Abstract:   We apply a level set formulation to the problem of surface advancement in three-dimensional topography simulation of deposition, etching, and lithography processes in integrated circuit fabrication. The level set formulation is based on solving a Hamilton-Jacobi-type equation for a propagating level set function, using techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. The equations of motion of a unified model, including the effects of isotropic and unidirectional deposition and etching, visibility, surface diffusion, reflection, and material dependent etch/deposition rates are presented and adapted to a level set formulation. In Part I of this paper, the basic equations and algorithms for two-dimensional simulations were developed. In this paper, the extension to three dimensions is presen!

Abstract:   We present a controlled image smoothing and enhancement method based on a curvature flow interpretation of the geometric heat equation. Compared to existing techniques, the model has several distinct advantages. (i) It contains just one enhancement parameter. (ii) The scheme naturally inherits a stopping criterion from the image; continued application of the scheme produces no further change. (iii) The method is one of the fastest possible schemes based on a curvature-controlled approach.

Abstract:   A novel interactive segmentation method has been developed which uses estimated boundaries, generated from cores, to initialize a scale-space boundary evolution process in greyscale medical images. Presented is an important addition to core extraction methodology that improves core generation for objects that are in the presence of interfering objects. The boundary at the scale of the core (BASOC) and its associated width information, both derived from the core, are used to initialize the second stage of the segmentation process. In this automatic refinement stage, the BASOC is allowed to evolve in a spline-snake-like manner that makes use of object-relevant width information to make robust measurements of local edge positions.

Abstract:   Object size inspection is an important task and has various applications in computer vision. For example, the automatic control of stone-breaking machines, which perform better if the sizes of the stones to be broken can be predicted. An algorithm is proposed for image segmentation in size inspection for almost round stones with high or low texture. Although our experiments are focused on stones, the algorithm can be applied to other 3-D objects. We use one fixed camera and four light sources at four different positions one at a time, to take four images. Then we compute the image differences and binarize them to extract edges. We explain, step by step, the photographing, the edge extraction, the noise removal, and the edge gap filling. Experimental results are presented.

Abstract:   We present a class of PDE-based algorithms suitable for image denoising and enhancement. The techniques are applicable to both salt-and-pepper gray-scale noise and full-image continuous noise present in black and white images, gray-scale images, texture images, and color images. At the core, the techniques rely on two fundamental ideas. First, a level set formulation is used for evolving curves; use of this technique to flow isointensity contours under curvature is known to remove noise and enhance images. Second, the particular form of the curvature how is governed by a minimax switch which selects a range of denoising dependent on the size of switching window. Our approach has several virtues. First, it contains only one enhancement parameter, which in most cases is automatically chosen. Second, the scheme automatically stops smoothing at a point which depends on the switching window size; continued application of the scheme produces no further change. Third, the method!

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:   This paper describes a new global shape parameterization for smoothly deformable three-dimensional (3-D) objects, such as those found in biomedical images, whose diversity and irregularity make them difficult to represent in terms of fixed features or parts. This representation is used for geometric surface matching to 3-D medical image data, such as from magnetic resonance imaging (MRI). The parameterization decomposes the surface into sinusoidal basis functions. Four types of surfaces are modeled: tori, open surfaces, closed surfaces and tubes. This parameterization allows a wide variety of smooth surfaces to be described with a small number of parameters. Extrinsic model-based information is incorporated by introducing prior probabilities on the parameters. Surface finding is formulated as an optimization problem, Results of the method applied to synthetic images and 3-D medical images of the heart and brain are presented.

Abstract:   In this paper, we analyze geometric active contour models from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new feature-based Riemannian metrics. This leads to a novel edge-detection paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus an edge-seeking curve is attracted very naturally and efficiently to the desired feature. Comparison with the Allen-Cahn model clarifies some of the choices made in these models, and suggests inhomogeneous models which may in return be useful in phase transitions. We also consider some 3-dimensional active surface models based on these ideas. The justification of this model rests on the careful study of the viscosity solutions of evolution equations derived from a level-set approach.

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:   Accurately segmenting and quantifying structures is a key issue in biomedical image analysis. The two conventional methods of image segmentation, region-based segmentation, and boundary finding, often suffer from a variety of limitations. Here we propose a method which endeavors to integrate the two approaches in an effort to form a unified approach that is robust to noise and poor initialization. Our approach uses Green's theorem to derive the boundary of a homogeneous region-classified area in the image and integrates this with a gray level gradient-based boundary finder. This combines the perceptual notions of edge/shape information with gray level homogeneity. A number of experiments were performed both on synthetic and real medical images of the brain and heart to evaluate the new approach, and it is shown that the integrated method typically performs better when compared to conventional gradient-based deformable boundary finding. Further, this method yields these im!

Abstract:   This paper examines the problem of obtaining a mathematical representation of the outer cortex of the human brain, which is a key problem in several applications, including morphological analysis of the brain, and spatial normalization and registration of brain images. A parameterization of the outer cortex is first obtained using a deformable surface algorithm which, motivated by the structure of the cortex, is constructed to find the central layer of thick surfaces. Based on this parameterization, a hierarchical representation of the outer cortical structure is proposed through its depth map and its curvature maps at various scales. Various experiments on magnetic resonance data are presented.

