Abstract:   In this paper, we propose a geometric partial differential equation (PDE) for tracking one or several moving objects from a sequence of images, which is based on a geometric model for active contours. The active contour approach permits us to simultaneously handle both aspects: finding the boundaries and tracking them. We also describe a numerical scheme to solve the geometric equation and we present some numerical experiments.

Abstract:   We present a shape-recovery technique in two dimensions and three dimensions with specific applications in modeling anatomical shapes from medical images. This algorithm models extremely corrugated structures like the brain, is topologically adaptable, and runs in O(N log N) time, where N is the total number of points in the domain. Our technique is based on a level set shape-recovery scheme recently introduced by the authors and the fast marching method for computing solutions to static Hamilton-Jacobi equations.

Abstract:   We present a unified approach to noise removal, image enhancement, and shape recovery in images. The underlying approach relies on the level set formulation of curve and surface motion, which leads to a class of PDE-based algorithms. Beginning with an image, the first stage of this approach removes noise and enhances the image by evolving the image under flow controlled by min/max curvature and by the mean curvature. This stage is applicable to both salt-and-pepper grey-scale noise and full-image continuous noise present in black and white images, grey-scale images, texture images, and color images. The noise removal/enhancement schemes applied in this stage contain only one enhancement parameter, which in most cases is automatically chosen. The other key advantage of our approach is that a stopping criteria is automatically picked from the image; continued application of the scheme produces no further change. The second stage of our approach is the shape recovery of a de!

Abstract:   A framework for contrast enhancement via image evolution hows and variational formulations is introduced in this paper. First, an algorithm for histogram modification via image evolution equations is presented. We show that the image histogram can be modified to achieve any given distribution as the steady state solution of this differential equation. We then prove that the proposed evolution equation solves an energy minimization problem. This gives a new interpretation to histogram modification and contrast enhancement in general. This interpretation is completely formulated in the image domain, in contrast with classical techniques for histogram modification which are formulated in a probabilistic domain. From this, new algorithms for contrast enhancement, including, for example, image and perception models, can be derived, Based on the energy formulation and its corresponding differential form, we show that the proposed histogram modification algorithm can be combined!

Abstract:   In this note, we employ the new geometric active contour models formulated in [25] and [26] for edge detection and segmentation of magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound medical imagery, Our method is based on defining feature-based metrics on a given image which in turn leads to a novel snake paradigm in which the feature of interest mag be considered to lie at the bottom of a potential well, Thus, the snake is attracted very quickly and efficiently to the desired feature.

Abstract:   A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical ''snakes'' based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of!

Abstract:   The explicit use of partial differential equations (PDEs) in image processing became a major research topic in the past years. In this work we present a framework for histogram (pixel-value distribution) modification via ordinary and partial differential equations. In this way, the image contrast is improved. We show that the histogram can be modified to achieve any given distribution as the steady state solution of an image now. The contrast modification can be performed while simultaneously reducing noise in a unique PDE, avoiding noise sharpening effects of classical algorithms. The approach is extended to local contrast enhancement as well. A variational interpretation of the flow is presented and theoretical results on the existence of solutions are given. (C) 1997 Academic Press.

Abstract:   A geometric approach for 3D object segmentation and representation is presented. The segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3D image. The model is based on curvature motion and the computation of surfaces with minimal areas, better known as minimal surfaces. The space where the surfaces are computed is induced from the 3D image (volumetric data) in which the objects are to be detected. The model links between classical deformable surfaces obtained via energy minimization, and intrinsic ones derived from curvature based flows. The new approach is stable, robust, and automatically handles changes in the surface topology during the deformation.

Abstract:   Optimization processes based on ''active models'' play central roles in many areas of computational vision as well as computational geometry. Unfortunately, current models usually require highly complex and sophisticated mathematical machinery and at the same time they suffer from a number of limitations which impose restrictions on their applicability. In this paper a simple class of discrete active models, called migration processes (MPs), is presented. The processes are based on iterated averaging over neighborhoods defined by constant geodesic distance. It is demonstrated that the MP model-a system of self-organizing active particles-has a number of advantages over previous models, both parametric active models (''snakes'') and implicit (contour evolution) models. Due to the generality of the MP model, the process can be applied to derive natural solutions to a variety of optimization problems,including defining (minimal) surface patches given their boundary curves; f!

Abstract:   In order to segment an image the use of information at multiple scales is invaluable. The hyperstack, a linking-model-based segmentation technique, uses intensity to link points in adjacent levels of a scale space stack. This approach has been successfully applied to linear multiscale representations. Multiscale representions which satisfy two scale space properties, viz. a causality criterion and a semigroup property in differential form, are valid inputs as well. In this paper we consider linear scale space, gradient-dependent diffusion, and the Euclidean shortening flow. Since no global scale parameter is available in the latter two approaches we compare scale levels based on evolution time, information theoretic measures, and by counting the number of objects. The multiscale representations are compared with respect to their performance in image segmentation tasks on test and MR images. The hyperstack proves to be rather insensitive to the underlying multiscale repres!

Abstract:   Variational methods for image segmentation try to recover a piecewise smooth function together with a discontinuity set which represents the boundaries of the segmentation. This paper deals with a variational method that constrains the formation of discontinuities along smooth contours. The functional to be minimized, which involves the computation of the geometrical properties of the boundaries, is approximated by a sequence of functionals which can be discretized in a straightforward way. Computer examples of real images are presented to illustrate the feasibility of the method. (C) 1997 Elsevier Science B.V.

Abstract:   A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model's energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the ''snake'' energy by including the internal regularization term in the external potential term. Our method is based on finding a path of minimal length in a Riemannian metric. We then make use of a new efficient numerical method to find this shortest path.It is shown that the proposed energy, though based only on a potential integrated along the curve, imposes a regularization effect like snakes. We explore the relation between the maximum curvature along the resulting contour and the potential generated from the image.The method is capable to close contours, given only one point on the objects' boundary by using a topology-based saddle search routine.We show examples of our method applied to real aerial and m!

Abstract:   Numerical analysis of conservation laws plays an important role in the implementation of curve evolution equations. This paper reviews the relevant concepts in numerical analysis and the relation between curve evolution, Hamilton-Jacobi partial differential equations, and differential conservation laws. This close relation enables us to introduce finite difference approximations, based on the theory of conservation laws, into curve evolution. It is shown how curve evolution serves as a powerful tool for image analysis, and how these mathematical relations enable us to construct efficient and accurate numerical schemes. Some examples demonstrate the importance of the CFL condition as a necessary condition for the stability of the numerical schemes.

Abstract:   A novel geometric approach for three dimensional object segmentation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected, We show that this model is related to the computation of surfaces of minimal area (local minimal surfaces). The space where these surfaces are computed is induced from the three dimensional image in which the objects are to be detected. The general approach also shows the relation between classical deformable surfaces obtained via energy minimization and geometric ones derived from curvature flows in the surface evolution framework. The scheme is stable, robust, and automatically handles changes in the surface topology during the deformation. Results related to existence, uniqueness, stability, and correctness of the solution to this geometric deformable model are presented as well. Based on an efficient numerical algorithm for surface evolution, we present a number of examples of object detectio!

