numerical assessment of time domain methods for the estimation of local arterial pulse wave speed a local estimation of pulse wave speed c an important predictor of cardiovascular events can be obtained at arterial locations where simultaneous measurements of blood pressure p and velocity u arterial diameter d and u flow rate q and cross sectional area a or p and d are available using the pu loop sum of squares 2 lndu loop qa loop or new d2p loop methods here these methods were applied to estimate c from numerically generated p u d q and a waveforms using a visco elastic one dimensional model of the 55 larger human systemic arteries in normal conditions theoretical c were calculated from the parameters of the model estimates of c given by the loop methods were closer to theoretical values and more uniform within each arterial segment than those obtained using the 2 the smaller differences between estimates and theoretical values were obtained using the d2p loop method with root mean square errors rmse smaller than 0 18ms 1 followed by averaging the two c given by the pu and lndu loops rmse 2 99ms 1 in general the errors of the pu lndu and qa loops decreased at locations where visco elastic effects were small and nearby junctions were well matched for forward travelling waves the 2 performed better at proximal locations

parametric surface diffeomorphometry for low dimensional embeddings of dense segmentations and imagery in the field of computational anatomy biological form including our focus neuroanatomy is studied quantitatively through the action of the diffeomorphism group on example anatomies a technique called diffeomorphometry here we design an algorithm within this framework to pass from dense objects common in neuromaging studies binary segmentations structural images to a sparse representation defined on the surface boundaries of anatomical structures and embedded into the low dimensional coordinates of a parametric model our main new contribution is to introduce an expanded group action to simultaneously deform surfaces through direct mapping of points as well as images through functional composition with the inverse this allows us to index the diffeomorphisms with respect to two dimensional surface geometries like subcortical gray matter structures but explicitly map onto cost functions determined by noisy 3 dimensional measurements we consider models generated from empirical covariance of training data as well as bandlimited laplace beltrami eigenfunction models when no such data is available we show applications to noisy or anomalous segmentations and other typical problems in neuroimaging studies we reproduce statistical results detecting changes in alzheimer s disease despite dimensionality reduction lastly we apply our algorithm to the common problem of segmenting subcortical structures from t1 mr images

self repelling snakes for topology preserving segmentation models the implicit framework of the level set method has several advantages when tracking propagating fronts indeed the evolving contour is embedded in a higher dimensional level set function and its evolution can be phrased in terms of a eulerian formulation the ability of this intrinsic method to handle topological changes merging and breaking makes it useful in a wide range of applications fluid mechanics computer vision and particularly in image segmentation the main subject of this paper nevertheless in some applications this topological flexibility turns out to be undesirable for instance when the shape to be detected has a known topology or when the resulting shape must be homeomorphic to the initial one the necessity of designing topology preserving processes arises in medical imaging for example in the human cortex reconstruction it is known that the human cortex has a spherical topology so throughout the reconstruction process this topological feature must be preserved therefore we propose in this paper a segmentation model based on an implicit level set formulation and on the geodesic active contours in which a topological constraint is enforced

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

a moving grid framework for geometric deformable models geometric deformable models based on the level set method have become very popular in the last decade to overcome an inherent limitation in accuracy while maintaining computational efficiency adaptive grid techniques using local grid refinement have been developed for use with these models this strategy however requires a very complex data structure yields large numbers of contour points and is inconsistent with the implementation of topology preserving geometric deformable models tgdms in this paper we investigate the use of an alternative adaptive grid technique called the moving grid method with geometric deformable models in addition to the development of a consistent moving grid geometric deformable model framework our main contributions include the introduction of a new grid nondegeneracy constraint the design of a new grid adaptation criterion and the development of novel numerical methods and an efficient implementation scheme the overall method is simpler to implement than using grid refinement requiring no large complex hierarchical data structures it also offers an extra benefit of automatically reducing the number of contour vertices in the final results after presenting the algorithm we demonstrate its performance using both simulated and real images

