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178
Deformable models in medical image analysis: A survey
 Medical Image Analysis
, 1996
"... This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They hav ..."
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Cited by 478 (7 self)
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This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottomup) constraints derived from the image data together with (topdown) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.
Topologically Adaptable Snakes
 Medical Image Analysis
, 1995
"... This paper presents a topologically adaptable snakes model for image segmentation and object representation. The model is embedded in the framework of domain subdivision using simplicial decomposition. This framework extends the geometric and topological adaptability of snakes while retaining all of ..."
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Cited by 202 (5 self)
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This paper presents a topologically adaptable snakes model for image segmentation and object representation. The model is embedded in the framework of domain subdivision using simplicial decomposition. This framework extends the geometric and topological adaptability of snakes while retaining all of the features of traditionalsnakes, such as user interaction, and overcoming many of the limitations of traditionalsnakes. By superposing a simplicial grid over the image domain and using this grid to iteratively reparameterize the deforming snakes model, the model is able to flow into complex shapes, even shapes with significant protrusions or branches, and to dynamically change topology as necessitated by the data. Snakes can be created and can split into multiple parts or seamlessly merge into other snakes. The model can also be easily converted to and from the traditional parametric snakes model representation. We apply a 2D model to various synthetic and real images in order to segment ...
Global Minimum for Active Contour Models: A Minimal Path Approach
, 1997
"... A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the ..."
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Cited by 202 (64 self)
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A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the internal regularization term in the external potential term. Our method is based on finding a path of minimal length in a Riemannian metric. We then make use of a new efficient numerical method to find this shortest path. It is shown that the proposed energy, though based only on a potential integrated along the curve, imposes a regularization effect like snakes. We explore the relation between the maximum curvature along the resulting contour and the potential generated from the image. The method is capable to close contours, given only one point on the objects’ boundary by using a topologybased saddle search routine. We show examples of our method applied to real aerial and medical images.
A survey of deformable modeling in computer graphics
, 1997
"... This paper presents a survey of the work done in modeling deformable objects within the computer graphics research community. The research has a long history and a wide variety of approaches have been used. This paper organizes the diversity of research by the technique used rather than by the appli ..."
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Cited by 166 (1 self)
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This paper presents a survey of the work done in modeling deformable objects within the computer graphics research community. The research has a long history and a wide variety of approaches have been used. This paper organizes the diversity of research by the technique used rather than by the application, although applications are discussed throughout. This paper presents some purely geometric approaches for modeling deformable objects, but focuses on physically based approaches. In the latter category are massspring models, nite element models, approximate continuum models, and low degree of freedom models. Special emphasis is placed on nite element models, which o er the greatest accuracy, but have seen limited use in computer graphics. The paper also suggests important areas for future research. 1
Computable elastic distances between shapes
 SIAM J. of Applied Math
, 1998
"... Abstract. We define distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally defined from a left invariant Riemannian distance on an infinite dimensional group acting on the curves, which can be explicitly comp ..."
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Cited by 124 (19 self)
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Abstract. We define distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally defined from a left invariant Riemannian distance on an infinite dimensional group acting on the curves, which can be explicitly computed. The obtained distance boils down to a variational problem for which an optimal matching between the curves has to be computed. An analysis of the distance when the curves are polygonal leads to a numerical procedure for the solution of the variational problem, which can efficiently be implemented, as illustrated by experiments.
Medical image analysis: progress over two decades and the challenges ahead
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2000
"... AbstractThe 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 techniquss lo another ..."
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Cited by 95 (5 self)
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AbstractThe 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 techniquss lo 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 dlscipline in its own right. Examples of these include: the types of image information that are acquired, the fully threedimensional 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 fiold over the last 20 years and suggest some of the challenges that remain for the years to come.
A Shrink Wrapping Approach to Remeshing Polygonal Surfaces
, 1999
"... Due to their simplicity and flexibility, polygonal meshes are about to become the standard representation for surface geometry in computer graphics applications. Some algorithms in the context of multiresolution representation and modeling can be performed much more efficiently and robustly if the ..."
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Cited by 78 (13 self)
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Due to their simplicity and flexibility, polygonal meshes are about to become the standard representation for surface geometry in computer graphics applications. Some algorithms in the context of multiresolution representation and modeling can be performed much more efficiently and robustly if the underlying surface tesselations have the special subdivision connectivity. In this paper, we propose a new algorithm for converting a given unstructured triangle mesh into one having subdivision connectivity. The basic idea is to simulate the shrink wrapping process by adapting the deformable surface technique known from image processing. The resulting algorithm generates subdivision connectivity meshes whose base meshes only have a very small number of triangles. The iterative optimization process that distributes the mesh vertices over the given surface geometry guarantees low local distortion of the triangular faces. We show several examples and applications including the progressi...
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...
Segmentation of Brain Tissue from Magnetic Resonance Images
, 1995
"... Segmentation of medical imagery is a challenging problem due to the complexity of the images, as well as to the absence of models of the anatomy that fully capture the possible deformations in each structure. Brain tissue is a particularly complex structure, and its segmentation is an important step ..."
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Cited by 61 (3 self)
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Segmentation of medical imagery is a challenging problem due to the complexity of the images, as well as to the absence of models of the anatomy that fully capture the possible deformations in each structure. Brain tissue is a particularly complex structure, and its segmentation is an important step for many problems, including studies in temporal change detection of morphology, and 3D visualizations for surgical planning. We present a method for segmentation of brain tissue from magnetic resonance images that is a combination of three existing techniques from the Computer Vision literature: Expectation /Maximization segmentation, binary mathematical morphology, and active contour models. Each of these techniques has been customized for the problem of brain tissue segmentation such that the resultant method is more robust than its components. Finally, we present the results of a parallel implementation of this method on
Interactive organ segmentation using graph cuts
 In Medical Image Computing and ComputerAssisted Intervention
, 2000
"... Abstract. An Ndimensional image is divided into “object ” and “background” segments using a graph cut approach. A graph is formed by connecting all pairs of neighboring image pixels (voxels) by weighted edges. Certain pixels (voxels) have to be a priori identified as object or background seeds prov ..."
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Cited by 61 (1 self)
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Abstract. An Ndimensional image is divided into “object ” and “background” segments using a graph cut approach. A graph is formed by connecting all pairs of neighboring image pixels (voxels) by weighted edges. Certain pixels (voxels) have to be a priori identified as object or background seeds providing necessary clues about the image content. Our objective is to find the cheapest way to cut the edges in the graph so that the object seeds are completely separated from the background seeds. If the edge cost is a decreasing function of the local intensity gradient then the minimum cost cut should produce an object/background segmentation with compact boundaries along the high intensity gradient values in the image. An efficient, globally optimal solution is possible via standard mincut/maxflow algorithms for graphs with two terminals. We applied this technique to interactively segment organs in various 2D and 3D medical images. 1