Abstract:   A framework for object segmentation in vector-valued images is presented in this paper. The first scheme proposed is based on geometric active contours moving toward the objects to be detected in the vector-valued image. Object boundaries are obtained as geodesics or minimal weighted-distance curves, where the metric is given by a definition of edges in vector-valued data. The curve flow corresponding to the proposed active contours holds formal existence, uniqueness, stability, and correctness results. The scheme automatically handles changes in the deforming curve topology. The technique is applicable, for example, to color and texture images as well as multiscale representations. We then present an extension of these vector active contours, proposing a possible image flow for vector-valued image segmentation. The algorithm is based on moving each one of the image level sets according to the proposed vector active contours. This extension also shows the relation between!

Abstract:   This paper presents a method for automatic segmentation of the tibia and femur in clinical magnetic resonance images of knees. Texture information is incorporated into an active contours framework through the use of vector-valued geodesic snakes with local variance as a second value at each pixel, in addition to intensity. This additional information enables the system to better handle noise and the non-uniform intensities found within the structures to be segmented. It currently operates independently on 2D images (slices of a volumetric image) where the initial contour must be within the structure but not necessarily near the boundary. These separate segmentations are stacked to display the performance on the entire 3D structure.

Abstract:   We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The absolute minimal Lipschitz extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range.

Abstract:   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 forte, 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.

Abstract:   A framework for contrast enhancement via image evolution hows and variational formulations is introduced in this paper. First, an algorithm for histogram modification via image evolution equations is presented. We show that the image histogram can be modified to achieve any given distribution as the steady state solution of this differential equation. We then prove that the proposed evolution equation solves an energy minimization problem. This gives a new interpretation to histogram modification and contrast enhancement in general. This interpretation is completely formulated in the image domain, in contrast with classical techniques for histogram modification which are formulated in a probabilistic domain. From this, new algorithms for contrast enhancement, including, for example, image and perception models, can be derived, Based on the energy formulation and its corresponding differential form, we show that the proposed histogram modification algorithm can be combined!

Abstract:   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, Recently, the evolution equation has been derived from first principles as the gradient dow that minimizes a modified length functional, tailored to features such as edges, However, because the how may be slow to converge in practice, a constant (hyperbolic) term is added to keep the curve/surface moving in the desired direction, In this paper, we derive a modification of this term based on the gradient how derived from a weighted area functional, with image dependent weighting factor, When combined with the earlier modified Length gradient dow, we obtain a partial differential equation (PDE) that offers a nu!

Abstract:   We are concerned with the retrieval of the unknown cross section of a homogeneous cylindrical obstacle embedded in a homogeneous medium and illuminated by time-harmonic electromagnetic line sources. The dielectric parameters of the obstacle and embedding materials are known and piecewise constant. That is, the shape (here, the contour) of the obstacle is sufficient for its full characterization. The inverse scattering problem is then to determine the contour from the knowledge of the scattered field measured for several locations of the sources and/or frequencies. An iterative process is implemented: given an initial contour, this contour is progressively evolved such as to minimize the residual in the data fit. This algorithm presents two main important points. The first concerns the choice of the transformation enforced on the contour. We will show that this involves the design of a velocity field whose expression only requires the resolution of an adjoint problem at ea!

Abstract:   In this paper implicit representations of deformable models for medical image enhancement and segmentation are considered. The advantage of implicit models over classical explicit models is that their topology can he naturally adapted to objects in the scene, A geodesic formulation of implicit deformable models is especially attractive since it has the energy minimizing properties of classical models, The aim of this pager is twofold, First, a modification to the customary geodesic deformable model approach is introduced by considering all the level sets in the image as energy minimizing contours. This approach is used to segment multiple objects simultaneously and for enhancing and segmenting cardiac computed tomography (CT) and magnetic resonance images. Second, the approach is used to effectively compare implicit and explicit models for specific tasks. This shows the complementary character of implicit models since in case of poor contrast boundaries or gaps in boundar!

Abstract:   An image segmentation method is proposed, which combines mathematical morphology tools and active contours in two stages. First, contours are coarsely approximated by means of morphological operators. Second, these initial contours evolve under the influence of geometric and grey-level information, owing to the model of active contours. The performance of the method is evaluated according to the noise and is compared to the watershed algorithm. Then an application is finally presented for biomedical images of tumour tissue. (C) 1998 Elsevier Science B.V. All rights reserved.

Abstract:   In this paper we undertake a systematic investigation of affine invariant object detection and image denoising. Edge detection is first presented from the point of view of the affine invariant scale-space obtained by curvature based motion of the image level-sets. In this case, affine invariant maps are derived as a weighted difference of images at different scales. We then introduce the affine gradient as an affine invariant differential function of lowest possible order with qualitative behavior similar to the Euclidean gradient magnitude. These edge detectors are the basis for the extension of the affine invariant scale-space to a complete affine flow for image denoising and simplification, and to define affine invariant active contours for object detection and edge integration. The active contours are obtained as a gradient flow in a conformally Euclidean space defined by the image on which the object is to be detected. That is, we show that objects can be segmented i!

Abstract:   Recently, Caselles et al. have shown the equivalence between a classical snake problem of Kass et al. and a geodesic active contour model. The PDE derived from the geodesic problem gives an evolution equation for active contours which is very powerfull for image segmentation since changes of topology are allowed using the level set implementation. However in Caselles' paper the equivalence with classical snake is only shown for 2D images and 1D curves, by using concepts of Hamiltonian theory which have no meanings for active surfaces. This paper propose to examine the notion of equivalence and to revisite Caselles et al. arguments. Then a notion equivalence is introduced and shown for classical snakes and geodesic active contours in the 2D (active contour) and 3D (active surface) case.

Abstract:   We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusion-transparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization.

Abstract:   A parameter-free approach for non-rigid image registration based on elasticity theory is presented. In contrast to traditional physically-based numerical registration methods, no forces have to be computed from image data to drive the elastic deformation. Instead, displacements obtained with the help of mapping boundary structures in the source and target image are incorporated as hard constraints into elastic image deformation. As a consequence, our approach does not contain any parameters of the deformation model such as elastic constants. The approach guarantees the exact correspondence of boundary structures in the images assuming that correct input data are available. The implemented incremental method allows to cope with large deformations. The theoretical background, the finite element discretization of the elastic model, and experimental results for 2D and 3D synthetic as well as real medical images are presented.

Abstract:   We use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model. The proposed scheme is useful for object segmentation in images, like tracking moving objects in a sequence of images. The method is based on the Weickert-Romeney-Viergever [33] AOS scheme. It is applied at small regions, motivated by Adalsteinsson-Sethian [1] level set narrow band approach, and uses Sethian's fast marching method [26] for re-initialization. Experimental results demonstrate the power of the new method for tracking in color movies.

Abstract:   In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. The model is a combination between more classical active contour models using mean curvature motion techniques, and the Mumford-Shah model for segmentation. We minimize an energy which can be seen as a particular case of the so-called 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. Finally, we will present various experimental results and in particular some examples for which the classical snak!