a new scheme for robust gradient vector estimation in color images gradient estimators are mostly designed to yield accurate and robust estimates of the gradient magnitude not the gradient direction this paper proposes a method for the accurate and robust estimation of both the gradient magnitude and direction it robustly estimates the gradient in the x and y directions the robustness against noise is achieved by prefiltering and postfiltering of the gradient in each direction to reduce edge blurring effects introduced by these filters the gradient in a certain direction is obtained by applying the prefilter and postfilter in the perpendicular direction the basic elements employed in each window are highpass lowpass and aggregation operators the highpass operator is used as a gradient estimator the lowpass operator is for prefiltering and postfiltering and the aggregation operator is for aggregating the prefiltered and postfiltered gradients four different combinations of highpass lowpass and aggregation operators are proposed mvd median mean mvd median max rcmg median mean and rcmg median max experimental results show that the rcmg median mean has the best performance in estimating the gradient and detecting the edges in noisy color images it is computationally more efficient than the state of the art gradient estimators and is able to accurately estimate the gradient direction as well as the gradient magnitude computer simulation results show that the proposed method outperforms other recently proposed color gradient estimators and edge detectors

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

a multiscale edge detection algorithm based on wavelet domain vector hidden markov tree model abstract the wavelet analysis is an efficient tool for the detection of image edges based on the wavelet analysis we present an unsupervised learning algorithm to detect image edges in this paper a wavelet domain vector hidden markov tree wd vhmt is employed in our algorithm to model the statistical properties of multiscale and multidirectional subband wavelet coefficients of an image with this model each wavelet coefficient is viewed as an observation of its hidden state and the hidden state indicates if the wavelet coefficient belongs to an edge the wd vhmt model can be learned by an expectation maximization algorithm after the model is learned we employ an extended viterbi algorithm to uncover the hidden state sequences according to the maximum a posterior estimation the experiment results of the edge detection for several images are provided to evaluate our algorithm

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

on affine plane curve evolution abstract an affine invariant curve evolution process is presented in this work the evolution studied is the affine analogue of the euclidean curve shortening flow evolution equations for both affine and euclidean invariants are developed an affine version of the classical euclidean isoperimetric inequality is proved this inequality is used to show that in the case of affine evolution of convex plane curves the affine isoperimetric ratio is a non decreasing function of time convergence of this affine isoperimetric ratio to the ellipse s value 8 2 as well as convergence in the hausdorff metric of the evolving curve to an ellipse is also proved

an iterative procedure with interface relaxation for domain decomposition methods a domain decomposition method for second order elliptic problems is considered an iterative procedure that reduces the problem to a sequence of mixed boundary value problems on each subdomain is proposed at each iteration a relaxation is accomplished at the subdomain interfaces in several circumstances a value of the relaxation parameter that yields exact convergence in a finite number of iterations is explicitly found moreover when such a value is not available an appropriate strategy for the automatic selection of the relaxation parameter at each iteration is indicated and analyzed this iterative method is then applied to the spectral collocation approximation of the differential problem the same kind of convergence results are proven many numerical experiments show the effectiveness of the method proposed here

noise robust edge detector combining isotropic and anisotropic gaussian kernels a new noise robust edge detector is proposed which combines a small scaled isotropic gaussian kernel and large scaled anisotropic gaussian kernels angks to obtain edge maps of images its main advantage is that noise reduction is attained while maintaining high edge resolution from the angks anisotropic directional derivatives andds are derived to capture the locally directional variation of an image the andd based edge strength map esm is constructed its noise robustness is determined by the scale alone and its edge resolution by the ratio of the scale to the anisotropic factor moreover the edge stretch effect in anisotropic smoothing is revealed the andd based esm and the gradient based esm with a small scaled isotropic gaussian kernel are fused into a noise robust esm with high edge resolution and little edge stretch embedding the fused esm into the routine of canny detector a noise robust edge detector is developed which includes two additional modifications contrast equalization and noise dependent lower threshold the aggregate test receiver operating characteristic roc curves and the pratt s figure of merit fom are used to evaluate the proposed detector by abundant experiments the experimental results show that the proposed detector can obtain high quality edge maps for noise free and noisy images

