such as the truncated singular value decomposition and the rank revealing qr decomposition play a central role in data analysis and scientific computing this work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low rank matrix approximation these techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets this paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions these methods use random sampling to identify a subspace that captures most of the action of a matrix the input matrix is then compressed either explicitly or implicitly to this subspace and the reduced matrix is manipulated deterministically to obtain the desired low rank factorization in many cases this approach beats its classical competitors in terms of accuracy robustness and or speed these claims are supported by extensive numerical experiments and a detailed error analysis the specific benefits of randomized techniques depend on the computational environment consider the model problem of finding the k dominant components of the singular value decomposition of an m times n matrix i for a dense input matrix randomized algorithms require bigo mn log k floating point operations flops in contrast to bigo mnk for classical algorithms ii for a sparse input matrix the flop count matches classical krylov subspace methods but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures iii for a matrix that is too large to fit in fast memory the randomized techniques require only a constant number of passes over the data as opposed to bigo k passes for classical algorithms in fact it is sometimes possible to perform matrix approximation with a single pass over the data

range image segmentation by an effective jump diffusion method this paper presents an effective jump diffusion method for segmenting a range image and its associated reflectance image in the bayesian framework the algorithm works on complex real world scenes indoor and outdoor which consist of an unknown number of objects or surfaces of various sizes and types such as planes conics smooth surfaces and cluttered objects like trees and bushes formulated in the bayesian framework the posterior probability is distributed over a solution space with a countable number of subspaces of varying dimensions the algorithm simulates markov chains with both reversible jumps and stochastic diffusions to traverse the solution space the reversible jumps realize the moves between subspaces of different dimensions such as switching surface models and changing the number of objects the stochastic langevin equation realizes diffusions within each subspace to achieve effective computation the algorithm precomputes some importance proposal probabilities over multiple scales through hough transforms edge detection and data clustering the latter are used by the markov chains for fast mixing the algorithm is tested on 100 1d simulated data sets for performance analysis on both accuracy and speed then the algorithm is applied to three data sets of range images under the same parameter setting the results are satisfactory in comparison with manual segmentations

object tracking in image sequences using point features this paper presents an object tracking technique based on the bayesian multiple hypothesis tracking mht approach two algorithms both based on the mht technique are combined to generate an object tracker the first mht algorithm is employed for contour segmentation the segmentation of contours is based on an edge map the segmented contours are then merged to form recognisable objects the second mht algorithm is used in the temporal tracking of a selected object from the initial frame an object is represented by key feature points that are extracted from it the key points mostly corner points are detected using information obtained from the edge map these key points are then tracked through the sequence to confirm the correctness of the tracked key points the location of the key points on the trajectory are verified against the segmented object identified in each frame if an acceptable number of key points lie on or near the contour of the object in a particular frame n th frame we conclude that the selected object has been tracked identified successfully in frame n

characterizing the distribution of completion shapes with corners using a mixture of random processes abstract we derive an analytic expression for the distribution of contours x t generated by fluctuations in x t x t t due to random impulses of two limiting types the first type are frequent but weak while the second are infrequent but strong the result has applications in computational theories of figural completion and illusory contours because it can be used to model the prior probability distribution of short smooth completion shapes punctuated by occasional discontinuities in orientation i e corners this work extends our previous work on characterizing the distribution of completion shapes which dealt only with the case of frequently acting weak impulses

an algebraic method for detection and recognition of polyhedral objects from a single image abstract this paper proposes an algorithm to recognize rotated scaled or overlapping polyhedral objects using only one orthographic projection the procedure is not based on the numerical solution of nonlinear equations and does not require any a priori knowledge it is an algebraic method for testing whether a cluster of edges and vertices in a line drawing correspond to an orthographic view of a given 3d model it has the advantage of being based on simple algebraic equations which are easy to solve and do not require time consuming numerical procedures