Abstract:   We present a supervised classification model based on a variational approach. This model is devoted to find an optimal partition compound of homogeneous classes with regular interfaces. We represent the regions of the image defined by the classes and their interfaces by level set functions, and we define a functional whose minimum is an optimal partition. The coupled Partial Differential Equations (PDE) related to the minimization of the functional axe considered through a dynamical scheme. Given an initial interface set (zero level set), the different terms of the PDE's are governing the motion of interfaces such that, at convergence, we get an optimal partition as defined above. Each interface is guided by internal forces (regularity of the interface), and external ones (data term, no vacuum, no regions overlapping). Several experiments were conducted on both synthetic an real images.

Abstract:   In this paper, we propose extensions to a powerful geometric shape modeling scheme introduced in [14]. The extension allows the model to automatically cope with topological changes and for the first time, introduces the concept of a global shape into geometric/geodesic snake models. The ability to characterize global shape of an object using very few parameters facilitates shape learning and recognition. In this new modeling scheme, object shapes are represented using a parameterized function - called the generator - which accounts for the global shape of an object and the pedal curve/surface of this global shape with respect to a geometric snake to represent any local detail. Traditionally, pedal curves/surfaces are defined as the loci of the feet of perpendiculars to the tangents of the generator from a fixed point called the pedal point. We introduce physics-based control for shaping these geometric models by using distinct pedal points - lying on a snake - for each po!

Abstract:   Automatic and semi-automatic magnetic resonance angiography (MRA) segmentation techniques can potentially save radiologists large amounts of time required for manual segmentation and can facilitate further data analysis. The proposed MRA segmentation method uses a mathematical modeling technique which is well-suited to the complicated curve-like structure of blood vessels. We define the segmentation task as an energy minimization over all 3D curves and use a level set method to search for a solution. Our approach is an extension of previous level set segmentation techniques to higher co-dimension.

Abstract:   In this paper we undertake a systematic investigation of affine invariant object detection and image denoising. Edge detection is first presented from the point of view of the affine invariant scale-space obtained by curvature based motion of the image level-sets. In this case, affine invariant maps are derived as a weighted difference of images at different scales. We then introduce the affine gradient as an affine invariant differential function of lowest possible order with qualitative behavior similar to the Euclidean gradient magnitude. These edge detectors are the basis for the extension of the affine invariant scale-space to a complete affine flow for image denoising and simplification, and to define affine invariant active contours for object detection and edge integration. The active contours are obtained as a gradient flow in a conformally Euclidean space defined by the image on which the object is to be detected. That is, we show that objects can be segmented i!

Abstract:   The method of curve evolution is a popular method for recovering shape boundaries. However, isotropic metrics have always been used to induce the how of the curve and potential steady states tend to be difficult to determine numerically, especially in noisy or tow-contrast situations. Initial curves shrink past the steady slate and soon vanish. In this paper, anisotropic metrics are considered to remedy the situation by taking the orientation of the feature gradient into account. The problem of shape recovery or segmentation is formulated as the problem of finding minimum cuts of a Riemannian manifold. Approximate methods, namely anisotropic geodesic flows and the solution of an eigenvalue problem, are discussed. (C) 2000 Academic Press.

Abstract:   This paper analyzes the problem of shape modeling using the principle of active geometric deformable models. While the basic modeling technique already exists in the literature, we highlight many of its drawbacks and discuss their source and steps to overcome them. We propose a new stopping criterion to address the stopping problem. We also propose to apply level set algorithm to implement the active geometric deformable models, thereby handling topology changes automatically. To alleviate the numerical problems associated with the implementation of the level set algorithm, we propose a new adaptive multigrid narrow band algorithm. All the proposed new changes have been illustrated with experiments with synthetic images and medical images.

Abstract:   This paper introduces the use of spatially adaptive components into the geodesic active contour segmentation method for application to volumetric medical images. These components are derived from local structure descriptors and are used both in regularization of the segmentation and in stabilization of the image-based vector field which attracts the contours to anatomical structures in the images. They are further used to incorporate prior knowledge about spatial location of the structures of interest. These components can potentially decrease the sensitivity to parameter settings inside the contour evolution system while increasing robustness to image noise. We show segmentation results on blood vessels in magnetic resonance angiography data and bone in computed tomography data.

Abstract:   We present a supervised classification model based on a variational approach. This model is devoted to find an optimal partition composed of homogeneous classes with regular interfaces. The originality of the proposed approach concerns the definition of a partition by the use of level sets. Each set of regions and boundaries associated to a class is defined by a unique level set function. We use as many level sets as different classes and all these level sets are moving together thanks to forces which interact in order to get an optimal partition. We show how these forces can be defined through the minimization of a unique fonctional. The coupled Partial Differential Equations (PDE) related to the minimization of the functional are considered through a dynamical scheme. Given an initial interface set (zero level set), the different terms of the PDE's are governing the motion of interfaces such that, at convergence, we get an optimal partition as defined above. Each interf!

Abstract:   In this paper, we use partial-differential-equation-based filtering as a preprocessing add post processing strategy for computer-aided cytology, We wish to accurately extract and classify. the shapes of nuclei from confocal microscopy images, which is a prerequisite to an accurate quantitative intranuclear (genotypic and phenotypic) and internuclear (tissue structure) analysis of tissue and cultured specimens. First, we study the use of a geometry-driven edge-preserving image smoothing mechanism before nuclear segmentation. We show how this biter outperforms other widely-used filters in that it provides higher edge fidelity. Then we apply the same filter,,vith a different initial condition, to smooth nuclear surfaces and obtain sub-pixel accuracy. Finally we use another instance of the geometrical filter to correct for misinterpretations of the nuclear surface by the segmentation algorithm. Our prefiltering and post filtering nicely complements our initial segmentation st!

Abstract:   In this paper, a partial-differential equations (PDE)-based system for detecting the boundary of skin lesions in digital clinical skin images is presented. The image is first preprocessed via contrast-enhancement and anisotropic diffusion. If the lesion is covered by hairs, a PDE-based continuous morphological filter that removes them is used as an additional preprocessing step. Following these steps, the skin lesion is segmented either by the geodesic active contours model or the geodesic edge tracing approach. These techniques are based on computing, again via PDEs, a geodesic curve in a space defined by the image content. Examples showing the performance of the algorithm are given.

Abstract:   Image segmentation plays a crucial role in many medical-imaging applications, by automating or facilitating the delineation of anatomical structures and other regions of interest. We present a critical appraisal of the current status of semi-automated and automated methods for the segmentation of anatomical medical images. Terminology and important issues in image segmentation are first presented. Current segmentation approaches are then reviewed with an emphasis on the advantages and disadvantages of these methods for medical imaging applications. We conclude with a discussion on the future of image segmentation methods in biomedical research.