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

variational denoising of partly textured images by spatially varying constraints denoising algorithms based on gradient dependent regularizers such as nonlinear diffusion processes and total variation denoising modify images towards piecewise constant functions although edge sharpness and location is well preserved important information encoded in image features like textures or certain details is often compromised in the process of denoising we propose a mechanism that better preserves fine scale features in such denoising processes a basic pyramidal structure texture decomposition of images is presented and analyzed a first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures a variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions our results show visual improvement as well as an increase in the signal to noise ratio over scalar fidelity term processes this type of processing can be used for a variety of tasks in partial differential equation based image processing and computer vision and is stable and meaningful from a mathematical viewpoint

parallel algorithms with local fourier basis abstract we present a nonoverlapping domain decomposition method with local fourier basis applied to a model problem in liquid flames the introduction of domain decomposition techniques in this paper is for numerical and parallel efficiency purposes when one requires a large number of grid points to catch complex structures we obtain then a high order accurate domain decomposition method that allows us to generalize our previous work on the use of local fourier basis to solve combustion problems with nonperiodic boundary conditions m garbey and d tromeur dervout j comput phys 145 316 1998 local fourier basis methodology fully uses the superposition principle to split the searched solution in a numerically computed part and an analytically computed part our present methodology generalizes the israeli et al 1993 j sci comput 8 135 method which applies domain decomposition with local fourier basis to the helmholtz s problem in the present work several new difficulties occur first the problem is unsteady and nonlinear which makes the periodic extension delicate to construct in terms of stability and accuracy second we use a streamfunction biharmonic formulation of the incompressible navier stokes equation in two space dimensions the application of domain decomposition with local fourier basis to a fourth order operator is more difficult to achieve than for a second order operator a systematic investigation of the influence of the method s parameters on the accuracy is done a detail parallel mimd implementation is given we give an a priori estimate that allows the relaxation of the communication between processors for the interface problem treatment results on nonquasi planar complex frontal polymerization illustrate the capability of the method

a morphological gradient approach to color edge detection a new color edge detector based on vector differences is proposed the basic technique gives as its output the maximum distance between the vectors within a mask when applied to scalar valued images the method reduces to the classic morphological gradient the technique is relatively computationally efficient and can also be readily applied to other vector valued images to improve the performance in the presence of noise a novel pairwise outlier rejection scheme is employed a quantitative evaluation using pratt s figure of merit shows the new technique to outperform other recently proposed color edge detectors in addition application to real images demonstrates the approach to be highly effective despite its low complexity

edge guided image gap interpolation using multi scale transformation this paper presents improvements in image gap restoration through the incorporation of edge based directional interpolation within multi scale pyramid transforms two types of image edges are reconstructed 1 the local edges or textures inferred from the gradients of the neighboring pixels and 2 the global edges between image objects or segments inferred using a canny detector through a process of pyramid transformation and downsampling the image is progressively transformed into a series of reduced size layers until at the pyramid apex the gap size is one sample at each layer an edge skeleton image is extracted for edge guided interpolation the process is then reversed from the apex at each layer the missing samples are estimated an iterative method is used in the last stage of upsampling up sampled and combined with the available samples of the next layer discrete cosine transform and a family of discrete wavelet transforms are utilized as alternatives for pyramid construction evaluations over a range of images in regular and random loss pattern at loss rates of up to 40 demonstrate that the proposed method improves peak signal to noise ratio by 1 5 db compared with a range of best published works

corner detection and classification using anisotropic directional derivative representations this paper proposes a corner detector and classifier using anisotropic directional derivative andd representations the andd representation at a pixel is a function of the oriented angle and characterizes the local directional grayscale variation around the pixel the proposed corner detector fuses the ideas of the contour and intensity based detection it consists of three cascaded blocks first the edge map of an image is obtained by the canny detector and from which contours are extracted and patched next the andd representation at each pixel on contours is calculated and normalized by its maximal magnitude the area surrounded by the normalized andd representation forms a new corner measure finally the nonmaximum suppression and thresholding are operated on each contour to find corners in terms of the corner measure moreover a corner classifier based on the peak number of the andd representation is given experiments are made to evaluate the proposed detector and classifier the proposed detector is competitive with the two recent state of the art corner detectors the he yung detector and cpda detector in detection capability and attains higher repeatability under affine transforms the proposed classifier can discriminate effectively simple corners y type corners and higher order corners

