high resolution schemes for conservation laws with locally varying time steps we develop upwind methods which use limited high resolution corrections in the spatial discretization and local time stepping for forward euler and second order time discretizations l infty stability is proven for both time stepping schemes for problems in one space dimension these methods are restricted by a local cfl condition rather than the traditional global cfl condition allowing local time refinement to be coupled with local spatial refinement numerical evidence demonstrates the stability and accuracy of the methods for problems in both one and two space dimensions

an explicit multi time stepping algorithm for aerodynamic flows an explicit multi time stepping algorithm with applications to aerodynamic flows is presented in the algorithm in different parts of the computational domain different time steps are taken and the flow is synchronized at the so called synchronization levels the algorithm is validated for aerodynamic turbulent flows for two dimensional flows speedups in the order of five with respect to single time stepping are obtained

oscillatory integrals with quadratic phase function on a real abstract wiener space abstract stochastic oscillatory integrals with quadratic phase function are studied in the case where amplitude functions are multiple wiener integrals we show that a principle of stationary phase holds when kernels of multiple wiener integrals are of trace class on the way we establish a new criterion for a wiener functional to be analytic

analysis of wiener functionals malliavin calculus and its applications to heat kernels on donne un expose facilement accessible du calcul de malliavin du calcul differentiel de dimension infinie sur l espace de wiener

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

temporal adaptive euler navier stokes algorithm involving unstructured dynamic meshes a temporal adaptive algorithm for the time integration of the two dimensional euler or navier stokes equations is presented the flow solver involves an upwind flux split spatial discretization for the convective terms and central differencing for the shear stress and heat flux terms on an unstructured mesh of triangles the temporal adaptive algorithm is a time accurate integration procedure that allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step

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

a posteriori error estimation for discontinuous galerkin solutions of hyperbolic problems abstract we analyze the spatial discretization errors associated with solutions of one dimensional hyperbolic conservation laws by discontinuous galerkin methods dgms in space we show that the leading term of the spatial discretization error with piecewise polynomial approximations of degree p is proportional to a radau polynomial of degree p 1 on each element we also prove that the local and global discretization errors are o x2 p 1 and o x2p 1 at the downwind point of each element this strong superconvergence enables us to show that local and global discretization errors converge as o xp 2 at the remaining roots of radau polynomial of degree p 1 on each element convergence of local and global discretization errors to the radau polynomial of degree p 1 also holds for smooth solutions as p these results are used to construct asymptotically correct a posteriori estimates of spatial discretization errors that are effective for linear and nonlinear conservation laws in regions where solutions are smooth

enhanced accuracy by post processing for finite element methods for hyperbolic equations we consider the enhancement of accuracy by means of a simple post processing technique for finite element approximations to transient hyperbolic equations the post processing is a convolution with a kernel whose support has measure of order one in the case of arbitrary unstructured meshes if the mesh is locally translation invariant the support of the kernel is a cube whose edges are of size of the order of x only for example when polynomials of degree k are used in the discontinuous galerkin dg method and the exact solution is globally smooth the dg method is of order k 1 2 in the l2 norm whereas the post processed approximation is of order 2k 1 if the exact solution is in l2 only in which case no order of convergence is available for the dg method the post processed approximation converges with order k 1 2 in l2 0 where 0 is a subdomain over which the exact solution is smooth numerical results displaying the sharpness of the estimates are presented

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

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

on the exponential decay of oscillatory integrals on an abstract wiener space abstract let x h be a real abstract wiener space the saddle point method is carried out on x and an exact formula for deformation of contour integration that is a formula transferring a fourier type integral to a fourier laplace one will be concluded as an application an exponentially fast decay of stochastic oscillatory integrals on x is studied

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

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

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

an efficient local time stepping scheme for solution of nonlinear conservation laws we develop an efficient local time stepping algorithm for the method of lines approach to numerical solution of transient partial differential equations the need for local time stepping arises when adaptive mesh refinement results in a mesh containing cells of greatly different sizes the global cfl number and hence the global time step are defined by the smallest cell size this can be inefficient as a few small cells may impose a restrictive time step on the whole mesh a local time stepping scheme allows us to use the local cfl number which reduces the total number of function evaluations the algorithm is based on a second order runge kutta time integration its important features are a small stencil and the second order accuracy in the l 2 and l norms

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

a time accurate explicit multi scale technique for gas dynamics abstract we present a new time accurate algorithm for the explicit numerical integration of the compressible euler equations of gas dynamics this technique is based on the discrete event simulation des methodology for nonlinear flux conservative pdes y a omelchenko h karimabadi self adaptive time integration of flux conservative equations with sources j comput phys 216 1 2006 179 194 des enables adaptive distribution of cpu resources in accordance with local time scales of the underlying numerical solution it distinctly stands apart from multiple local time stepping algorithms in that it requires neither selecting a global synchronization time step nor pre determining a sequence of time integration operations for individual parts of a heterogeneous numerical system in this paper we extend the des methodology in three important directions i we apply des to a system of coupled gas dynamics equations discretized via a central upwind scheme a kurganov e tadmor new high resolution central schemes for nonlinear conservation laws and convection diffusion equations j comput phys 160 2000 241 282 a kurganov s noelle g petrova semidiscrete central upwind schemes for hyperbolic conservation laws and hamilton jacobi equations siam j sci comput 23 3 2001 707 740 ii we introduce a new preemptive event processing pep technique which automatically enforces synchronous execution of events with sufficiently close update times iii we significantly improve the accuracy of the previous algorithm y a omelchenko h karimabadi self adaptive time integration of flux conservative equations with sources j comput phys 216 1 2006 179 194 by applying locally second order in time flux conserving corrections to the solution obtained with the forward euler scheme the performance of the new technique is demonstrated in a series of one dimensional gas dynamics test problems by comparing numerical solutions obtained in event driven and equivalent time stepping simulations