Abstract:   Eye tracking is one of the key problems in controlled active vision. Because of modelling uncertainty and noise in the signals, it becomes a challenging problem for robust control. In this paper, we outline some of the key issues involved as well as some possible solutions. We will need to make contact with techniques from machine vision and multi-scale image processing in carrying out this task. In particular, we will sketch some of the necessary methods from computer vision and image processing including optical flow, active contours ('snakes'), and geometric driven flows. The paper will thus have a tutorial flavor as well. Copyright (C) 2000 John Wiley & Sons, Ltd.

Abstract:   We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvature-constrained snake is a cubic spline, irrespective of the form of the external energy held, Unfortunately, such regularized snakes suffer from slow convergence speed because of a large number of control points, as well as from difficulties in determining the weight factors associated to the internal energies of the curve. We therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori; this Leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies (i.e., the regularization term), In other words, we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knot!

Abstract:   In this paper, we introduce a novel geometric shape modeling scheme which allows for representation of global and local shape characteristics of an object. Geometric models are traditionally well-suited for representing global shapes without local detail. However, we propose a powerful geometric shape modeling scheme which allows for the representation of global shapes with local detail and permits model shaping as well as topological changes via physics-based control. The proposed modeling scheme consists of representing shapes by pedal curves and surfaces-pedal curves/surfaces are the loci of the foot of perpendiculars to the tangents of a fixed curve/surface from a fixed point called the pedal point. By varying the location of the pedal point, one can synthesize a large class of shapes which exhibit both local and global deformations. We introduce physics-based control for shaping these geometric models by letting the pedal point vary and use a snake to represent the p!

Abstract:   Herein, we present a variational model devoted to image classification coupled with an edge-preserving regularization process. The discrete nature of classification (i.e., to attribute a label to each pixel) has led to the development of many probabilistic image classification models, but rarely to variational ones. In the last decade, the variational approach has proven its efficiency in the field of edge-preserving restoration. In this paper, we add a classification capability which contributes to provide images composed of homogeneous regions with regularized boundaries, a region being defined as a set of pixels belonging to the same class. The soundness of our model is based on the works developed on the phase transition theory in mechanics. The proposed algorithm is fast, easy to implement, and efficient. We compare our results on both synthetic and satellite images with the ones obtained by a stochastic model using a Potts regularization.

Abstract:   We present a model and algorithm for segmentation of images with missing boundaries. In many situations. the human visual system fills in missing gaps in edges and boundaries, building and completing information that is not present This presents a considerable challenge in computer vision, since most algorithms attempt to exploit existing data. Completion models, which postulate how to construct missing data, are popular but are often trained and specific to particular images. In this paper, we take the following perspective: We consider a reference point within an image as given and then develop an algorithm that tries to build missing information on the basis of the given point of view and the available information as boundary data to the algorithm. We test the algorithm on some standard images, including the classical triangle of Kanizsa and low signal:noise ratio medical images.

Abstract:   In this paper, we propose an active contour algorithm for object detection in vector-valued images (such as RGB or multispectral). The model is an extension of the scalar Chan-Vese algorithm to the vector-valued case [1]. The model minimizes a Mumford-Shah functional over the length of the contour, plus the sum of the fitting error over each component of the vector-valued image. Like the Chan-Vese model, our vector-valued model can detect edges both with or without gradient. We show examples where our model detects vector-valued objects which are undetectable in any scalar representation. For instance, objects with different missing parts in different channels are completely detected (such as occlusion). Also, in color images, objects which are invisible in each channel or in intensity can be detected by our algorithm. Finally, the model is robust with respect to noise, requiring no a priori denoising step. (C) 2000 Academic Press.

Abstract:   We propose two variational models for supervised classification of multispectral data. Both models take into account contour and region information by minimizing a functional compound of a data term (2D surface integral) taking into account the observation data and knowledge on the classes, and a regularization term (1D length integral) minimizing the length of the interfaces between regions. This is a free discontinuity problem and we have proposed two different ways to reach such a minimum, one using a Gamma-convergence approach and the other using a level set approach to model contours and regions.Both methods have been previously developed in the case of monospectral observations. Multispectral techniques allow to take into account information of several spectral bands of satellite or aerial sensors. The goal of this paper is to present the extension of both variational classification methods to multispectral data. We show an application on real data from SPOT (XS mod!

Abstract:   A number of geometric active contour and surface models have been proposed for shape segmentation in the literature. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) so that it clings to the features of interest in an intensity image. Several of these models have been derived, using a variational formulation, as gradient flows which minimize or maximize a particular energy functional. However, in practice these models often fail on images of low contrast or narrow structures. To address this problem we have recently proposed the idea of maximizing the rate of increase of flux of an auxiliary vector field through a curve. This has lead to an interpretation as a 2D gradient flow, which is essentially parameter free. In this paper we extend the analysis to 3D and prove that the form of the gradient flow does not change. We illustrate its potential with level-set based segmentations of blood vessels in a large 3D computed rotational angiography (CRA) data !

Abstract:   In this paper, we present a fast and simple discrete approach for active contours. It is based on discrete contour evolution, which operates on the boundary of digital shape, by iterative growth processes on the boundary of the shape. We consider a curve to be the boundary of a discrete shape, We attach at each point of the boundary a cost function and deform this shape according to that cost function. The method presents some advantages. It is a discrete method, which takes an implicit representation and uses discrete algorithm with a simple data structure.

Abstract:   Segmentation of bright blobs in an image is an important problem in computer vision and particularly in biomedical imaging. In retinal angiography, segmentation of drusen, a yellowish deposit located on the retina, is a serious challenge in proper diagnosis and prevention of further complications.Drusen extraction using classic segmentation methods does not lead to good results. We present a new segmentation method based on new transformations we introduced in mathematical morphology. It is based on the search for a new class of regional maxima components of the image. These maxima correspond to the regions inside the drusen.We present experimental results for drusen extraction using images containing examples having different types and shapes of drusen. We also apply our segmentation technique to two important cases of dynamic sequences of drusen images. The first case is for tracking the average gray level of a particular drusen in a sequence of angiographic images duri!

Abstract:   In medical microscopy, image analysis offers to pathologist a modern tool, which can be applied to several problems in cancerology: quantification of DNA content, quantification of immunostaining, nuclear mitosis counting, characterization of tumor tissue architecture. However, these problems need an accurate and automatic segmentation. In most cases, the segmentation is concerned with the extraction of cell nuclei or cell clusters. In this paper, we address the problem of the fully automatic segmentation of grey level intensity or color images from medical microscopy. An automatic segmentation method combining fuzzy clustering and multiple active contour models is presented. Automatic and fast initialization algorithm based on fuzzy clustering and morphological tools are used to robustly identify and classify all possible seed regions in the color image. These seeds axe propagated outward simultaneously to refine contours of all objects. A fast level set formulation is u!

Abstract:   In this paper, we develop new methods for de-noising and edge detection in images by the solution of nonlinear diffusion partial differential equations. Many previous methods in this area obtain a de-noising u of the noisy image I as the solution of an equation of the form partial derivative (t)u = L(g(\del upsilon\), delu, u - I), when g controls the speed of the diffusion and defines the edge map. The usual choice for g(s) is (1 + ks(2))(-1) and the function upsilon is always some smoothing of u. Previous choices include upsilon = u, upsilon = G(sigma) * u, and upsilon = G sigma * I. Numerical results indicate that the choice of upsilon plays a very important role in the quality of the images obtained. Notice that all these choices involve an isotropic smoothing of u, which sometimes fails to presence important corners and junctions, and this may also fail to resolve small features which are closely grouped together. This paper obtains u as the solution of a nonlinear d!