separators for sphere packings and nearest neighbor graphs a collection of n balls in d dimensions forms a k ply system if no point in the space is covered by more than k balls we show that for every k ply system there is a sphere s that intersects at most o k 1 d n 1 1 d balls of and divides the remainder of into two parts those in the interior and those in the exterior of the sphere s respectively so that the larger part contains at most 1 1 d 2 n balls this bound of o k 1 d n 1 1 d is the best possible in both n and k we also present a simple randomized algorithm to find such a sphere in o n time our result implies that every k nearest neighbor graphs of n points in d dimensions has a separator of size o k 1 d n 1 1 d in conjunction with a result of koebe that every triangulated planar graph is isomorphic to the intersection graph of a disk packing our result not only gives a new geometric proof of the planar separator theorem of lipton and tarjan but also generalizes it to higher dimensions the separator algorithm can be used for point location and geometric divide and conquer in a fixed dimensional space

3d object classification using multi object kohonen networks the problem of three dimensional planar faced opaque object recognition from one single perspective view is addressed in this paper a view parameterization based on hough transform is described classification is accomplished by multiple multi object kohonen networks a new object grouping criterion has been investigated to assign disjoint subsets of objects to each kohonen network of the system on the basis of input space topology recognition tests are presented on both synthetic and real world 3d objects even in the presence of partial occlusion

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

perceptual grouping by selection of a logically minimal model this paper presents a logic based approach to grouping and perceptual organization called minimal model theory and presents efficient methods for computing interpretations in this framework grouping interpretations are first defined as logical structures built out of atomic qualitative scene descriptors regularities that are derived from considerations of non accidentalness these interpretations can then be partially ordered by their degree of regularity or constraint measured numerically by their logical depth the genericity constraint the principle that interpretations should minimize coincidences in the observed configuration dictates that the preferred interpretation will be the minimum in this partial order i e the interpretation with maximum depth this maximum depth interpretation also called the minimal model or minimal interpretation is in a sense the simplest algebraically minimal interpretation available of the image configuration as a side effect the most salient or most structured part of the scene can be identified as the maximum depth subtree of the minimal model an efficient o n2 method for computing the minimal interpretation is presented along with examples computational experiments show that the algorithm performs well under a wide range of parameter settings

group membership reinforcement for straight edges based on bayesian networks a probabilistic approach to edge reinforcement is proposed that is based on bayesian networks of two dimensional 2 d fields of variables the proposed net is composed of three nodes each devoted to estimating a field of variables the first node contains available observations the second node is associated with a coupled random field representing the estimates of the actual values of observed data and of their discontinuities at the third node a field of variables is used to represent parameters describing the membership of a discontinuity into a group the edge reinforcement problem is stated in terms of minimization of local functionals each associated with a different node and made up of terms that can be computed locally it is shown that a distributed minimization is equivalent to the minimization of a global reinforcement criterion results concerning the reinforcement of straight lines in synthetic and real images are reported and applications to synthetic aperture radar sar images are described

mathematical analysis and numerical approximation of a general linearized poro hyperelastic model abstract we describe the behavior of a deformable porous material by means of a poro hyperelastic model that has been previously proposed in chapelle and moireau 2014 under general assumptions for mass and momentum balance and isothermal conditions for a two component mixture of fluid and solid phases in particular we address here a linearized version of the model based on the assumption of small displacements we consider the mathematical analysis and the numerical approximation of the problem more precisely we carry out firstly the well posedness analysis of the model then we propose a numerical discretization scheme based on finite differences in time and finite elements for the spatial approximation stability and numerical error estimates are proved particular attention is dedicated to the study of the saddle point structure of the problem that turns out to be interesting because velocities of the fluid phase and of the solid phase are combined into a single quasi incompressibility constraint our analysis provides guidelines to select the componentwise polynomial degree of approximation of fluid velocity solid displacement and pressure to obtain a stable and robust discretization based on taylor hood type finite element spaces interestingly we show how this choice depends on the porosity of the mixture i e the volume fraction of the fluid phase