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:   Finding the shortest path between points on a surface is a challenging global optimization problem. It is difficult to devise an algorithm that is computationally efficient, locally accurate and guarantees to converge to the globally shortest path. In this paper a two stage coarse-to-fine approach for finding the shortest paths is suggested. In the first stage the algorithm of Ref. 10 that combines a 3D length estimator with graph search is used to rapidly obtain an approximation to the globally shortest path. In the second stage the approximation is refined to become a shorter geodesic curve, i.e., a locally optimal path. This is achieved by using an algorithm that deforms an arbitrary initial curve ending at two given surface points via geodesic curvature shortening flow. The 3D curve shortening how is transformed into an equivalent 2D one that is implemented using an efficient numerical algorithm for curve evolution with fixed end points, introduced in Ref. 9.

Abstract:   In this paper. we introduce an unsupervised contour estimation strategy based on parametrically deformable models. The problem is formulated in a (statistical) parameter estimation framework with the parameters of both the contour the and observation model (the likelihood function) being considered unknown. Although other choices could fit in our formulation, we focus on Fourier and B-spline contour descriptors. To estimate the optimal parametrization order (e.g,, the number of Fourier coefficients) we adopt the minimum description length (MDL) principle. The result is a parametrically deformable contour with an adaptive degree of smoothness and which also autonomously estimates the observation model parameters.

Abstract:   The range of surface evolution problems in etching, deposition, and lithography development offers significant challenge for numerical methods in front tracking. Level set methods for evolving interfaces are specifically designed for profiles which can develop sharp corners, change topology, and undergo orders of magnitude changes in speed, They are based on solving a Hamilton-Jacobi type equation for a level set function, using techniques borrowed from hyperbolic conservation laws. Over the past few years, a body of level set methods have been developed with application to microfabrication problems, In this paper, we give an overview of these techniques, describe the implementation in etching, deposition, and lithography simulations, and present a collection of fast level set methods, each aimed at a particular application, In the case of photoresist development and isotropic etching/deposition, the fast marching level set method, introduced by Sethian in [39], [40], can!

Abstract:   This paper presents a general framework to generate multi-scale representations of image data. The process is considered as an initial value problem with an acquired image as initial condition and a geometrical invariant as ''driving force'' of an evolutionary process. The geometrical invariants are extracted using the family of Gaussian derivative operators. These operators naturally deal with scale as a free parameter and solve the ill-posedness problem of differentiation. Stability requirements for numerical approximation of evolution schemes using Gaussian derivative operators are derived and establish an intuitive connection between the allowed time-step and scale. This approach has been used to generalize and implement a variety of nonlinear diffusion schemes. Results on test images and medical images are shown.

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:   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:   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:   Flexible polyurethane foam is based on a 3-dimensional cellular network. The mechanical properties of foam material depend upon cell structure and cell size distribution. In this work, we use laser confocal microscopy to image the foam cells and recover its 3-dimensional cellular network. Based on this technique we provide a statistical analysis and compare several foam samples. Confocal microscopic images are also used to visualize foam compression. Images for foam network structure under different mechanical compressions are also obtained. Limitations of confocal microscope are discussed and a new method - nuclear magnetic resonance imaging is proposed.

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:   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:   Efficient and powerful topologically adaptable deformable surfaces can be created by embedding and defining discrete deformable surface models in terms of an Affine Cell Decomposition (ACD) framework. The ACD framework, combined with a novel and original reparameterization algorithm, creates a simple but elegant mechanism for multiresolution deformable curve, surface, and solid models to ''flow'' or ''grow'' into objects with complex geometries and topologies, and adapt their shape to recover the object boundaries. ACD-based models maintain the traditional parametric physics-based formulation of deformable models, allowing them to incorporate a priori knowledge in the form of energy and force-based constraints, and provide intuitive interactive capabilities. This paper describes ACD-based deformable surfaces and demonstrates their potential for extracting and reconstructing some of the most complex biological structures from medical image volumes.

Abstract:   The Perona-Malik equation is a formally ill-posed parabolic equation for which simple discretizations are nevertheless numerically found to be stable. After discussing the background of this paradox in computer vision, this paper shows the nonexistence of weak solutions even in those cases where computations are successful, and introduces a notion of generalized solutions for this equation, which do evolve smoothly and possess many of the features of numerical calculations.

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:   This paper describes an image segmentation technique in which an arbitrarily shaped contour was deformed stochastically until it fitted around an object of interest. The evolution of the contour was controlled by a simulated annealing process which caused the contour to settle into the global minimum of an image-derived ''energy'' function. The nonparametric energy function was derived from the statistical properties of previously segmented images, thereby incorporating prior experience. Since the method was based on a state space search for the contour with the best global properties, it was stable in the presence of image errors which confound segmentation techniques based on local criteria, such as connectivity. Unlike ''snakes'' and other active contour approaches, the new method could handle arbitrarily irregular contours in which each interpixel crack represented an independent degree of freedom. Furthermore, since the contour evolved toward the global minimum of th!