Abstract:   A new anisotropic nonlinear diffusion model incorporating time-delay regularization into curvature-based diffusion is proposed for image restoration and edge detection. A detailed mathematical analysis of the proposed model in the form of the proof of existence, uniqueness and stability of the "viscosity" solution of the model is presented. Furthermore, implementation issues and computational methods for the proposed model are also discussed in detail. The results obtained from testing our denoising and edge detection algorithm on several synthetic and real images showed the effectiveness of the proposed model in prserving sharp edges and fine structures while removing noise.

Abstract:   This paper presents an approach for the extraction of vasculature from angiography images by using a wave propagation and traceback mechanism. We discuss both the theory and the implementation of the approach. Using a dual-sigmoidal filter, we label each pixel in an angiogram with the likelihood that it is within a vessel. Representing the reciprocal of this likelihood image as an array of refractive indexes, we propagate a digital wave through the image from the base of the vascular tree. This wave "washes" over the vasculature, ignoring local noise perturbations. The extraction of the vasculature becomes that of tracing the wave along the local normals to the waveform, While the approach is inherently single instruction stream multiple data stream (SIMD), we present an efficient sequential algorithm for the wave propagation and discuss the traceback algorithm, We demonstrate the effectiveness of our integer image neighborhood-based algorithm and its robustness to image !

Abstract:   Three-dimensional (3-D) imaging of the heart is a rapidly del eloping area of research in medical imaging, Advances in hardware and methods for fast spatio-temporal cardiac imaging are extending the frontiers of clinical diagnosis and research on cardiovascular diseases.In the last few Sears, many approaches hare been proposed to analyze images and extract parameters of cardiac shape and function from a variety of cardiac imaging modalities. In particular, techniques based on spatio-temporal geometric models have received considerable attention. This paper surveys the literature of tno decades of research on cardiac modeling. The contribution of the paper is three-fold: 1) to serve as a tutorial of the field for both clinicians and technologists, 2) to provide an extensive account of modeling techniques in a comprehensive and systematic manner, and 3) to critically review these approaches in terms of their performance and degree of clinical evaluation with respect to the !

Abstract:   Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during recent years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implementations of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Extending this continuous connection to the fully discrete setting enables us to derive many structural similarities between efficient numerical algorithms for both frameworks. These results provide a perspective for uniform implementations of nonlinear variational models and diffusion filters on parallel architectures.

Abstract:   This paper presents a new variational method for the segmentation of a moving object against a still background, over a sequence of [two-dimensional or three-dimensional (3-D)] image frames. The method is illustrated in application to myocardial gated single photon emission computed tomography (SPECT) data, and incorporates a level set framework to handle topological changes while providing closed boundaries.The key innovation is the introduction of a geometrical constraint into the derivation of the Euler-Lagrange equations, such that the segmentation of each individual frame can be interpreted as a closed boundary of an object (an isolevel of a set of hyper-surfaces) while integrating information over the entire sequence. This results in the definition of an evolution velocity normal to the object boundary. Applying this method to 3-D myocardial gated SPECT sequences, the left ventricle endocardial and epicardial limits can be computed in each frame.This space-time segm!

Abstract:   The level set method was devised by S. Osher and J. A. Sethian (1988, J. Comput, Phys. 79, 12-49) as a simple and versatile method for computing and analyzing the motion of an interface Gamma in two or three dimensions, Gamma bounds a (possibly multiply connected) region Omega. The goal is to compute and analyze the subsequent motion of Gamma under a velocity field v. This velocity can depend on position, time. the geometry of the interface, and the external physics. The interface is captured for later time as the zero level set of a smooth (at least Lipschitz continuous) function phi (x. t); i.e., Gamma (t) = {x \ phi (x, t) = 0}. phi is positive inside Omega, negative outside Omega. and is zero on Gamma (t). Topological merging and breaking are well defined and easily performed. In this review article we discuss recent variants and extensions, including the motion of curves in three dimensions, the dynamic surface extension method. fast methods for steady state problems!

Abstract:   A variety of numerical techniques are available for tracking moving interfaces. In this review, we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions: to hyperbolic conservation laws. This link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws. We discuss the evolution of these techniques, the fundamental numerical approximations, involved. implementation details, and applications. Tn particular, we review some work on three aspects of materials sciences: semiconductor process simulations. seismic processing, and optimal structural topology design. (C) 2001 Academic Press.

Abstract:   The vasculature is of utmost importance in neurosurgery. Direct visualization of images acquired with current imaging modalities, however, cannot provide a spatial representation of small vessels. These vessels, and their branches which show considerable variations, are most important in planning and performing neurosurgical procedures. In planning they provide information on where the lesion draws its blood supply and where it drains. During surgery the vessels serve as landmarks and guidelines to the lesion. The more minute the information is, the more precise the navigation and localization of computer guided procedures. Beyond neurosurgery and neurological study, vascular information is also crucial in cardiovascular surgery, diagnosis, and research. This paper addresses the problem of automatic segmentation of complicated curvilinear structures in three-dimensional imagery, with the primary application of segmenting vasculature in magnetic resonance angiography (MRA)!

Abstract:   This paper. describes a fast process of parametric snake evolution with a multiresolution strategy. Conventional parametric evolution method relies on matrix inversion throughout the iteration intermittently, in contrast the proposed method relaxes the matrix inversion which is: costly and time consuming in cases where the resulting snake is flexible. The proposed method also eliminates the input of snake rigidity parameters when the snake is flexible. Also, a robust and definite termination criterion for both conventional and proposed methods is demonstrated ill this paper. (C) 2001 pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

Abstract:   We use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model. The proposed scheme is useful for object segmentation in images, like tracking moving objects in a sequence of images. The method is based on the Weickert-Romeney-Viergever (additive operator splitting) AOS scheme. It is applied at small regions, motivated by Adalsteinsson-Sethian level set narrow band approach, and uses Sethian's fast marching method for re-initialization. Experimental results demonstrate the power of the new method for tracking in color movies.

Abstract:   In this work, we first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah paradigm from a curve evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Each gradient step involves solving an optimal estimation problem for the data within each region, connecting curve evolution and the Mumford-Shah functional with the theory of boundary-value stochastic processes. The resulting active contour model offers a tractable implementation of the original Mumford-Shah model (i.e., without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation) to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner. Various implementations of this algorithm are introduced to in!

Abstract:   In this paper, we propose significant extensions to the "snake pedal" model, a powerful geometric shape modeling scheme introduced in (Vemuri and Guo, 1998). The extension allows the model to automatically cope with topological changes and for the first time, introduces the concept of a compact global shape into geometric active models. The ability to characterize global shape of an object using very few parameters facilitates shape learning and recognition. In this new modeling scheme, object shapes are represented using a parameterized function-called the generator-which accounts for the global shape of an object and the pedal curve (surface) of this global shape with respect to a geometric snake to represent any local detail. Traditionally, pedal curves (surfaces) are defined as the loci of the feet of perpendiculars to the tangents of the generator from a fixed point called the pedal point. Local shape control is achieved by introducing a set of pedal points-lying on !