a bayesian multiple hypothesis approach to edge grouping and contour segmentation a contour segmentation algorithm is presented that takes an edge map and extracts continuous curves of arbitrary smoothness correctly handling curve intersections and capable of extrapolating over significant measurement gaps the algorithm incorporates noise models of the edge detection process and limited scene statistics it is based on an explicit contour model and employs a statistical distance measure to quantify the likelihood of each segmentation hypothesis a bayesian multiple hypothesis tree organizes possible segementations making it possible to postpone grouping decisions until a sufficient amount of information is available we have demonstrated its performance on real and synthetic images

edge detection and linear feature extraction using a 2 d random field model the edge detection problem is posed as one of detecting step discontinuities in the observed correlated image using directional derivatives estimated with a random field model specifically the method consists of representing the pixels in a local window by a 2 d causal autoregressive ar model whose parameters are adaptively estimated using a recursive least squares algorithm the directional derivatives are functions of parameter estimates an edge is detected if the second derivative in the direction of the estimated maximum gradient is negatively sloped and the first directional derivative and a local estimate of variance satisfy some conditions because the ordered edge detector may not detect edges of all orientations well the image scanned in four different directions and the union of the four edge images is taken as the final output the performance of the edge detector is illustrated using synthetic and real images comparisons to other edge detectors are given a linear feature extractor that operates on the edges produced by the ar model is presented

parallel accelerated cyclic reduction preconditioner for three dimensional elliptic pdes with variable coefficients abstract we present a robust and scalable preconditioner for the solution of large scale linear systems that arise from the discretization of elliptic pdes amenable to rank compression the preconditioner is based on hierarchical low rank approximations and the cyclic reduction method the setup and application phases of the preconditioner achieve log linear complexity in memory footprint and number of operations and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment numerical experiments with linear systems that feature symmetry and nonsymmetry definiteness and indefiniteness constant and variable coefficients demonstrate the preconditioner applicability and robustness furthermore it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations and the tuning of the admissibility condition parameter together these parameters allow for optimization of the memory requirements and performance of the preconditioner

an efficient implementation of reid s multiple hypothesis tracking algorithm and its evaluation for the purpose of visual tracking an efficient implementation of reid s multiple hypothesis tracking mht algorithm is presented in which the k best hypotheses are determined in polynomial time using an algorithm due to murly 1968 the mht algorithm is then applied to several motion sequences the mht capabilities of track initiation termination and continuation are demonstrated together with the latter s capability to provide low level support of temporary occlusion of tracks between 50 and 150 corner features are simultaneously tracked in the image plane over a sequence of up to 51 frames each corner is tracked using a simple linear kalman filter and any data association uncertainty is resolved by the mht kalman filter parameter estimation is discussed and experimental results show that the algorithm is robust to errors in the motion model an investigation of the performance of the algorithm as a function of look ahead tree depth indicates that high accuracy can be obtained for tree depths as shallow as three experimental results suggest that a real time mht solution to the motion correspondence problem is possible for certain classes of scenes

robust and efficient detection of salient convex groups this paper describes an algorithm that robustly locates salient convex collections of line segments in an image the algorithm is guaranteed to find all convex sets of line segments in which the length of the gaps between segments is smaller than some fixed proportion of the total length of the lines this enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise we give an expected case analysis of the algorithm performance this demonstrates that salient convexity is unlikely to occur at random and hence is a strong clue that grouped line segments reflect underlying structure in the scene we also show that our algorithm run time is o n sup 2 log n nm when we wish to find the m most salient groups in an image with n line segments we support this analysis with experiments on real data and demonstrate the grouping system as part of a complete recognition system

feti dp bddc and block cholesky methods the feti dp and bddc algorithms are reformulated using block cholesky factorizations an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations instead of introducing lagrange multipliers to enforce the coarse level primal continuity constraints in these algorithms a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom with the new formulation of these algorithms a simplified proof is provided that the spectra of a pair of feti dp and bddc algorithms with the same set of primal constraints are essentially the same numerical experiments for a two dimensional laplace s equation also confirm this result copyright 2005 john wiley sons ltd

on the geometric interpretation of image contours abstract in this paper we suggest a computational model for the 3d interpretation of a 2d view based on contour classification and contour interpretation we concentrate on those contours arising from discontinuities in surface orientation we combine a generic surface description well suited for visual tasks with a model of the image formation process in order to derive image contour configurations that are likely to be interpreted in terms of surface contours next we describe a computer algorithm which attempts to interpret image contours on the following grounds first an image analysis process produces a description in terms of contours and relationships between them second among these contours we select those which form a desired configuration third the selected contours are combined with constraints available with the image formation process in order to be interpreted in terms of discontinuities in surface orientation as a consequence there is a dramatic reduction in the number of possible orientations of the associated scene surfaces