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:   Subpixel methods that locate curves and their singularities, and that accurately measure geometric quantities, such as orientation and curvature, are of significant importance in computer vision and graphics. Such methods often use local surface fits or structural models for a local neighborhood of the curve to obtain the interpolated curve. Whereas their performance is good in smooth regions of the curve, it is typically poor in the vicinity of singularities. Similarly, the computation of geometric quantities is often regularized to deal with noise present in discrete data. However, in the process, discontinuities are blurred over, leading to poor estimates at them and in their vicinity. In this paper we propose a geometric interpolation technique to overcome these limitations by locating curves and obtaining geometric estimates while (1) not blurring across discontinuities and (2) explicitly and accurately placing them, The essential idea is to avoid the propagation of !

Abstract:   We describe a system that is being used to segment gray matter from magnetic resonance imaging (MRI) and to create connected cortical representations for functional MRI visualization (fMRI). The method exploits knowledge of the anatomy of the cortex and incorporates structural constraints into the segmentation, First, the white matter and cerebral spinal fluid (CSF) regions in the MR volume are segmented using a novel techniques of posterior anisotropic diffusion, Then, the user selects the cortical white matter component of interest, and its structure is verified by checking for cavities and handles. After this, a connected representation of the gray matter is created by a constrained growing-out from the white matter boundary, Because the connectivity is computed, the segmentation can be used as input to several methods of visualizing the spatial pattern of cortical activity within gray matter, In our case, the connected representation of gray matter is used to create a!

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:   We describe a system that is being used to segment gray matter from magnetic resonance imaging (MRI) and to create connected cortical representations for functional MRI visualization (fMRI). The method exploits knowledge of the anatomy of the cortex and incorporates structural constraints into the segmentation, First, the white matter and cerebral spinal fluid (CSF) regions in the MR volume are segmented using a novel techniques of posterior anisotropic diffusion, Then, the user selects the cortical white matter component of interest, and its structure is verified by checking for cavities and handles. After this, a connected representation of the gray matter is created by a constrained growing-out from the white matter boundary, Because the connectivity is computed, the segmentation can be used as input to several methods of visualizing the spatial pattern of cortical activity within gray matter, In our case, the connected representation of gray matter is used to create a!

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:   In many applications of dynamic scene analysis, the objects or structures to be analyzed undergo deformations that have to be modeled. In this paper, we develop a hierarchical statistical modeling framework for the representation, segmentation, and tracking of 2D deformable structures in image sequences. The model relies on the specification of a template, on which global as well as local deformations are defined. Global deformations are modeled using a statistical modal analysis of the deformations observed on a representative population. Local deformations are represented by a (first-order) Markov random process. A model-based segmentation of the scene is obtained by a joint bayesian estimation of global deformation parameters and local deformation variables. Spatial or spatio-temporal observations are considered in this estimation procedure, yielding an edge-based or a motion-based segmentation of the scene. The segmentation procedure is combined with a temporal tracki!

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:   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:   This paper presents a method for segmentation and tracking of cardiac structures in ultrasound image sequences. The developed algorithm is based on the active contour framework. This approach requires initial placement of the contour close to the desired position in the image, usually an object outline. Best contour shape and position are then calculated, assuming that at this configuration a global energy function, associated with a contour, attains its minimum. Active contours can be used for tracking by selecting a solution from a previous frame as an initial position in a present frame. Such an approach, however, fails for large displacements of the object of interest. This paper presents a technique that incorporates the information on pixel velocities (optical flow) into the estimate of initial contour to enable tracking of fast-moving objects. The algorithm was tested on several ultrasound image sequences, each covering one complete cardiac cycle. The contour succe!

Abstract:   Characterization of pulmonary nodules plays a significant role in the differential diagnosis of lung cancer. This paper presents a method to quantify surface characteristics of small pulmonary nodules with well-defined surface based on thin-section CT images. The segmentation of the three-dimensional (3-D) nodule images are obtained by a 3-D deformable surfaces approach. The feature extraction algorithms are designed to quantify the surface characteristic parameters from 3-D nodule images by using surface curvatures and ridge lines. Experimental results of our method, applied to patients 3-D nodule images, demonstrate it performance.

Abstract:   The application of a discrete dynamic contour model for segmentation of the hippocampus from brain MRT has been investigated. Solutions to several common problems of dynamic contours in this case and similar cases have been developed. A new method for extracting the discontinuous boundary of a structure with multiple edges near the structure has been developed. The method is based on detecting and following edges by external forces. The reliability of the final contour and the model stability have been improved by using a continuous mapping of the external energy and limiting movements of the contour. The problem of optimizing the internal force weight has been overcome by making it dependent on the amount of the external force. Finally, the results of applying the proposed algorithm, which implements the above modifications, to multiple applications have been evaluated. (C) 1998 Elsevier Science Ltd. All rights reserved.

Abstract:   This paper describes a framework for the estimation of shape from sparse or incomplete range data. It uses a shape representation called blending, which allows for the geometric combination of shapes into a unified model-selected regions of the component shapes are cut-out and glued together. Estimation of shape using this representation is realized using a physics-based framework, and also includes a process for deciding how to adapt the structure and topology of the model to improve the fit. The blending representation helps avoid abrupt changes in model geometry during fitting by allowing the smooth evolution of the shape, which improves the robustness of the technique. We demonstrate this framework with a series of experiments showing its ability to automatically extract structured representations from range data given both structurally and topologically complex objects.