Abstract:   We present a novel mathematical, physical and logical framework for describing an input image of the dynamics of physical fields, in particular the optic field dynamics. Our framework is required to be invariant under a particular gauge group, i.e., a group or set of transformations consistent with the symmetries of that physical field dynamics enveloping renormalisation groups. It has to yield a most concise field description in terms of a complete and irreducible set of equivalences or invariants. Furthermore, it should be robust to noise, i.e., unresolvable perturbations (morphisms) of the physical field dynamics present below a specific dynamic scale, possibly not covered by the gauge group, do not affect Lyapunov or structural stability measures expressed in equivalences above that dynamic scale. The related dynamic scale symmetry encompasses then a gauge invariant similarity operator with which similarly prepared ensembles of physical field dynamics are probed and s!

Abstract:   In this paper, we propose a general Eulerian framework for region-based active contours named DREAM(2)S. We introduce a general criterion including both region-based and boundary-based terms where the information on a region is named "descriptor". The originality of this work is twofold. Firstly we propose to use shape optimization principles to compute the evolution equation of the active contour that will make it evolve as fast as possible towards a minimum of the criterion. Secondly, we take into account the variation of the descriptors during the propagation of the curve. Indeed, a descriptor is generally globally attached to the region and thus "region-dependent". This case arises for example if the mean or the variance of a region are chosen as descriptors. We show that the dependence of the descriptors with the region induces additional terms in the evolution equation of the active contour that have never been previously computed. DREAM(2)S gives an easy way to tak!

Abstract:   An automatic cortical gray matter segmentation from a three-dimensional (3-D) brain images [magnetic resonance (MR) or computed tomography] is a well known problem in medical image processing. In this paper, we first formulate it as a geometric variational problem for propagation of two coupled bounding surfaces. An efficient numerical scheme is then used to implement the geodesic active surface model. Experimental results of cortex segmentation on real 3-D MR data are provided.

Abstract:   Several geometric active contour models have been proposed for segmentation in computer vision and image analysis. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) under constraints from image forces so that it clings to features of interest in an intensity image. Recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented. However, it is still unclear how to apply these techniques to images of narrow elongated structures, such as blood vessels, where intensity contrast may be low and reliable region statistics cannot be computed. To address this problem, we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve (in 2D) or a surface (in 3D). The key idea is to exploit the direction of the vector field along with its magnitude. The calculations lead to a simple and elegant interpretation which is e!

Abstract:   We discuss two image-based 3D modeling methods based on a multiresolution evolution of a volumetric function's level set. in the former method, the role of the level set implosion is to fuse ("sew" and "stitch") together several partial reconstructions (depth maps) into a closed model. In the later, the level set's implosion is steered directly by the texture mismatch between views. Both solutions share the characteristic of operating in an adaptive multiresolution fashion, in order to boost up computational efficiency and robustness.

Abstract:   In this paper, we develop a novel region-based approach to snakes designed to optimally separate the values of certain image statistics over a known number of region types. Multiple sets of contours deform according to a coupled set of curve evolution equations derived from a single global cost functional. The resulting active contour model, in contrast to many other edge and region based models, is fully global in that the evolution of each curve depends at all times upon every pixel in the image and is directly coupled to the evolution of every other curve regardless of their mutual proximity. As such evolving contours enjoy a very wide "field of view," endowing the algorithm with a robustness to initial contour placement above and beyond the significant improvement exhibited by other region based snakes over earlier edge based snakes. (C) 2002 Elsevier Science (USA).

Abstract:   Diffusion generated motion has been used to generate a variety of interface motions. In this paper, we present a new shape recovery model with diffusion generated motion. The approach is based on alternately diffusing and sharpening the initial region to move the sharp interface toward the boundaries of the desired objects. The shapes are recovered by an anisotropic inter-face motion with a local image property dependent speed. Our algorithm is simple and easy to implement. It automatically captures topological changes and works for both 2D and 3D image data. Experimental results for synthetic and real images are presented. (C) 2002 Elsevier Science (USA).

Abstract:   The class of geometric deformable models, also known as level sets, has brought tremendous impact to medical imagery due to its capability of topology preservation and fast shape recovery. In an effort to facilitate a clear and full understanding of these powerful state-of-the-art applied mathematical tools, this paper is an attempt to explore these geometric methods, their implementations and integration of regularizers to improve the robustness of these topologically independent propagating curves/surfaces. This paper first presents the origination of level sets, followed by the taxonomy of level sets. We then derive the fundamental equation of curve/surface evolution and zero-level curves/surfaces. The paper then focuses on the first core class of level sets, known as "level sets without regularizers." This class presents five prototypes: gradient, edge, area-minimization, curvature-dependent and application driven. The next section is devoted to second core class of l!

Abstract:   We present a geometric model and a computational method for segmentation of images with missing boundaries. In many situations, the human visual system fills in missing gaps in edges and boundaries, building and completing information that is not present, Boundary completion presents a considerable challenge in computer vision, since most algorithms attempt to exploit existing data. A large body of work concerns, completion models, which postulate how to construct missing data; these models are often trained and specific to particular images. In this paper, we take the following, alternative perspective: we consider a given reference point within the image, and then develop an algorithm which tries to build missing information on the basis of the given point of view and the available information as boundary data to the algorithm. Starting from this point of view, a surface is constructed. It is then evolved with the mean curvature flow in the metric induced by the image u!

Abstract:   This paper presents a novel variational framework for dealing with frame partition problems in computer vision by the propagation of curves. This framework integrates boundary- and region-based frame partition modules under a curve-based objective function, which aims at finding a set of minimal length curves that preserve three main properties: (i) they are regular and smooth, (ii) they are attracted by the boundary points (boundary-based information), (iii) and they create a partition that is optimal according to the expected region properties of the different hypotheses (region-based information). The defined objective function is minimized using a gradient descent method. According to the obtained motion equations, the set of initial curves is propagated toward the best partition under the influence of boundary- and region-based forces, and is constrained by a regularity force. The changes of topology are naturally handled thanks to the level set implementation. Furth!

Abstract:   The years 1985-2000 have seen the emergence of several nonlinear P.D.E. models in image restoration and image analysis. Before that date, the heat equation and the reverse heat equation had been considered as relevant, one as a model of image smoothing compatible with Shannon conditions, and one as a restoration model proposed by Gabor. We try in this review to organize the P.D.E. models according to their genealogy from the initial heat equation and according to their very diverse use : some are useful for image denoising, some for image deblurring, some for invariant smoothing in view of shape recognition. Some permit to define easily active contours (snakes), some may be used for a nonlinear interpolation of sparse images. We show many experiments illustrating these different applicative aspects.