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

a fast direct solver for elliptic problems on general meshes in 2d we present a fast direct algorithm for solutions to linear systems arising from 2d elliptic equations we follow the approach in xia et al 2009 on combining the multifrontal method with hierarchical matrices we present a variant of that approach with additional hierarchical structure extend it to quasi uniform meshes and detail an adaptive decomposition procedure for general meshes linear time complexity is shown for a quasi regular grid and demonstrated via numerical results for the adaptive algorithm

stochastic differential equations and geometric flows in previous years curve evolution applied to a single contour or to the level sets of an image via partial differential equations has emerged as an important tool in image processing and computer vision curve evolution techniques have been utilized in problems such as image smoothing segmentation and shape analysis we give a local stochastic interpretation of the basic curve smoothing equation the so called geometric heat equation and show that this evolution amounts to a tangential diffusion movement of the particles along the contour moreover assuming that a priori information about the shapes of objects in an image is known we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise we also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features in contrast to the original geometric heat flow which tends to circularize any closed curve

potentials valleys and dynamic global coverings we present a new approach to effect the transition between local and global representations it is based on the notion of a covering or a collection of objects whose union is equivalent to the full one the mathematics of computing global coverings are developed in the context of curve detection where an intermediate representation the tangent field provides a reliable local description of curve structure this local information is put together globally in the form of a potential distribution the elements of the covering are then short curves each of which evolves in parallel to seek the valleys of the potential distribution the initial curve positions are also derived from the tangent field and their evolution is governed by variational principles when stationary configurations are achieved the global dynamic covering is defined by the union of the local dynamic curves

a fast block low rank dense solver with applications to finite element matrices this article presents a fast solver for the dense frontal matrices that arise from the multifrontal sparse elimination process of 3d elliptic pdes the solver relies on the fact that these matrices can be efficiently represented as a hierarchically off diagonal low rank hodlr matrix to construct the low rank approximation of the off diagonal blocks we propose a new pseudo skeleton scheme the boundary distance low rank approximation that picks rows and columns based on the location of their corresponding vertices in the sparse matrix graph we compare this new low rank approximation method to the adaptive cross approximation aca algorithm and show that it achieves better speedup specially for unstructured meshes using the hodlr direct solver as a preconditioner with a low tolerance to the gmres iterative scheme we can reach machine accuracy much faster than a conventional lu solver numerical benchmarks are provided for frontal matrices arising from 3d finite element problems corresponding to a wide range of applications

detection of curvilinear structures and reconstruction of their regions in gray scale images in this paper we present a new method for detecting curvilinear structures and reconstructing their regions in gray scale images the concept of skeleton extraction is introduced to detect more general structures such as tapering structures a candidate skeleton is extracted from the euclidean distance map that is constructed based on the edge map of an input image the extracted skeleton is usually noisy due to small protrusions and gaps existing on edge contours unnecessary skeletal points are e6ectively removed with a method combining previously proposed and our own methods then each skeletal point is classi7ed as one of three types ridge ravine o rstair and connected points of the same type are grouped to form a skeletal segment finally the reconstruction of curvilinear structure regions is performed based on the skeletal segment classi7cation result experimental results show that our detector contains many of the desirable properties required of a curvilinear structure detector furthermore since the range of widths that our detector can detect at one time is wide it is very useful for example when an input image includes curvilinear structures of various widths or tapering structures whose width varies greatly our algorithm for reconstructing curvilinear structure regions enables us to decompose an image into several types of regions the reconstruction result together with the skeleton extraction result is expected to be useful to make a simpli7ed scene description of an image 2002 pattern recognition society published by elsevier science ltd all rights reserved