Abstract:   This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application domain. The resulting optimization problem is solved by an incremental process of deformation. We represent a deformable surface as the level set of a discretely sampled scalar function of three dimensions, i.e., a volume. Such level-set models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume. The result is a voxel-based modeling technology that offers several advantages over conventional parametric models, including flexible topology, no need for reparameterization, concise descriptions of differential structure, and a natural scale space for hierarchical representations. This paper bu!

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 review the recently published work on deformable models. We have chosen to concentrate on 2D deformable models and relate the energy minimization approaches to the Bayesian formulations. We categorize the various active contour systems according to the definition of the deformable model. We also present in detail one particular formulation for deformable templates which combines edge, texture, color and region information for the external energy and model deformations using wavelets, splines or Fourier descriptors. We explain how these models can be used for segmentation, image retrieval in a large database and object tracking in a video sequence. (C) 1998 Elsevier Science B.V. All rights reserved.

Abstract:   The cortex is the outermost thin layer of gray matter in the brain; geometric measurement of the cortex helps in understanding brain anatomy and function. In the quantitative analysis of the cortex from MR images, extracting the structure and obtaining a representation for various measurements are key steps. While manual segmentation is tedious and labor intensive, automatic, reliable and efficient segmentation and measurement of the cortex remain challenging problems due to its convoluted nature. A new approach of coupled surfaces propagation using level set methods is presented here for the problem of the segmentation and measurement of the cortex. Our method is motivated by the nearly constant thickness of the cortical mantle and takes this tight coupling as an important constraint. By evolving two embedded surfaces simultaneously, each driven by its own image-derived information while maintaining the coupling, a final representation of the cortical bounding surfaces a!

Abstract:   A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries. (C) 1999 Elsevier Science B.V. All rights reserved.

Abstract:   Robust segmentation of structures from an image is essential for a variety of image analysis problems. However, the conventional methods of region-based segmentation and gradient-based boundary finding are often frustrated by poor image quality. Here we propose a method to integrate the two approaches using game theory in an effort to form a unified approach that is robust to noise and poor initialization. This combines the perceptual notions of complete boundary information using edge data and shape priors with gray-level homogeneity using two computational modules. The novelty of the method is that this is a bidirectional framework, whereby both computational modules improve their results through mutual information sharing. A number of experiments were performed both on synthetic datasets and datasets of real images to evaluate the new approach and it is shown that the integrated method typically performs better than conventional gradient-based boundary finding.

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:   A method for deforming curves in a given image to a desired position in a second image is introduced in this paper. The algorithm is based on deforming the first image toward the second one via a partial differential equation, while tracking the deformation of the curves of interest in the first image with an additional, coupled, partial differential equation. The tracking is performed by projecting the velocities of the first equation into the second one. In contrast with previous PDE based approaches, both the images and the curves on the frames/slices of interest axe used for tracking. The technique can be applied to object tracking and sequential segmentation. The topology of the deforming curve can change, without any special topology handling procedures added to the scheme. This permits for example the automatic tracking of scenes where, due to occlusions, the topology of the objects of interest changes from frame to frame. In addition, this work introduces the conc!

Abstract:   Level set methods provide a robust way to implement geometric flows, but they suffer from two problems which are relevant when using smoothing flows to unfold the cortex: the lack of point-correspondence between scales and the inability to implement tangential velocities. In this paper, we suggest to solve these problems by driving the nodes of a mesh with an ordinary differential equation. We state that this approach does not suffer from the known problems of Lagrangian methods since all geometrical properties axe computed on the fixed (Eulerian) grid. Additionally, tangential velocities can be given to the nodes, allowing the mesh to follow general evolution equations, which could be crucial to achieving the final goal of minimizing local metric distortions. To experiment with this approach, we derive area and volume preserving mean curvature flows and use them to unfold surfaces extracted from MRI data of the human brain.

Abstract:   This paper is concerned with the simulation of the Partial Differential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately the solution to this equation is not a distance function. As a consequence, the practical application of the level set method is plagued with such questions as when do we have to "reinitialize" the distance function? How do we "reinitialize" the distance function? Etc... which reveal a disagreement between the theory and its implementation. This paper proposes an alternative to the use of Hamilton-Jacobi equations which eliminates this contradiction: in our method the implicit representation always remains a distance function by construction, and the implementation does not differ f!

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:   Since the work by Osher and Sethian on level-sets algorithms for numerical shape evolutions, this technique has been used for a large number of applications in numerous fields. In medical imaging, this numerical technique has been successfully used for example in segmentation and cortex unfolding algorithms. The migration from a Lagrangian implementation to an Eulerian one via implicit representations or level-sets brought some of the main advantages of the technique, mainly, topology independence and stability. This migration means also that the evolution is parametrization free, and therefore we do not know exactly how each part of the shape is deforming, and the point-wise correspondence is lost. In this note we present a technique to numerically track regions on surfaces that are being deformed using the level-sets method. The basic idea is to represent the region of interest as the intersection of two implicit surfaces, and then track its deformation from the deforma!

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:   In this paper we present and briefly describe a Windows user-friendly system designed to assist with the analysis of images in general, and biomedical images in particular. The system, which is being made publicly available to the research community, implements basic 2D image analysis operations based on partial differential equations (PDE's). The system is under continuous development, and already includes a large number of image enhancement and segmentation routines that have been tested for several applications.