Abstract:   Extensive growth in functional brain imaging, perfusion-weighted imaging, diffusion-weighted imaging, brain mapping and brain scanning techniques has led tremendously to the importance of the cerebral cortical segmentation, both in 2-D and 3-D, from volumetric brain magnetic resonance imaging data sets. Besides that, recent growth in deformable brain segmentation techniques in 2-D and 3-D has brought the engineering community, such as the areas of computer vision, image processing, pattern recognition and graphics, closer to the medical community, such as to neuro-surgeons, psychiatrists, oncologists, neuro-radiologists and internists. This paper is an attempt to review the state-of-the-art 2-D and 3-D cerebral cortical segmentation techniques from brain magnetic resonance imaging based on three main classes: region-based, boundary/surface-based and fusion of boundary/surface-based with region-based techniques. In the first class, region-based techniques, we demonstrated !

Abstract:   A new constraint on geometric active contour has been proposed, that is capable of propagating adaptively (bidirectional) and extracting the shape of the object more accurately. The constraint used is an image based steering function derived from histogram features in a non-overlapped distribution function, as against the conventional method that uses gradient-based edge stopping function. (C) 2002 Elsevier Science B.V. All rights reserved.

Abstract:   A new variational framework of geometric active contours to track multiple non-rigid moving objects in the clutter background is presented. Incorporating motion edge information, it consists of motion detection and tracking stages. The results of experiments are promising and demonstrate the validity of the proposed framework.

Abstract:   A segmentation model that combines the Mumford-Shah( M-S) model and narrow band scheme of level set was presented. The disadvantage of Mumford-Shah model is computationally time-consuming. In each step of its iteration, the data of whole image have to be renewed, which is unbearable for segmentation of large image or 3D image. Therefore, a fast segmentation model was introduce, which combines the M-S model and narrow band scheme by a new initialization method. The new initialization method is based on fast marching method, and the computing time decreases to O(N). In each step of iteration, the new segmentation model only deals with the data in a narrow band instead of the whole image. The experiments show that the two models can obtain almost the same segmentation result, but the computing time of new narrow band M-S model is much less than that of M-S model.

Abstract:   Feature detection is important in various mesh processing techniques, such as mesh editing, mesh morphing, mesh compression, and mesh signal processing. In spite of much research in computer vision, automatic feature detection even for images still remains a difficult problem. To avoid this dfficulty, semi-automatic or interactive techniques for image feature detection have been investigated. In this paper, we propose a geometric snake as an interactive tool for feature detection on a 3D triangular mesh. A geometric snake is an extension of an image snake, which is an active contour model that slithers from its initial position specified by the user to a nearby feature while minimizing an energy functional. To constrain the movement of a geometric snake onto the surface of a mesh, we use the parameterization of the surrounding region of a geometric snake. Although the definition of a feature may vary among applications, we use the normal changes of faces to detect feature!

Abstract:   Some known models in phase separation theory (Hele-Shaw, nonlocal mean curvature motion) and their approximations by means of Cahn-Hilliard and nonlocal Allen-Cahn equations are proposed as a tool to generate planar curve-shortening flows without shrinking. This procedure can be seen as a level set approach to area-preserving geometric flows in the spirit of Sapiro and Tannenbaum [38], with application to shape recovery. We discuss the theoretical validation of this method and its implementation to problems of shape recovery in Computer Vision. The results of some numerical experiments on image processing are presented.

Abstract:   In this paper we propose a level set method to segment MR cardiac images. Our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints. The visual information is expressed through a gradient vector flow-based boundary component and a region term that aims at best separating the cardiac contours/regions according to their global intensity properties. In order to deal with misleading visual support, an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance. The resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme, the Additive Operator Splitting. Encouraging experimental results are provided using real data.

Abstract:   In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the segmented contour to the prior shape. The active contour is able to find boundaries that are similar in shape to the prior, even when the entire boundary is not visible in the image (i.e., when the boundary has gaps). A level set formulation of the active contour is presented. The existence of the solution to the energy minimization is also established.We also report experimental results of the use of this contour on 2d synthetic images, ultrasound images and fMRI images. Classical active contours cannot be used in many of these images.

Abstract:   In this paper we consider long time behavior of a mean curvature flow of nonparametric surface in R-n, with respect to a conformal Riemannian metric. We impose zero boundary value, and we prove that the solution tends to 0 exponentially fast as t --> infinity. Its normalization u/sup u tends to the first eigenfunction of the associated linearized problem. (C) 2002 Elsevier Science (USA). All rights reserved.

Abstract:   The in vivo investigation of joint kinematics in normal and injured wrist requires the segmentation of carpal bones from 3D (CT) images, and their registration over time. The non-uniformity of bone tissue, ranging from dense cortical bone to textured spongy bone, the irregular shape of closely packed carpal bones, small inter-bone spaces compared to the resolution of CT images, along with the presence of blood vessels, and the inherent blurring of CT imaging render the segmentation of carpal bones a challenging task. We review the performance of statistical classification, deformable models (active contours), region growing, region competition, and morphological operations for this application. We then propose a model which combines several of these approaches in a unified framework. Specifically, our approach is to use a curve evolution implementation of region growing from initialized seeds, where growth is modulated by a skeletally-mediated competition between neighbor!

Abstract:   We consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals. We show that one can go from one class to the other by solving Poisson's or Helmholtz's equation with well-chosen boundary conditions. Using this equivalence, we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding Euler - Lagrange equations. We revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals. We also de. ne a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding Gateaux derivatives and Euler - Lagrange equations. Fi!

Abstract:   In this paper we present a new variational framework in level set form for image segmentation, which incorporates both a prior shape and prior fixed locations of a small number of points. The idea underlying the model is the creation of two energy terms in the energy function for the geodesic active contours. The first energy term is for the shape, the second for the locations of the points In this model, segmentation is achieved through a registration technique, which combines a rigid transformation and a local deformation. The rigid transformation is determined explicitly by using shape information, while the local deformation is determined implicitly by using image gradients and prior locations. We report experimental results on both synthetic and ultrasound images. These results compared with the results obtained by using a previously reported model, which only incorporates a shape prior into the active contours.

Abstract:   This paper presents a novel method for surface recovery from discrete 3D point data sets. In order to produce improved reconstruction results, the algorithm presented in this paper combines the advantages of a parametric approach to model local surface structure, with the generality and the topological adaptability of a geometric flow approach. This hybrid method is specifically designed to preserve discontinuities in 3D, to be robust to noise, and to reconstruct objects with arbitrary topologies. The key ideas are to tailor a curvature consistency algorithm to the case of a set of points in 3D and to then incorporate a flux maximizing geometric flow for surface reconstruction. The approach is illustrated with experimental results on a variety of data sets.

Abstract:   Poor convergence to concave shapes is a main limitation of snakes as a standard segmentation and shape modelling technique. The gradient of the external energy of the snake represents a force that pushes the snake into concave regions, as its internal energy increases when new inflexion points are created. In spite of the improvement of the external energy by the gradient vector flow technique, highly non convex shapes can not be obtained, yet. In the present paper, we develop a new external energy based on the geometry of the curve to be modelled. By tracking back the deformation of a curve that evolves by minimum curvature flow, we construct a distance map that encapsulates the natural way of adapting to non convex shapes. The gradient of this map, which we call curvature vector flow (CVF), is capable of attracting a snake towards any contour, whatever its geometry. Our experiments show that, any initial snake condition converges to the curve to be modelled in optimal t!