new prospects in line detection by dynamic programming the detection of lines in satellite images has drawn a lot of attention within the last 15 years problems of resolution noise and image understanding are involved and one of the best methods developed so far is the f algorithm of fischler which achieves robustness rightness and rapidity like other methods of dynamic programming it consists of defining a cost which depends on local information then a summation minimization process in the image is performed the authors present herein a mathematical formalization of the f algorithm which allows them to extend the cost both to cliques of more than two points to deal with the contrast and to neighborhoods of size larger than one to take into account the curvature thus all the needed information contrast grey level curvature is synthesized in a unique cost function defined on the digital original image this cost is used to detect roads and valleys in satellite images spot

combining local filtering and multiscale analysis for edge ridge and curvilinear objects detection this paper presents a general method for detecting curvilinear structures like filaments or edges in noisy images this method relies on a novel technique the feature adapted beamlet transform fabt which is the main contribution of this paper it combines the well known beamlet transform bt introduced by donoho with local filtering techniques in order to improve both detection performance and accuracy of the bt moreover as the desired feature detector is chosen to belong to the class of steerable filters our transform requires only o n log n operations where n n 2 is the number of pixels besides providing a fast implementation of the fabt on discrete grids we present a statistically controlled method for curvilinear objects detection to extract significant objects we propose an algorithm in four steps 1 compute the fabt 2 normalize beamlet coefficients 3 select meaningful beamlets thanks to a fast energy based minimization and 4 link beamlets together in order to get a list of objects we present an evaluation on both synthetic and real data and demonstrate substantial improvements of our method over classical feature detectors

an adaptive contour closure algorithm and its experimental evaluation the potential of edge based complete image segmentation into regions has not gained the due attention in the literature thus far the present paper attempts to explore this potential by proposing an adaptive grouping algorithm to solve the contour closure problem that is the key to a successful edge based complete image segmentation the effectiveness of the proposed algorithm is extensively tested in the range image domain and compared to several region based segmentation methods within a rigorous comparison framework on three range image databases of varying quality acquired by different range scanners it is shown that the proposed approach is able to achieve very appealing performance with respect to both segmentation quality and computation time

an efficient and provably correct algorithm for the multiscale estimation of image contours by means of polygonal lines a large portion of image contours is characterized by local properties such as sharp variations of the image intensity across the contour the integration of local image descriptors estimated by using these local properties into curvilinear descriptors is a difficult problem from a theoretical viewpoint because of the combinatorially large number of possible curvilinear descriptors to deal with this difficulty the notion of compressible graphs is introduced and a contour data model is defined leading to an efficient linear time algorithm which provably recovers contours with an upper bound on the approximation error

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

structure and motion from straight line segments abstract a method to determine both the camera location and scene structure from image straight segment correspondences is presented the proposed method considers the finite segment length in order to use stronger constraints than do those that use the infinite line that supports the image segment the constraints between image segments involve a weak pairing between image segment midpoints this allows deviations of the midpoint only in the segment direction experimental results are presented of structure and motion computations from the image straight line segment matching using two real images

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

a gaussian mixture based image segmentation algorithm this paper focuses on the formulation development and evaluation of an autonomous segmentation algorithm which can segment targets in a wide class of highly degraded images a segmentation algorithm based on a gaussian mixture model of a two class image is selected because it has the potential for effective segmentation provided that the histogram of the image approximates a gaussian mixture and the parameters of the model can be estimated accurately a selective sampling approach based on the laplacian of the image is developed to transform the histogram of any image into an approximation of a gaussian mixture and a new estimation method which uses information derived from the tails of the mixture density is formulated to estimate the model parameters the resulting selective sampling gaussian mixture parameter estimation segmentation algorithm is tested and evaluated on a set of real degraded target images and the results show that the algorithm is able to accurately segment diverse images

a lagrange multiplier method for a stokes biot fluid poroelastic structure interaction model we study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium the free fluid is governed by the stokes equations while the flow in the poroelastic medium is modeled using the biot poroelasticity system equilibrium and kinematic conditions are imposed on the interface a mixed darcy formulation is employed resulting in continuity of flux condition of essential type a lagrange multiplier method is employed to impose weakly this condition a stability and error analysis is performed for the semi discrete continuous in time and the fully discrete formulations a series of numerical experiments is presented to confirm the theoretical convergence rates and to study the applicability of the method to modeling physical phenomena and the robustness of the model with respect to its parameters

circular shortest paths by branch and bound shortest path algorithms are used for a large variety of optimisation problems in network and transportation analysis they are also used in image analysis for object segmentation disparity estimation path finding and crack detection sometimes the topology of the problem demands that the path be circular such circular path constraints occur in polar object segmentation disparity estimation for panoramic stereo images and in shortest paths around a cylinder in this paper we present a new efficient algorithm for circular shortest path determination on a u by v trellis in o u 1 6 v average time we impose a binary search tree on the set of path endpoints and use a best first branch and bound search technique to efficiently obtain the global minimum circular path the typical running time of our circular shortest path algorithm on a 256 times 256 image is in the order of 0 1 seconds on a 1ghz dell p3 workstation under the linux operating system applications to crack detection and object segmentation are presented

a probabilistic spectral framework for grouping and segmentation this paper presents an iterative spectral framework for pairwise clustering and perceptual grouping our model is expressed in terms of two sets of parameters firstly there are cluster memberships which represent the affinity of objects to clusters secondly there is a matrix of link weights for pairs of tokens we adopt a model in which these two sets of variables are governed by a bernoulli model we show how the likelihood function resulting from this model may be maximised with respect to both the elements of link weight matrix and the cluster membership variables we establish the link between the maximisation of the log likelihood function and the eigenvectors of the link weight matrix this leads us to an algorithm in which we iteratively update the link weight matrix by repeatedly refining its modal structure each iteration of the algorithm is a three step process first we compute a link weight matrix for each cluster by taking the outer product of the vectors of current cluster membership indicators for that cluster second we extract the leading eigenvector from each modal link weight matrix third we compute a revised link weight matrix by taking the sum of the outer products of the leading eigenvectors of the modal link weight matrices

contour grouping based on contour skeleton duality in this paper we present a method for grouping relevant object contours in edge maps by taking advantage of contour skeleton duality regularizing contours and skeletons simultaneously allows us to combine both low level perceptual constraints as well as higher level model constraints in a very effective way the models are represented using paths in symmetry sets skeletons are treated as trajectories of an imaginary virtual robot in a discrete space of symmetric points obtained from pairs of edge segments boundaries are then defined as the maps obtained by grouping the associated pairs of edge segments along the trajectories casting the grouping problem in this manner makes it similar to the problem of simultaneous localization and mapping slam hence we adapt the state of the art probabilistic framework namely rao blackwellized particle filtering that has been successfully applied to slam we use the framework to maximize the joint posterior over skeletons and contours

coarse to fine dynamic programming we introduce an extension of dynamic programming we call coarse to fine dynamic programming cfdp ideally suited to dp problems with large state space cfdp uses dynamic programming to solve a sequence of coarse approximations which are lower bounds to the original dp problem these approximations are developed by merging states in the original graph into superstates in a coarser graph which uses an optimistic arc cost between superstates the approximations are designed so that cfdp terminates when the optimal path through the original state graph has been found cfdp leads to significant decreases in the amount of computation necessary to solve many dp problems and can in some instances make otherwise infeasible computations possible cfdp generalizes to dp problems with continuous state space and we offer a convergence result for this extension we demonstrate applications of this technique to optimization of functions and boundary estimation in mine recognition