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

a parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension a parallel fast direct solution method for linear systems with separable block tridiagonal matrices is considered such systems appear for example when discretizing the poisson equation in a rectangular domain using the five point finite difference scheme or the piecewise linear finite elements on a triangulated possibly nonuniform rectangular mesh the method under consideration has the arithmetical complexity mathcal o n log n and it is closely related to the cyclic reduction method but instead of using the matrix polynomial factorization the so called partial solution technique is employed hence in this paper the method is called the partial solution variant of the cyclic reduction method pscr method the method is presented and analyzed in a general radix q framework and based on this analysis the radix 4 variant is chosen for parallel implementation using the mpi standard the generalization of the method to the case of arbitrary block dimension is described the numerical experiments show the sequential efficiency and numerical stability of the pscr method compared to the well known blktri implementation of the generalized cyclic reduction method the good scalability properties of the parallel pscr method are demonstrated in a distributed memory cray t3e 750 computer

pulse wave propagation in a model human arterial network assessment of 1 d visco elastic simulations against in vitro measurements a numerical model based on the nonlinear one dimensional 1 d equations of pressure and flow wave propagation in conduit arteries is tested against a well defined experimental 1 1 replica of the human arterial tree the tree consists of 37 silicone branches representing the largest central systemic arteries in the human including the aorta carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs the set up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow terminal branches end in simple resistance models consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure the parameters required by the numerical algorithm are directly measured in the in vitro set up and no data fitting is involved comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1 d time domain formulation to capture the main features of pulse wave propagation measured throughout the system test as a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation the experimental set up generates waveforms at terminal branches with additional non physiological oscillations the frequencies of these oscillations are well captured by the 1 d model even though amplitudes are overestimated adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect suggesting that wall visco elasticity might play an important role in the experimental results nevertheless average relative root mean square errors between simulations and experimental waveforms are smaller than 4 for pressure and 19 for the flow at all 70 locations studied

global regularizing flows with topology preservation for active contours and polygons active contour and active polygon models have been used widely for image segmentation in some applications the topology of the object s to be detected from an image is known a priori despite a complex unknown geometry and it is important that the active contour or polygon maintain the desired topology in this work we construct a novel geometric flow that can be added to image based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon we emphasize that unlike other methods for topology preservation the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change the flow also serves as a global regularity term for the evolving contour and has smoothness properties similar to curvature flow these properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes the proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles the evolution of a single point on the contour depends on all other points of the contour which is different from traditional curve evolutions in the computer vision literature

weighted level set evolution based on local edge features for medical image segmentation level set methods have been widely used to implement active contours for image segmentation applications due to their good boundary detection accuracy in the context of medical image segmentation weak edges and inhomogeneities remain important issues that may hinder the accuracy of any segmentation method based on active contours implemented using level set methods this paper proposes a method based on active contours implemented using level set methods for segmentation of such medical images the proposed method uses a level set evolution that is based on the minimization of an objective energy functional whose energy terms are weighted according to their relative importance in detecting boundaries this relative importance is computed based on local edge features collected from the adjacent region located inside and outside of the evolving contour the local edge features employed are the edge intensity and the degree of alignment between the image s gradient vector flow field and the evolving contour s normal we evaluate the proposed method for segmentation of various regions in real mri and ct slices x ray images and ultra sound images evaluation results confirm the advantage of weighting energy forces using local edge features to reduce leakage these results also show that the proposed method leads to more accurate boundary detection results than the state of the art edge based level set segmentation methods particularly around weak edges

a topology preserving level set method for shape optimization the classical level set method which represents the boundary of the unknown geometry as the zero level set of a function has been shown to be very effective in solving shape optimization problems the present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints we propose a logarithmic barrier penalty which acts to enforce the constraints leading to an approximate solution to shape design problems

directional filtering in edge detection two dimensional 2 d edge detection can be performed by applying a suitably selected optimal edge half filter in n directions computationally such a two dimensional n directional filter can be represented by a pair of real masks that is by one complex number matrix regardless of the number of filtering directions n specific calculations of the edge strength were conducted using a 2 d tridirectional filter based on a petrou kittler 1991 one dimensional 1 d detector optimized for the ramp edges which are characteristic of posterior eye capsule images that were used here as a test set in applications to image segmentation tridirectional filtering results in co occurrence arrays of low dimensionality