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:   Deformable models, which include deformable contours (the popular snakes) and deformable Surfaces, are a powerful model-based medical image analysis technique. We develop a new class of deformable models by formulating deformable surfaces in terms of an affine cell image decomposition (ACID). Our approach significantly extends standard deformable surfaces, while retaining their interactivity and other desirable properties. In particular, the ACID induces an efficient reparameterization mechanism that enables parametric deformable surfaces to evolve into complex geometries, even modifying their topology as necessary. We demonstrate that our new ACID-based deformable surfaces, dubbed T-surfaces, can effectively segment complex anatomic structures from medical volume images.

Abstract:   The cortex is the outermost thin layer of gray matter in the brain; geometric measurement of the cortex helps in understanding brain anatomy and function. In the quantitative analysis of the cortex from MR images, extracting the structure and obtaining a representation for various measurements are key steps. While manual segmentation is tedious and labor intensive, automatic reliable efficient segmentation and measurement of the cortex remain challenging problems, due to its convoluted nature. Here we present a new approach of coupled-surfaces propagation, using level set methods to address such problems, Our method is motivated by the nearly constant thickness of the cortical mantle and takes this tight coupling as an important constraint. By evolving two embedded surfaces simultaneously, each driven by its own image-derived information while maintaining the coupling, a final representation of the cortical bounding surfaces and an automatic segmentation of the cortex are!

Abstract:   We have been developing a theory for the generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and moderate changes in viewpoint.

Abstract:   Algorithms for object segmentation are crucial in many image processing applications. During past years, active contour models (snakes) have been widely used for finding the contours of objects. This segmentation strategy is classically edge-based in the sense that the snake is driven to fit the maximum of an edge map of the scene. In this paper, we propose a region snake approach and we determine fast algorithms for the segmentation of an object in an image. The algorithms developed in a Maximum Likelihood approach are based on the calculation of the statistics of the inner and the outer regions (defined by the snake). It has thus been possible to develop optimal algorithms adapted to the random fields which describe the gray levels in the input image if we assume that their probability density function family are known. We demonstrate that this approach is still efficient when no boundary's edge exists in the image. We also show that one can obtain fast algorithms by tr!

Abstract:   External energies of active contours are often formulated as Euclidean are length integrals. In this paper, we show that such formulations are biased. By this we mean that the minimum of the external energy does not occur at an image edge. In addition, we also show that for certain forms of external energy the active contour is unstable-when initialized at the true edge, the contour drifts away and becomes jagged. Both of these phenomena are due to the use of Euclidean are length integrals.We propose a non-Euclidean are length which eliminates these problems. This requires a reformulation of active contours where a single external energy function is replaced by a sequence of energy functions and the contour evolves as an integral curve of the gradient of these energies. The resulting active contour not only has unbiased external energy, but is also more controllable,Experimental evidence is provided in support of the theoretical claims.

Abstract:   We discuss a procedure for synthesizing controllers for safety specifications for hybrid systems. The procedure depends on the construction of the set of states of a continuous dynamical system that can be driven to a subset of the state space, avoiding another subset of the state space (the Reach-Avoid set). We present a new characterization of the Reach-Avoid set in terms of the solution of a pair of coupled Hamilton-Jacobi partial differential equations. We also discuss a computational algorithm for solving such partial differential equations and demonstrate its effectiveness on numerical examples.

Abstract:   In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and efficient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The different tasks performed during the reconstruction include the segmentation of given objects in the scene, the extrapolation of missing data, and the control of smoothness, density, and geometric quality of the reconstructed meshes. The reconstruction takes place in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure. Then, after a few iterations, the mesh topology can be modified by creating holes or by increasing its genus. Finally, an iterative refinement algorithm decreases the dista!

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:   Since the work by Osher and Sethian on level-sets algorithms for numerical shape evolutions, this technique has been used for a large number of applications in numerous fields. In medical imaging, this numerical technique has been successfully used for example, in segmentation and cortex unfolding algorithms. The migration from a Lagrangian implementation to a Eulerian one via implicit representations or level-sets brought some of the main advantages of the technique, i.e., topology independence and stability. This migration means also: that the evolution is parametrization free. Therefore, we do not know exactly how each part of the shape is deforming and the point-wise correspondence is lost. In this note we present a technique to numerically track regions on surfaces that are being deformed. using the level-sets method. The basic idea is to represent the region of interest as the intersection of two implicit surfaces and then track its deformation from the deformation !

Abstract:   Spatio-temporal life cycle of meteorological structures is an important part of study of routine numerical weather analysis. In this paper we present an algorithm to track tracer clouds in INSAT image sequence. Given a pair of sequence images taken at a 30 min interval, the objective of cloud tracking is to derive the path of movement of a cloud contour in the source image to the corresponding contour of the destination image. This has direct relevance to cloud motion vector (CMV) analysis by which wind speed and direction are estimated. We have utilized an improved algorithm to generate a set of initial estimates of possible cloud motion vectors which are then filtered through a shape-based approach. The contour of cloud mass is modelled as a perfectly flexible string, and depending on initial estimates of CMV, the source cloud contours are deformed. The CMV direction for which the deformed contour best matches the destination contour, gives the optimum path of cloud mov!