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

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

runge kutta based explicit local time stepping methods for wave propagation locally refined meshes severely impede the efficiency of explicit runge kutta rk methods for the simulation of time dependent wave phenomena by taking smaller time steps precisely where the smallest elements are located local time stepping lts methods overcome the bottleneck caused by the stringent stability constraint of but a few small elements in the mesh starting from classical or low storage explicit rk methods explicit lts methods of arbitrarily high accuracy are derived when combined with an essentially diagonal finite element mass matrix the resulting time marching schemes retain the high accuracy stability and efficiency of the original rk methods while circumventing the geometry induced stiffness numerical experiments with continuous and discontinuous galerkin finite element discretizations corroborate the expected rates of convergence and illustrate the usefulness of these lts rk methods

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

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

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

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

finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions abstract we give an approach to the theory of oscillatory integrals in infinite dimensions starting from finite dimensional oscillatory integrals we also provide detailed asymptotic expansions by a method of stationary phase in infinite dimensions with convergence and estimates for the remainder provided by a strong control on finite dimensional approximations

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

hp version discontinuous galerkin methods for hyperbolic conservation laws a parallel adaptive strategy this paper describes a parallel algorithm based on discontinuous hp finite element approximations of linear scalar hyperbolic conservation laws the paper focuses on the development of an effective parallel adaptive strategy for such problems numerical experiments suggest that these techniques are highly parallelizable and exponentially convergent thereby yielding efficiency many times superior to conventional schemes for hyperbolic problems

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

fourth order energy preserving locally implicit time discretization for linear wave equations a family of fourth order coupled implicit explicit time schemes is presented as a special case of fourth order coupled implicit schemes for linear wave equations the domain of interest is decomposed into several regions where different fourth order time discretization are used chosen among a family of implicit or explicit fourth order schemes the coupling is based on a lagrangian formulation on the boundaries between the several non conforming meshes of the regions a global discrete energy is shown to be preserved and leads to global fourth order consistency in time numerical results in 1d and 2d for the acoustic and elastodynamics equations illustrate the good behavior of the schemes and their potential for the simulation of realistic highly heterogeneous media or strongly refined geometries for which using everywhere an explicit scheme can be extremely penalizing accuracy up to fourth order reduces the numerical dispersion inherent to implicit methods used with a large time step and makes this family of schemes attractive compared to second order accurate methods

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

numerical approximations to nonlinear conservation laws with locally varying time and space grids an explicit time differencing technique is introduced to approximate nonlinear conservation laws this differencing technique links together an arbitrary number of space regimes containing fine and coarse time increments previous stability requirements i e the cfl condition placed a global bound on the size of the time increments for scalar monotone approximations in one space dimension using this variable step time differencing convergence to the correct physical solution is proven given only a local cfl condition

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

implicit runge kutta methods and discontinuous galerkin discretizations for linear maxwell s equations in this paper we consider implicit runge kutta methods for the time integration of linear maxwell s equations we first present error bounds for the abstract cauchy problem which respect the unboundedness of the differential operators using energy techniques the error bounds hold for algebraically stable and coercive methods such as gauss and radau collocation methods the results for the abstract evolution equation are then combined with a discontinuous galerkin discretization in space using upwind fluxes for the case that permeability and permittivity are piecewise constant functions we show error bounds for the full discretization where the constants do not deteriorate if the spatial mesh width tends to zero

application of implicit explicit high order runge kutta methods to discontinuous galerkin schemes despite the popularity of high order explicit runge kutta erk methods for integrating semi discrete systems of equations erk methods suffer from severe stability based time step restrictions for very stiff problems we implement a discontinuous galerkin finite element method dgfem along with recently introduced high order implicit explicit runge kutta imex rk schemes to overcome geometry induced stiffness in fluid flow problems the imex algorithms solve the non stiff portions of the domain using explicit methods and isolate and solve the more expensive stiff portions using an l stable stiffly accurate explicit singly diagonally implicit runge kutta method esdirk furthermore we apply adaptive time step controllers based on the embedded temporal error predictors we demonstrate in a number of numerical test problems that imex methods in conjunction with efficient preconditioning become more efficient than explicit methods for systems exhibiting high levels of grid induced stiffness

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

hp version discontinuous galerkin methods for hyperbolic conservation laws abstract the development of hp version discontinuous galerkin methods for hyperbolic conservation laws is presented in this work a priori error estimates are derived for a model class of linear hyperbolic conservation laws these estimates are obtained using a new mesh dependent norm that reflects the dependence of the approximate solution on the local element size and the local order of approximation the results generalize and extend previous results on mesh dependent norms to hp version discontinuous galerkin methods a posteriori error estimates which provide bounds on the actual error are also developed in this work numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution

analytic functions cauchy formula and stationary phase on a real abstract wiener space abstract a new complexification of a real abstract wiener space will be introduced and some analogs of the algebra of analytic functions on finite dimensional euclidean space will be considered analytic functions on the original space their holomorphic prolongation to the complexified space and holomorphic functions and a cauchy formula on the complexified space the cauchy formula is a key tool to study probabilistic quantities via deformation of the contour integration namely it will be applied to establish i an explicit representation of stochastic oscillatory integrals with quadratic phase function and ii a stationary phase estimation of the integrals further the later estimation is applicable to study gevrey type smoothness of density functions an integration by parts formula on a totally real submanifold in the complexified space is also studied

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