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

experimental evaluation of local wave speed in the presence of reflected waves wave speed also called pulse wave velocity is the speed by which disturbance travels along the medium and it depends on the mechanical and geometrical properties of the vessel and on the density of the blood wave speed is a parameter of clinical relevance because it is an indicator of arterial stiffness and cardiovascular diseases the aim of this work is to compare different methods for the determination of local wave speed in bench experiments and investigate their relative accuracy when reflections are present pressure p flow q and diameter d were measured along a flexible tube far and close to three positive and three negative reflection sites wave speed was calculated using pu loop lnd u loop qaloop d 2 p loop sum of squares and characteristic impedance methods results were compared to the foot to foot method we found that far from the reflections almost all methods give uniform results close to positive reflections the methods that rely on p and q or u overestimate the wave speed value while techniques based on d or a and q or u underestimate it on the contrary close to negative reflections the methods that rely on p and q or u underestimate the wave speed value while techniques based on d or a and q or u overestimate it the d 2 p loop does not seem to be affected by positive or negative

enhanced patterns of oriented edge magnitudes for face recognition and image matching a good feature descriptor is desired to be discriminative robust and computationally inexpensive in both terms of time and storage requirement in the domain of face recognition these properties allow the system to quickly deliver high recognition results to the end user motivated by the recent feature descriptor called patterns of oriented edge magnitudes poem which balances the three concerns this paper aims at enhancing its performance with respect to all these criteria to this end we first optimize the parameters of poem and then apply the whitened principal component analysis dimensionality reduction technique to get a more compact robust and discriminative descriptor for face recognition the efficiency of our algorithm is proved by strong results obtained on both constrained face recognition technology feret and unconstrained labeled faces in the wild lfw data sets in addition with the low complexity impressively our algorithm is about 30 times faster than those based on gabor filters furthermore by proposing an additional technique that makes our descriptor robust to rotation we validate its efficiency for the task of image matching

a short time existence uniqueness result for a nonlocal topology preserving segmentation model motivated by a prior applied work of vese and the second author dedicated to segmentation under topological constraints we derive a slightly modified model phrased as a functional minimization problem and propose to study it from a theoretical viewpoint the mathematical model leads to a second order nonlinear pde with a singularity at nabla u 0 and containing a nonlocal term a suitable setting is thus the one of the viscosity solution theory and in this framework we establish a short time existence uniqueness result as well as a lipschitz regularity result for the solution

geodesic active contours and level sets for the detection and tracking of moving objects this paper presents a new variational framework for detecting and tracking multiple moving objects in image sequences motion detection is performed using a statistical framework for which the observed interframe difference density function is approximated using a mixture model this model is composed of two components namely the static background and the mobile moving objects one both components are zero mean and obey laplacian or gaussian law this statistical framework is used to provide the motion detection boundaries additionally the original frame is used to provide the moving object boundaries then the detection and the tracking problem are addressed in a common framework that employs a geodesic active contour objective function this function is minimized using a gradient descent method a new approach named hermes is proposed which exploits aspects from the well known front propagation algorithms and compares favorably to them very promising experimental results are provided using real video sequences

a topology preserving level set method for geometric deformable models active contour and surface models also known as deformable models are powerful image segmentation techniques geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior parameterization independence and ease of implementation however a long claimed advantage of geometric deformable models the ability to automatically handle topology changes turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved we present a new class of geometric deformable models designed using a novel topology preserving level set method which achieves topology preservation by applying the simple point concept from digital topology these new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces moreover since the topology preserving constraint is enforced efficiently through local computations the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