Abstract:   Levelset methods were introduced in medical images segmentation by Malladi et al. in 1995. In this paper, we propose several improvements of the original method to speed up the algorithm convergence and to improve the quality of the segmentation in the case of cardiac gated SPECT images.We studied several evolution criterions, taking into account the dynamic property of heart image sequences. For each step of the segmentation algorithm, we have compared different solutions in order to both reduce time and improve. quality.We have developed a modular segmentation tool with 3D+T visualization capabilities to experiment the proposed solutions and tune the algorithm parameters. We show segmentation results on both simulated and real SPECT images.

Abstract:   This paper presents a method for accurate location of the vessel borders based on boosting of classifiers and feature selection. Intravascular Ultrasound Images (IVUS) are an excellent tool for direct visualization of vascular pathologies and evaluation of the lumen and plaque in coronary arteries. Nowadays, the most common methods to separate the tissue from the lumen are based on gray levels providing non-satisfactory segmentations. In this paper, we propose and analyze a new approach to separate tissue from lumen based on an ensemble method for classification and feature selection. We perform a supervised learning of local texture patterns of the plaque and lumen regions and build a large feature space using different texture extractors. A classifier is constructed by selecting a small number of important features using AdaBoost. Feature selection is achieved by a modification of the AdaBoost. A snake is set to deform to achieve continuity on the classified image. Diff!

Abstract:   Objective. Prostate diseases are very common in adult and elderly men, and prostate boundary detection from ultrasonographic images plays a key role in prostate disease diagnosis and treatment. However, because of the poor quality of ultrasonographic images, prostate boundary detection still remains a challenging task. Currently, this task is performed manually, which is arduous and heavily user dependent. To improve the efficiency by automating the boundary detection process, numerous methods have been proposed. We present a review of these methods, aiming to find a good solution that could efficiently detect the prostate boundary on ultrasonographic images. Methods. A full description of various methods is beyond the scope of this article; instead, we focus on providing an introduction to the different methods with a discussion of their advantages and disadvantages. Moreover, verification methods for estimating the accuracies of the algorithms reported in the literature!

Abstract:   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. In this paper, 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 con!

Abstract:   Traditionally, segmentation and registration have been solved as two independent problems, even though it is often the case that the solution to one impacts the solution to the other. In this paper, we introduce a geometric, variational framework that uses active contours to simultaneously segment and register features from multiple images. The key observation is that multiple images may be segmented by evolving a single contour as well as the mappings of that contour into each image. (C) 2003 Elsevier Science B.V. All rights reserved.

Abstract:   We view the fundamental edge integration problem for object segmentation in a geometric variational framework. First we show that the classical zero-crossings of the image Laplacian edge detector as suggested by Marr and Hildreth, inherently provides optimal edge-integration with regard to a very natural geometric functional. This functional accumulates the inner product between the normal to the edge and the gray level image-gradient along the edge. We use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models. We also incorporate a 2D geometric variational explanation to the Haralick edge detector into the geometric active contour framework.

Abstract:   We cast the problem of multiframe stereo reconstruction of a smooth surface as the global region segmentation of a collection of images of the scene. Dually, the problem of segmenting multiple calibrated images of an object becomes that of estimating the solid shape that gives rise to such images. We assume that the radiance of the scene results in piecewise homogeneous image statistics. This simplifying assumption covers Lambertian scenes with constant albedo as well as fine homogeneous textures, which are known challenges to stereo algorithms based on local correspondence. We pose the segmentation problem within a variational framework, and use fast level set methods to find the optimal solution numerically. Our algorithm does not work in the presence of strong photometric features, where traditional reconstruction algorithms do. It enjoys significant robustness to noise under the assumptions it is designed for.

Abstract:   This paper deals with image and video segmentation using active contours. We propose a general form for the energy functional related to region-based active contours. We compute the associated evolution equation using shape derivation tools and accounting for the evolving region-based terms. Then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented. Experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions. As an example, it has been successfully applied to face segmentation in real video sequences.

Abstract:   A new contour tracking algorithm is presented. Tracking is posed as a matching problem between curves constructed out of edges in the image, and some shape space describing the class of objects of interest. The main contributions of the paper are to present an algorithm which solves this problem accurately and efficiently, in a provable manner. In particular, the algorithm's efficiency derives from a novel tree-search algorithm through the shape space, which allows for much of the shape space to be explored with very little effort. This latter property makes the algorithm effective in highly cluttered scenes, as is demonstrated in an experimental comparison with a condensation tracker.

Abstract:   We propose a shape-based approach to curve evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras [15], we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional se!

Abstract:   In this paper we review the algorithm development and applications in high resolution shock capturing methods, level set methods, and PDE based methods in computer vision and image processing. The emphasis is on Stanley Osher's contribution in these areas and the impact of his work. We will start with shock capturing methods and will review the Engquist-Osher scheme, TVD schemes, entropy conditions, ENO and WENO schemes, and numerical schemes for Hamilton-Jacobi type equations. Among level set methods we will review level set calculus, numerical techniques, fluids and materials, variational approach, high codimension motion, geometric optics, and the computation of discontinuous solutions to Hamilton-Jacobi equations. Among computer vision and image processing we will review the total variation model for image denoising, images on implicit surfaces, and the level set method in image processing and computer vision. (C) 2003 Elsevier Science B.V. All rights reserved.

Abstract:   The research presented in this paper is to develop a technique of virtual human modeling for the garment industry from two photographs of a human body in two orthogonal views. Firstly, an efficient segmentation method is applied on the two photographs to obtain the contours of the human body. After this, a template-based feature extraction algorithm is introduced to determine the feature points on the human contours by human morphology rules. Finally, a view-dependent deformation technique is described to construct the virtual human body by using human contours. Our segmentation algorithm is derived from the Mumford-Shah segmentation technology and the level set formulation, and it is accelerated by applying multi-pyramid levels. The deformation technique is related to axial deformation. With our deformation method, the reference silhouettes (the front-view and right-view silhouettes of the template human model) and the target silhouettes (the front-view and right-view si!

Abstract:   Active contour modeling is a powerful technique for modeling object boundaries. Various methods introduced for this purpose, however, have certain difficulties such as getting stuck in local minima, poor modeling of long concavities, and producing inaccurate results when the initial contour is chosen simple or far from the object boundary. A modified form of time adaptive self-organizing map network with a variable number of neurons is proposed here for active contour modeling which does not show such difficulties and automatically determines the required number of control points. The initial contour for the object boundary can be defined inside, outside, or across the boundary. This contour can be open or closed, may be as simple as desired, and can be placed far from the object boundary. In addition, the boundary may contain long concavities. The proposed algorithm is tested for modeling different objects and shows very good performance. (C) 2002 Elsevier Science B.V. A!