a method for shift rotation and scale invariant pattern recognition using the form and arrangement of pattern specific features abstract a new computer based method for visual pattern recognition is described the process extracts shape features from binary edge images represented in either real valued or discrete coordinates both separate and overlapping features are extracted maximizing their completeness and continuity without using templates or mathematical feature descriptions these features and their arrangement are encoded in a shift rotation and scale invariant manner and used to recognize incoming patterns from a set of previously encoded patterns stored in memory new patterns may be automatically classified and stored in memory allowing the system to learn and generalize without operator intervention testing shows the system to be completely shift rotation and scale invariant and insensitive to local image distortion

a contour based recovery of image flow iterative transformation method the authors present an iterative algorithm for the recovery of 2 d motion i e for the determination of a transformation that maps one image onto another the local ambiguity in measuring the motion of contour segments the aperture problem implies a reliance on measurements along the normal direction since the measured normal flow does not agree with the actual normal flow the full flow recovered from this erroneous flow also possesses substantial error and any attempt to recover the 3 d motion from such full flow fails the proposed method is based on the observation that a polynomial approximation of the image flow provides sufficient information for 3 d motion computation the use of an explicit flow model results in improved normal flow estimates through an iterative process the authors discuss the adequacy and the convergence of the algorithm the algorithm was tested on some synthetic and some simple natural time varying images the image flow recovered from this scheme is sufficiently accurate to be useful in 3 d structure and motion computation

the regular polygon detector this paper describes a robust regular polygon detector given image edges we derive the a posteriori probability for a mixture of regular polygons and thus the probability density function for the appearance of a set of regular polygons likely regular polygons can be isolated quickly by discretising and collapsing the search space into three dimensions we derive a complete formulation for efficiently recovering the remaining dimensions using maximum likelihood at the locations of the most likely polygons results show robustness to noise the ability to find and differentiate different shape types and to perform real time sign detection for driver assistance

generalized inf sup conditions for chebyshev spectral approximation of the stokes problem a mixed problem and its approximation in an abstract framework are considered they are proved to be well posed if and only if several inf sup conditions are satisfied these results are applied to the stokes equations in a square formulated in chebyshev weighted sobolev spaces and their approximations two kinds of spectral discretizations are analyzed a galerkin method and a collocation method at the chebyshev nodes

edge expression based on tree structure abstract it is a difficult problem to construct the edge structure of an object from its defective line drawing after the low level image processing phase a tree structure edge expression is proposed in which the tree expresses the contiguous line segments and all the trees constitute a forest for the object some medium level processing algorithms such as line connecting pruning and appending are derived by using the tree structure experiments are conducted which show the advantages of the expression and corresponding algorithms

fast 3d frequency domain full waveform inversion with a parallel block low rank multifrontal direct solver application to obc data from the north sea wide azimuth long offset obc obn surveys provide a suitable framework to perform computationally efficient frequency domain full waveform inversion fwi with a few discrete frequencies frequency domain seismic modeling is performed efficiently with moderate computational resources for a large number of sources with a sparse multifrontal direct solver gauss elimination techniques for sparse matrices approximate solutions of the time harmonic wave equation are computed using a block low rank blr approximation leading to a significant reduction in the operation count and in the volume of communication during the lu factorization as well as offering a great potential for reduction in the memory demand moreover the sparsity of the seismic source vectors is exploited to speed up the forward elimination step during the computation of the monochromatic wavefields the relevance and the computational efficiency of the frequency domain fwi performed in the visco acoustic vti approximation is shown with a real 3d obc case study from the north sea the fwi subsurface models show a dramatic resolution improvement relative to the initial model built by reflection traveltime tomography the amplitude errors introduced in the modeled wavefields by the blr approximation for different low rank thresholds have a negligible footprint in the fwi results with respect to a standard multifrontal sparse direct factorization and without compromise on the accuracy of the imaging the blr approximation can bring a reduction of the lu factor size by a factor up to three this reduction is not yet exploited to reduce the effective memory usage ongoing work the flop reduction can be larger than a factor of 10 and can bring a factor of time reduction of around three moreover this reduction factor tends to increase with frequency namely with the matrix size frequency domain visco acoustic vti fwi can be viewed as an efficient tool to build an initial model for elastic fwi of 4 c obc data

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area