Abstract:   In this paper, the authors present general views of computer vision and image processing based on optimization. Relaxation and regularization in both broad and narrow senses are used in various fields and problems of computer vision and image processing, and they are currently being combined with general-purpose optimization algorithms. The principle and case examples of relaxation and regularization are discussed; the application of optimization to shape description that is a particularly important problem in the field is described; and the use of a genetic algorithm (GA) as a method of optimization is introduced.

Abstract:   We present a new active contour model for boundary tracking and position prediction of nonrigid objects, which results from applying a velocity control to the class of elastodynamical contour models, known as snakes, The proposed control term minimizes an energy dissipation function which measures the difference between the contour velocity and the apparent velocity of the image. Treating the image video-sequence as continuous measurements along time, it is shown that the proposed control results in robust tracking. This is in contrast to the original snake model which is proven to have tracking errors relative to image (object) velocity, thus resulting in high sensitivity to image clutter. The motion estimation further allows for position prediction of nonrigid boundaries. Based on the proposed central approach, we propose a new class of real time tracking contours, varying from models with batch-mode control estimation to models with real time adaptive controllers. (C) !

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:   Three-dimensional ultrasound is emerging as a viable resource for the imaging of internal organs. Quantitative studies correlating ultrasonic volume measurements with MRI data continue to validate this modality as a more efficient alternative for 3D imaging studies. However, the processing required to form 3D images from a set of 2D images may result in a loss of spatial resolution and may give rise to artifacts. This paper examines a method of automatic feature extraction and data quantification in 3D data sets as compared with original 2D data. This work will implement an active contour algorithm to automatically extract the endocardial borders of septal defects in echocardiographic images, and compare the size of the defects in the original 2D images and the 3D data sets. (C) 2000 Elsevier Science Ltd. AU rights reserved.

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:   A method for deforming curves in a given image to a desired position in the second image is introduced in this paper. The algorithm is based on deforming the first image toward the second one via a Partial Differential Equation (PDE), while tracking the deformation of the curves of interest in the first image with an additional, coupled, PDE. The tracking is performed by projecting the velocities of the first equation into the second one. In contrast with previous PDE-based approaches, both the images and the curves on the frames/slices of interest are used for tracking. The technique can be applied to object tracking and sequential segmentation. The topology of the deforming curve can change without any special topology handling procedures added to the scheme. This permits, for example, the automatic tracking of scenes where, due to occlusions, the topology of the objects of interest changes from frame to frame. In addition, this work introduces the concept of projecting!

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:   We propose a novel method for object tracking using prototype-based deformable template models. To track an object in an image sequence, we use a criterion which combines two terms: the frame-to-frame deviations of the object shape and the fidelity of the modeled shape to the Input image. The deformable template model utilizes the prior shape information which is extracted from the previous frames along with a systematic shape deformation scheme to model the object shape in a new frame. The following image information Is used in the tracking process: 1) edge and gradient information: the object boundary consists of pixels with large image gradient, 2) region consistency: the same object region possesses consistent color and texture throughout the sequence, and 3) interframe motion: the boundary of a moving object is characterized by large interframe motion. The tracking proceeds by optimizing an objective function which combines both the shape deformation and the fidelity!

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:   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 is concerned with the simulation of the partial differential equation driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian have proposed to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately the solution to this equation is not a distance function. As a consequence, the practical application of the level set method is plagued with such questions as When do we have to reinitialize the distance function? How do we reinitialize the distance function?, which reveal a disagreement between the theory and its implementation. This paper proposes an alternative to the use of Hamilton-Jacobi equations which eliminates this contradiction: in our method the implicit representation always remains a distance function by construction, and the implementation does not differ from the th!

Abstract:   The problem considered in this paper is how to localize and extract object boundaries (salient contours) in an image. To this end, we present a new active contour model, which is a neural network, based on self-organization. The novelty of the model consists in exploiting the principles of spatial isomorphism and self-organization in order to create flexible contours that characterize shapes in images. The flexibility of the model is effectuated by a locally co-operative and globally competitive self-organizing scheme, which enables the model to cling to the nearest salient contour in the test image. To start with this deformation process, the model requires a rough boundary as the initial contour. As reported here, the implemented model is semi-automatic, in the sense that a user-interface is needed for initializing the process. The model's utility and versatility are illustrated by applying it to the problems of boundary extraction, stereo vision, bio-medical image anal!

Abstract:   We propose a new active contour model for shape extraction of objects in grey-valued two-dimensional images based on an energy-minimization formulation. The energy functional that we consider takes into account the two requirements of object isolation and smoothness of the contour. After deriving the Euler-Lagrange equations corresponding to the energy functional, we bring out some important geometric properties of a solution to these equations. The discussion on our solution method-with the help of which we try to minimize the energy functional by evolving an initial curve-also focuses on how to prescribe the initial curve fully automatically. The effectiveness of our algorithms is demonstrated with the help of experimental results. Copyright (C) 2000 John Wiley & Sons, Ltd.

Abstract:   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, where a flow deforms the initial curve towards the minimum of the objective function, under the influence of internal and external image dependent forces. Using the lev!

Abstract:   An algebraic curve is defined as the zero set of a polynomial in two variables. Algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics. The main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data. Usually, arguments against using algebraic curves involve references to mathematicians Wilkinson (see [1, ch. 7] and Runge (see [3, ch. 4]). The first goal of this article is to understand the stability issue of algebraic curve fitting. Then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed, and its properties are investigated. The fitting algorithm is of sufficient stability for very fast position-invariant shape recognition, position estimation, and shape tracking, based on invariants and new representations. Among appropriate applications are shape-based indexing into image databas!

Abstract:   The analysis of medical images has been woven into the fabric of the Pattern Analysis and Machine Intelligence (PAMI) community since the earliest days of these Transactions. Initially, the efforts in this area were seen as applying pattern analysis and computer vision techniques to another interesting dataset. However, over the last two to three decades, the unique nature of the problems presented within this area of study have led to the development of a new discipline in its own right. Examples of these include: the types of image information that are acquired, the fully three-dimensional image data, the nonrigid nature of object motion and deformation, and the statistical variation of both the underlying normal and abnormal ground truth. In this paper, we look at progress in the field over the last 20 years and suggest some of the challenges that remain for the years to come.

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:   Image denoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications. In this paper, we present a nonlinear PDE-based model for image denoising and segmentation which unifies the popular model of Alvarez, Lions and Morel (ALM) for image denoising and the Caselles, Kimmel and Sapiro model of geodesic "snakes". Our model includes nonlinear diffusive as well as reactive terms and leads to quality denoising and segmentation results as depicted in the experiments presented here. We present a proof for the existence, uniqueness, and stability of the viscosity solution of this PDE-based model. The proof is in spirit similar to the proof of the ALM model; how ever, there are several differences which arise due to the presence of the reactive terms that require careful treatment/consideration. A fast implementation of our model is realized by embedding the model in a scale space and then achieving the solution vi!

Abstract:   We present a new class of deformable contours (snakes) and apply them to the segmentation of medical images. Our snakes are defined in terms of an affine cell image decomposition (ACID). The 'snakes in ACID' framework significantly extends conventional snakes, enabling topological flexibility among other features. The resulting topology adaptive snakes, or 'T-snakes', can be used to segment some of the most complex-shaped biological structures from medical images in an efficient and highly automated manner. (C) 2000 Elsevier Science BN. All rights reserved.

Abstract:   This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities and which must be reconciled. Surface registration can be roughly partitioned into three issues: choice of transformation, elaboration of surface representation and similarity criterion, and matching and global optimization. The first issue concerns the assumptions made about the nature of relationships between the two modalities, e.g. whether a rigid-body assumption applies, and if nor, what type and how general a relation optimally maps one modality onto the other. The second issue determines what type of information we extract from the 3D surfaces, which typically characterizes their local or global shape, and how we !

Abstract:   This paper is concerned with the simulation of the Partial Differential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately the solution to this equation is not a distance function. As a consequence, the practical application of the level set method is plagued with such questions as when do we have to "reinitialize" the distance function? How do we "reinitialize" the distance function? Etc... which reveal a disagreement between the theory and its implementation. This paper proposes an alternative to the use of Hamilton-Jacobi equations which eliminates this contradiction: in our method the implicit representation always remains a distance function by construction, and the implementation does not differ f!

Abstract:   Segmentation of the skull in medical imagery is an important stage in applications that require the construction of realistic models of the head. Such models are used, for example, to simulate the behavior of electro-magnetic fields in the head and to model the electrical activity of the cortex in EEG and MEG data. in this paper, we present a new approach for segmenting regions of bone in MRI volumes using deformable models. Our method takes into account the partial volume effects that occur with MRI data, thus permitting a precise segmentation of these bone regions. At each iteration of the propagation of the model, partial volume is estimated in a narrow band around the deformable model, Our segmentation method begins with a pre-segmentation stage, in which a preliminary segmentation of the skull is constructed using a region-growing method. The surface that bounds the pre-segmented skull region offers an automatic 3D initialization of the deformable model. This surface!

Abstract:   This paper is concerned with the use of the level set formalism to segment anatomical structures in 3D medical images (ultrasound or magnetic resonance images.). A closed 3D surface propagates towards the desired boundaries through the iterative evolution of a 4D implicit function. The major contribution of this work is the design of a robust evolution model based on adaptive parameters depending on the data. First the iteration step and the external propagation force, both usually constant, are automatically computed at each iteration. Additionally, region-based information rather than the gradient is used, via an estimation of intensity probability density functions over the image. As a result, the method can be applied to various kinds of data. Quantitative and qualitative results on brain MR images and 3D echographies of carotid arteries are discussed.

Abstract:   A common challenge for automated segmentation techniques is differentiation between images of close objects that have similar intensities, whose boundaries are often blurred due to partial-volume effects. We propose a novel approach to segmentation of two-dimensional images, which addresses this challenge. Our method, which we call intrinsic shape for segmentation (ISeg), analyzes isolabel-contour maps to identify coherent regions that correspond to major objects. ISeg generates an isolabel-contour map for an image by multilevel thresholding with a fine partition of the intensity range, ISeg detects object boundaries by comparing the shape of neighboring isolabel contours from the map. ISeg requires only little effort from users; it does not require construction of shape models of target objects. In a formal validation with computed-tomography angiography data, we showed that ISeg was more robust than conventional thresholding, and that ISeg's results were comparable to r!