modeling viscoelastic behavior of arterial walls and their interaction with pulsatile blood flow fluid structure interaction describing wave propagation in arteries driven by the pulsatile blood flow is a complex problem whenever possible simplified models are called for one dimensional models are typically used in arterial sections that can be approximated by the cylindrical geometry allowing axially symmetric flows although a good first approximation to the underlying problem the one dimensional model suffers from several drawbacks the model is not closed an ad hoc velocity profile needs to be prescribed to obtain a closed system and the model equations are quasi linear hyperbolic oversimplifying the viscous fluid dissipation typically producing shock wave solutions not observed in healthy humans in this manuscript we derived a simple closed reduced model that accounts for the viscous fluid dissipation to the leading order the resulting fluid structure interaction system is of hyperbolic parabolic type arterial walls were modeled by a novel linearly viscoelastic cylindrical koiter shell model and the flow of blood by the incompressible viscous navier stokes equations kelvin voigt type viscoelasticity was used to capture the hysteresis behavior observed in the measurements of the arterial stress strain response using the a priori estimates obtained from an energy inequality together with the asymptotic analysis and ideas from homogenization theory for porous media flows we derived an effective model which is an 2 approximation to the three dimensional axially symmetric problem whereis the aspect ratio of the cylindrical arterial section our model shows two interesting features of the underlying problem bending rigidity often times neglected in the arterial wall models plays a nonnegligible role in the 2 approximation of the original problem and the viscous fluid dissipation imparts long term viscoelastic memory effects on the motion of the arterial walls this does not to the leading order influence the hysteresis behavior of arterial walls the resulting model although two dimensional is in the form that allows the use of one dimensional finite element method techniques producing fast numerical solutions we devised a version of the douglas rachford time splitting algorithm to solve the underlying hyperbolic parabolic problem the results of the numerical simulations were compared with the experimental flow measurements performed at the texas heart institute and with the data corresponding to the hysteresis of the human femoral artery and the canine abdominal aorta excellent agreement was observed

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

on optimal linear filtering for edge detection in this paper we revisit the analytical expressions of the three canny s 1983 criteria for edge detection quality good detection good localization and low multiplicity of false detections our work differs from canny s work on two essential points here the criteria are given for discrete sampled signals i e for the real implemented filters instead of a single step edge as input signal we use pulses of various width the proximity of other edges affects the quality of the detection process this is taken into account in the new expressions of these criteria we derive optimal filters for each of the criteria and for any combination of them in particular we define an original filter which maximizes detection and localization and a simple approximation of the optimal filter for the simultaneous maximization of the three criteria the upper bounds of the criteria are computed which allow users to measure the absolute and relative performance of any filter exponential deriche 1987 and first derivative of gaussian filters are evaluated our criteria can also be used to compute the optimal value of the scale parameter of a given filter when the resolution of the detection is fixed

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

anti impulse noise edge detection via anisotropic morphological directional derivatives traditional differential based edge detection suffers from abrupt degradation in performance when images are corrupted by impulse noises the morphological operators such as the median filters and weighted median filters possess the intrinsic ability to counteract impulse noise in this paper by combining the biwindow configuration with weighted median filters anisotropic morphological directional derivatives amdds robust to impulse noise are proposed to measure the local grayscale variation around a pixel for ideal step edges the amdd spatial response and directional representation are derived the characteristics and edge resolution of two kinds of typical biwindows are analyzed thoroughly in terms of the amdd spatial response and directional representation of ideal step edges the spatial matched filter is used to extract the edge strength map esm from the amdds of an image the spatial and directional matched filters are used to extract the edge direction map edm embedding the extracted esm and edm into the standard route of the differential based edge detection an anti impulse noise amdd based edge detector is constructed it is compared with the existing state of the art detectors on a recognized image dataset for edge detection evaluation the results show that it attains competitive performance in noise free and gaussian noise cases and the best performance in impulse noise cases

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

optimized schwarz methods optimized schwarz methods are a new class of schwarz methods with greatly enhanced convergence properties they converge uniformly faster than classical schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical schwarz methods if the overlap is of the order of the mesh parameter which is often the case in practical applications they achieve this performance by using new transmission conditions between subdomains which greatly enhance the information exchange between subdomains and are motivated by the physics of the underlying problem we analyze in this paper these new methods for symmetric positive definite problems and show their relation to other modern domain decomposition methods like the new finite element tearing and interconnect feti variants

