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505
A Dynamic Finite Element Surface Model for Segmentation and Tracking in Multidimensional Medical Images with Application to Cardiac 4D Image Analysis
 Computerized Medical Imaging and Graphics
, 1995
"... This paper presents a physicsbased approach to anatomical surface segmentation, reconstruction, and tracking in multidimensional medical images. The approach makes use of a dynamic "balloon" modela spherical thinplate under tension surface spline which deforms elastically to fit the i ..."
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Cited by 118 (6 self)
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This paper presents a physicsbased approach to anatomical surface segmentation, reconstruction, and tracking in multidimensional medical images. The approach makes use of a dynamic "balloon" modela spherical thinplate under tension surface spline which deforms elastically to fit the image data. The fitting process is mediated by internal forces stemming from the elastic properties of the spline and external forces which are produced from the data. The forces interact in accordance with Lagrangian equations of motion that adjust the model's deformational degrees of freedom to fit the data. We employ the finite element method to represent the continuous surface in the form of weighted sums of local polynomial basis functions. We use a quintic triangular finite element whose nodal variables include positions as well as the first and second partial derivatives of the surface. We describe a system, implemented on a high performance graphics workstation, which applies the model fitting ...
General Object Reconstruction based on Simplex Meshes
, 1999
"... 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 e cient manner. Our reconst ..."
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Cited by 112 (16 self)
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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 e cient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The di erent 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 modi ed by creating holes or by increasing its genus. Finally, aniterativere nement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality. Several reconstruction examples are provided with quantitative and qualitative results.
A topology preserving level set method for geometric deformable models
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implement ..."
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Cited by 90 (5 self)
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Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models—the ability to automatically handle topology changes—turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved. In this paper, we present a new class of geometric deformable models designed using a novel topologypreserving level set method, which achieves topology preservation by applying the simple point concept from digital topology. These new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces. Moreover, since the topologypreserving constraint is enforced efficiently through local computations, the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models. Several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm.
Fast extraction of minimal paths in 3D images and applications to virtual endoscopy
, 2001
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A Finite Element Model for 3D Shape Reconstruction and Nonrigid Motion Motion
 Proc. 2nd ICCV
, 1991
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A common framework for curve evolution, segmentation and anisotropic diffusion
 In Proceedings IEEE CVPR'96
, 1996
"... Abstract1 In recent years, curve evolution has developed into an important tool in Computer Vision and has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. The underlying principle is the evolution of a simple closed curve whose points move i ..."
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Cited by 79 (9 self)
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Abstract1 In recent years, curve evolution has developed into an important tool in Computer Vision and has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. The underlying principle is the evolution of a simple closed curve whose points move in the direction of the normal with prescribed velocity. A fundamental limitation of the method as it stands is that it cannot deal with important image features such as triple points. The method also requires a choice of an “edgestrength ” function, defined over the image domain, indicating the likelihood of an object boundary being present at any point in the image domain. This implies a separate preprocessing step, in essence precomputing approximate boundaries in the presence of noise. One also has to choose the initial curve. It is shown here that the different versions of curve evolution used in Computer Vision together with the preprocessing step can be integrated in the form of a new segmentation functional which overcomes these limitations and extends curve evolution models. Moreover, the numerical solutions obtained retain sharp discontinuities or “shocks”, thus providing sharp demarcation of object boundaries. 1.
Topology Adaptive Deformable Surfaces for Medical Image Volume Segmentation
 IEEE Transactions on Medical Imaging
, 1999
"... Deformable models, which include deformable contours (the popular "snakes") and deformable surfaces, are a powerful modelbased medical image analysis technique. We develop a new class of deformable models by formulating deformable surfaces in terms of an Affine Cell Image Decomposition (A ..."
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Cited by 74 (1 self)
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Deformable models, which include deformable contours (the popular "snakes") and deformable surfaces, are a powerful modelbased 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 ACIDbased deformable surfaces, dubbed "Tsurfaces", can effectively segment complex anatomic structures from medical volume images. KeywordsSegmentation, deformable models, deformable surfaces. I. Introduction The imperfections typical of medical images, such as partial volume averaging, intensity inhomogeneities, limited resolution, and i...
Minimal Surfaces Based Object Segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... 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 m ..."
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Cited by 72 (13 self)
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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. Index Terms3D segmentation, minimal surfaces, deformable models, mean curvature motion, medical images.  F  1I NTRODUCTION ONE of the basic problems in image analysis is object detection. It can be associated with the problem of boundary detection, when boundaries are defined as curves or surfaces separating homogeneous regions. "Snakes," or active contours, were proposed by Kass et al. in [16] to solve this problem, and were later extended to 3D surfaces. The classical snakes and 3D deformable surfaces approach are based on deforming an initial contour or surface towards the boundary of the object to be detected. The deformation is obtained by minimizing a functional designed so that its (local) minima is at the boundary of the object [3], [33]. The energy usually involves two terms, one that controls the smoothness of the surface and the other that attracts it to the object's boundary. The topology of the final surface is, in general, as that of the initial one, unless special procedures are used to detect possible spli...
Coupled Geodesic Active Regions for Image Segmentation: A Level Set Approach
 In European Conference in Computer Vision
, 1999
"... . This paper presents a novel variational method for image segmentation that unifies boundary and regionbased information sources under the Geodesic Active Region framework. A statistical analysis based on the Minimum Description Length criterion and the Maximum Likelihood Principle for the obs ..."
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Cited by 72 (2 self)
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. This paper presents a novel variational method for image segmentation that unifies boundary and regionbased information sources under the Geodesic Active Region framework. A statistical analysis based on the Minimum Description Length criterion and the Maximum Likelihood Principle for the observed density function (image histogram) using a mixture of Gaussian elements, indicates the number of the different regions and their intensity properties. Then, the boundary information is determined using a probabilistic edge detector, while the region information is estimated using the Gaussian components of the mixture model. The defined objective function is minimized using a gradientdescent method where a level set approach is used to implement the resulting PDE system. According to the motion equations, the set of initial curves is propagated toward the segmentation result under the influence of boundary and regionbased segmentation forces, and being constrained by a regul...
Stereoscopic Segmentation
, 2001
"... We cast the problem of multiframe stereo reconstruction of a smooth shape as the global region segmentation of a collection of images of the scene. Dually, the problem of segmenting multiple calibrated images of an object becomes that of estimating the solid shape that gives rise to such images. We ..."
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Cited by 70 (17 self)
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We cast the problem of multiframe stereo reconstruction of a smooth shape as the global region segmentation of a collection of images of the scene. Dually, the problem of segmenting multiple calibrated images of an object becomes that of estimating the solid shape that gives rise to such images. We assume that the radiance has smooth statistics. This assumption covers Lambertian scenes with smooth or constant albedo as well as fine homogeneous textures, which are known challenges to stereo algorithms based on local correspondence. We pose the segmentation problem within a variational framework, and use fast level set methods to approximate the optimal solution numerically. Our algorithm does not work in the presence of strong textures, where traditional reconstruction algorithms do. It enjoys significant robustness to noise under the assumptions it is designed for. 1