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:   This paper presents a novel method for blending images, Image blending refers to the process of creating a set of discrete samples of a continuous, one-parameter family of images that connects a pair of input images. Image blending has uses in a variety of computer graphics and image processing applications. In particular, it can be used for image morphing, which is a method for creating video streams that depict transformations of objects in scenes based solely on pairs of images and sets of user-defined fiducial points. Image blending also has applications for video compression and image-based rendering.The proposed method for image blending relies on the progressive minimization of a difference metric which compares the level sets between two images. This strategy results in an image blend which is the solution of a pair of coupled, nonlinear, first-order, partial differential equations that model multidimensional level-set propagations. When compared to interpolation !

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:   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 have developed an automated segmentation method for three-dimensional vascular ultrasound images. The method consists of two steps: an automated initial contour identification, followed by application of a geometrically deformable model (GDM). The formation of the initial contours requires the input of a single seed point by the user, and was shown to be insensitive to the placement of the seed within a structure. The GDM minimizes contour energy, providing a smoothed final result. It requires only three simple parameters, all with easily selectable values. The algorithm is fast, performing segmentation on a 336 x 352 x 200 volume in 25 s when running on a 100 MHz 9500 Power Macintosh prototype. The segmentation algorithm was tested on stenosed vessel phantoms with known geometry, and the segmentation of the cross-sectional areas was found to be within 3% of the true area. The algorithm was also applied to two sets of patient carotid images, one acquired with a mechani!

Abstract:   In recent years, the field of active contour-based image segmentation has seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parametric) manner corresponding to the Lagrangian formulation. The second approach represents active contours in an implicit manner corresponding to the Eulerian framework. After comparing these two approaches, we describe several new topological and physical constraints applied to parametric active contours in order to combine the advantages of these two contour representations. More precisely, we introduce three algorithms related to the control of the contour topology, geometry, and deformation. The first algorithm controls both vertex spacing and contour smoothness in an independent and intrinsic manner. The second algorithm controls the contour resolution (number of vertices) while the third algorithm automatically creates or fuses connected components on closed or opened!

Abstract:   In this paper we study evolution of plane curves satisfying a geometric equation v = beta (k,v), where v is the normal velocity and k and are the curvature and tangential angle of a plane curve. We follow the direct approach and we analyze the so-called intrinsic heat equation governing the motion of plane curves obeying such a geometric equation. The intrinsic heat equation is modi ed to include an appropriate nontrivial tangential velocity functional. We show how the presence of a nontrivial tangential velocity can prevent numerical solutions from forming various instabilities. From an analytical point of view we present some new results on short time existence of a regular family of evolving curves in the degenerate case when beta (k,v) = gamma (v)k(m), 0 < m 2, and the governing system of equations includes a nontrivial tangential velocity functional.

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:   Segmenting individual cell nuclei from microscope images normally involves volume labelling of the nuclei with a DNA stain. However, this method often fails when the nuclei are tightly clustered in the tissue, because there is little evidence from the images on where the borders of the nuclei are. In this paper we present a method which solves this limitation and furthermore enables segmentation of whole cells. Instead of using volume stains, we used stains that specifically label the surface of nuclei or cells: lamins for the nuclear envelope and alpha-6 or beta-1 integrins for the cellular surface. The segmentation is performed by identifying unique seeds for each nucleus/cell and expanding the boundaries of the seeds until they reach the limits of the nucleus/cell, as delimited by the lamin or integrin staining, using gradient-curvature flow techniques. We tested the algorithm using computer-generated objects to evaluate its robustness against noise and applied it to c!

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:   Topography simulations are widely used in the microelectronics industry to study the evolution of surface profiles during such processes as deposition or etching. Comparisons between simulations and experiments are used to test proposed transport and chemistry models. The method used to move the surface (the moving algorithm) should not interfere with this testing process; i.e., it should not introduce artifacts. The reference method, shown to be accurate by several groups in many studies, is conservation law based "front tracking." Level set approaches are being increasingly used, largely for their robustness to topological changes. They have not been tested against front tracking to determine their accuracy. In this article, we present guidelines on the use of level set methods for two-dimensional surface evolutions as commonly used. Specifically, we deal with two major issues with level set algorithms: the need for "extension velocities" and the rounding of sharp corne!

Abstract:   Topography simulations are widely used in the microelectronics industry to study the evolution of surface profiles during such processes as deposition or etching. Comparisons between simulations and experiments are used to test proposed transport and chemistry models. The method used to move the surface (the moving algorithm) should not interfere with this testing process; i.e., it should not introduce artifacts. The reference method, shown to be accurate by several groups in many studies, is conservation law based "front tracking." Level set approaches are being increasingly used, largely for their robustness to topological changes. They have not been tested against front tracking to determine their accuracy. In this article, we present guidelines on the use of level set methods for two-dimensional surface evolutions as commonly used. Specifically, we deal with two major issues with level set algorithms: the need for "extension velocities" and the rounding of sharp corne!

Abstract:   This paper presents a strategy for the segmentation of brain from volumetric MR images which integrates 3D segmentation and 3D registration processes. The segmentation process is based on the level set formalism. A closed 3D surface propagates towards the desired boundaries through the iterative evolution of a 4D implicit function. In this work, the propagation relies on a robust evolution model including adaptive parameters. These depend on the input data and on statistical distribution models. The main contribution of this p