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

area and length minimizing flows for shape segmentation a number of active contour models have been proposed that unify the curve evolution framework with classical energy minimization techniques for segmentation such as snakes the essential idea is to evolve a curve in two dimensions or a surface in three dimensions under constraints from image forces so that it clings to features of interest in an intensity image the evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional tailored to features such as edges however because the flow may be slow to converge in practice a constant hyperbolic term is added to keep the curve surface moving in the desired direction we derive a modification of this term based on the gradient flow derived from a weighted area functional with image dependent weighting factor when combined with the earlier modified length gradient flow we obtain a partial differential equation pde that offers a number of advantages as illustrated by several examples of shape segmentation on medical images in many cases the weighted area flow may be used on its own with significant computational savings

topological well composedness and glamorous glue a digital gluing algorithm for topologically constrained front propagation we propose a new approach to front propagation algorithms based on a topological variant of well composedness which contrasts with previous methods based on simple point detection this provides for a theoretical justification based on the digital jordan separation theorem for digitally gluing evolved well composed objects separated by well composed curves or surfaces additionally our framework can be extended to more relaxed topologically constrained algorithms based on multisimple points for both methods this framework has the additional benefit of obviating the requirement for both a user specified connectivity and a topologically consistent marching cubes squares algorithm in meshing the resulting segmentation

canny edge detection enhancement by scale multiplication the technique of scale multiplication is analyzed in the framework of canny edge detection a scale multiplication function is defined as the product of the responses of the detection filter at two scales edge maps are constructed as the local maxima by thresholding the scale multiplication results the detection and localization criteria of the scale multiplication are derived at a small loss in the detection criterion the localization criterion can be much improved by scale multiplication the product of the two criteria for scale multiplication is greater than that for a single scale which leads to better edge detection performance experimental results are presented

resolving the time lag between pressure and flow for the determination of local wave speed in elastic tubes and arteries it is well established that wave speed can be determined using the initial linear part of the pressure velocity loop pu loop however the frequency response of most flow measuring devices is usually slower than that of solid state pressure transducers making flow waveforms lagging in time behind pressure waveforms if this lag which is traditionally determined by eye is not corrected prior to the analysis the pu loop method may provide inaccurate wave speeds the main aim of this work is therefore to introduce an objective technique to establish the value of this lag the new technique relies on the linearity between pressure and velocity in the absence of reflections and determines the highest correlation factor between pressure and velocity in the range of minimum pressure to maximum velocity we shifted the flow waveform backwards in time steps equal to the sampling interval and the time shift associated with the highest correlation indicates the correct time lag of the flow waveform we first tested the new technique in vitro using a uniform latex tube and compared the results to those established using the traditional by eye method whilst varying the filter setting of the flowmeter then we applied the new technique to pressure and flow measured in the ascending aorta of anaesthetised open chested dogs we found the time lag between pressure and velocity calculated by the new technique in good agreement with that determined by eye in vitro and that increasing the filtering power generated greater delay between the measured pressure and flow the results obtained in vivo using the new technique were also in good agreement with those determined by eye we therefore conclude that the new technique provides a convenient and objective way of correcting the lag and can reliably align pressure and flow

the aitken like acceleration of the schwarz method on nonuniform cartesian grids in this paper we present a family of domain decomposition based on an aitken like acceleration of the schwarz method seen as an iterative procedure with a linear rate of convergence this paper is a generalization of the method first introduced at the 12th international conference on domain decomposition that was restricted to regular cartesian grids the potential of this method to provide scalable parallel computing on a geographically broad grid of parallel computers was demonstrated for some linear and nonlinear elliptic problems discretized by finite differences on a cartesian mesh the main purpose of this paper is to present a generalization of the method to nonuniform cartesian meshes the salient feature of the method consists of accelerating the sequence of traces on the artificial interfaces generated by the schwarz procedure using a good approximation of the main eigenvectors of the trace transfer operator for linear separable elliptic operators our solver is a direct solver for nonlinear operators we use an approximation of the eigenvectors of the jacobian of the trace transfer operator the acceleration is then applied to the sequence generated by the schwarz algorithm applied directly to the nonlinear operator

noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative matrix in this paper a noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative andd matrix is proposed in order to alleviate the conflict between high edge resolution and noise robustness in the color canny detector where the isotropic gaussian kernels and gradient matrix of the r g b components are used the andds of the three components of a color image are arranged into the andd matrix from its singular value decomposition svd the andd based color edge strength map cesm is constructed and is relevant to the pixelwise optimal fusion of the andds of the three components in the sense of color edge enhancement the merits and defects of the andd based cesm and gradient based cesm are contrasted to show their complementarity in color edge detection the two cesms are fused to develop a new color edge detector it is compared with the color canny detector and two recent color edge detectors the results show that the proposed detector attains better detection performance for noiseless and noisy color images corrupted by white gaussian noise or impulsive noise of small percentage a color edge detector using gradient matrix and andd matrix is proposed the svd of the andd matrix is used to determine cesm and cesd of a color image the new detector has both high edge resolution and noise robustness it attains better performance than the two existing color edge detectors

salient closed boundary extraction with ratio contour we present ratio contour a novel graph based method for extracting salient closed boundaries from noisy images this method operates on a set of boundary fragments that are produced by edge detection boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency we encode the gestalt laws of proximity and continuity in a novel boundary saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary this new measure attempts to remove a possible bias toward short boundaries we present a polynomial time algorithm for finding the most salient closed boundary we also present supplementary preprocessing steps that facilitate the application of ratio contour to real images we compare ratio contour to two closely related methods for extracting closed boundaries elder and zucker s method based on the shortest path algorithm and williams and thornber s method based on spectral analysis and a strongly connected components algorithm this comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images

acceleration of the schwarz method for elliptic problems in this paper we present a family of domain decomposition methods based on aitken like acceleration of the schwarz method which is an iterative procedure with linear rate of convergence this paper is a generalization of our method first introduced in 2000 that was restricted to cartesian grids we consider the finite volume fv approximation on general quadrangle meshes introduced by faille in 1992 we first present the so called aitken schwarz procedure for a linear differential operator this solver is a direct solver but its computational cost in the general case might be prohibitive second we introduce the steffensen schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems we show that this iterative solver has reasonable numerical efficiency and can be applied successfully to several classes of linear and nonlinear elliptic problems however the salient feature of our method is that our algorithm has high tolerance for slow networks in the context of distributed parallel computing and is attractive to use with computer architectures for which performance is limited by the memory bandwidth rather than the flop performance of the cpu this is currently the case for most parallel computers using risc processor architecture such as beowulf systems

discrete region competition for unknown numbers of connected regions we present a discrete unsupervised multiregion competition algorithm for image segmentation over different energy functionals the number of regions present in an image does not need to be known a priori nor their photometric properties the algorithm jointly estimates the number of regions their photometries and their contours the required regularization is provided by defining a region as a connected set of pixels the evolving contours in the image are represented by computational particles that move as driven by an energy minimization algorithm we present an efficient discrete algorithm that allows minimizing a range of well known energy functionals under the topological constraint of regions being connected components the presented framework and algorithms are implemented in the open source insight toolkit image processing library

pde based random valued impulse noise removal based on new class of controlling functions this paper is concerned with partial differential equation pde based image denoising for random valued impulse noise we introduce the notion of eni the abbreviation for edge pixels noisy pixels and interior pixels that denotes the number of homogeneous pixels in a local neighborhood and is significantly different for edge pixels noisy pixels and interior pixels we redefine the controlling speed function and the controlling fidelity function to depend on eni according to our two controlling functions the diffusion and fidelity process at edge pixels noisy pixels and interior pixels can be selectively carried out furthermore a class of second order improved and edge preserving pde denoising models is proposed based on the two new controlling functions in order to deal with random valued impulse noise reliably we demonstrate the performance of the proposed pdes via application to five standard test images corrupted by random valued impulse noise with various noise levels and comparison with the related second order pde models and the other special filtering methods for random valued impulse noise our two controlling functions are extended to automatically other pde models

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners