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16
Skeleton Based Shape Matching and Retrieval
, 2003
"... In this paper, we describe a novel method for searching and comparing 3D objects. The method encodes the geometric and topological information in the form of a skeletal graph and uses graph matching techniques to match the skeletons and to compare them. The skeletal graphs can be manually annotated ..."
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Cited by 100 (1 self)
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In this paper, we describe a novel method for searching and comparing 3D objects. The method encodes the geometric and topological information in the form of a skeletal graph and uses graph matching techniques to match the skeletons and to compare them. The skeletal graphs can be manually annotated to refine or restructure the search. This helps in choosing between a topological similarity and a geometric (shape) similarity. A feature of skeletal matching is the ability to perform partmatching, and its inherent intuitiveness, which helps in defining the search and in visualizing the results. Also, the matching results, which are presented in a pernode basis can be used for driving a number of registration algorithms, most of which require a good initial guess to perform registration. In this paper, we also describe a visualization tool to aid in the selection and specification of the matched objects.
An Active Contour Model For Mapping The Cortex
 IEEE TRANS. ON MEDICAL IMAGING
, 1995
"... A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approac ..."
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Cited by 64 (13 self)
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A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approach are proposed to achieve this goal. The primary difference between this formulation and that of snakes is in the specification of the external force acting on the active contour. A study of the uniqueness and fidelity of solutions is made through convexity and frequency domain analyses, and a criterion for selection of the regularization coefficient is developed. Examples demonstrating the performance of this method on simulated and real data are provided.
Euclidean Skeletons
, 1998
"... We present a new method for the skeletonization of 2dimensional or 3dimensional objects. First, we introduce two local measures, φ and d, to characterize skeleton points, whose good localization is ensured by Euclidean distance mapping techniques. These measures allow us to control the detail ..."
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Cited by 40 (2 self)
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We present a new method for the skeletonization of 2dimensional or 3dimensional objects. First, we introduce two local measures, φ and d, to characterize skeleton points, whose good localization is ensured by Euclidean distance mapping techniques. These measures allow us to control the detail of the resulting skeleton. Thresholding these measures generally does not yield welldefined skeleton: a low threshold preserves the original object's topology but produces a noisesensitive skeleton, while a higher threshold produces a more robust skeleton but it is generally not homotopic with the original object it comes from. To overcome these drawbacks, more complex measures can be introduced. Although they generally yield good experimental results, they are still sensitive to noise. Instead, we introduce a global step, called topological reconstruction, which will provide the skeleton with robustness with respect to noise and ensure homotopy with the original object. Moreover, this method is not...
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
 Algorithmica
, 2004
"... The medial axis of a surface in 3D is the closure of all points that have two or more closest points on the surface. It is an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue ..."
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Cited by 34 (7 self)
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The medial axis of a surface in 3D is the closure of all points that have two or more closest points on the surface. It is an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to improve their approximations. Voronoi diagrams turn out to be useful for this approximation. Although it is known that Voronoi vertices for a sample of points from a curve in 2D approximate its medial axis, similar result does not hold in 3D. Recently, it has been discovered that only a subset of Voronoi vertices converge to the medial axis as sample density approaches infinity. However, most applications need a nondiscrete approximation as opposed to a discrete one. To date no known algorithm can compute this approximation straight from the Voronoi diagram with a guarantee of convergence. We present such an algorithm and its convergence analysis in this paper. One salient feature of the algorithm is that it is scale and density independent. Experimental results corroborate our theoretical claims.
An augmented fast marching method for computing skeletons and centerlines
 in Proc. of the Symposium on Data Visualisation (VisSymâ€™02), 2002
"... We present a simple and robust method for computing skeletons for arbitrary planar objects and centerlines for 3D objects. We augment the Fast Marching Method (FMM) widely used in level set applications 11 by computing the paramterized boundary location every pixel came from during the boundary evol ..."
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Cited by 30 (6 self)
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We present a simple and robust method for computing skeletons for arbitrary planar objects and centerlines for 3D objects. We augment the Fast Marching Method (FMM) widely used in level set applications 11 by computing the paramterized boundary location every pixel came from during the boundary evolution. The resulting parameter field is then thresholded to produce the skeleton branches created by boundary features of a given size. The presented algorithm is straightforward to implement, has low memory costs and short execution times, and is robust with respect to the used threshold and initial shape noisiness. The produced skeletons are very similar to the ones delivered by more complex algorithms. Various 2D and 3D applications are presented. 1.
Curveskeleton applications
 in Proc. IEEE Visualization, 2005
"... Curveskeletons are a 1D subset of the medial surface of a 3D object and are useful for many visualization tasks including virtual navigation, reducedmodel formulation, visualization improvement, mesh repair, animation, etc. There are many algorithms in the literature describing extraction methodol ..."
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Cited by 22 (1 self)
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Curveskeletons are a 1D subset of the medial surface of a 3D object and are useful for many visualization tasks including virtual navigation, reducedmodel formulation, visualization improvement, mesh repair, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are. In this paper, we provide an overview of many curveskeleton applications and compile a set of desired properties of such representations. We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms.
Parameter Controlled Skeletonization of Three Dimensional Objects
, 1997
"... Skeletons are useful shape abstractions and have varied applications in visualization. The complexity of the desired skeletal structure depends on the application. Current techniques for extracting skeletons do not allow control over the complexity. In this paper, we describe an algorithm which ..."
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Cited by 10 (2 self)
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Skeletons are useful shape abstractions and have varied applications in visualization. The complexity of the desired skeletal structure depends on the application. Current techniques for extracting skeletons do not allow control over the complexity. In this paper, we describe an algorithm which uses a thinness parameter to control the density of the skeleton. We present applications from CFD and medical visualization and show how the skeletal structure can be used in these domains. We also illustrate a technique which uses the skeleton to extract the centerline for surgical navigation. Keywords:Scientific Visualization, Medical Visualization, Skeleton, Volume Thinning, Centerline, Surgical Navigation ii Acknowledgement The research reported here was made possible through the support of the New Jersey Commission on Science and Technology and the CAIP Center's Industrial Members. The work for this paper was done at the Laboratory for Visiometrics and Modeling at Rutgers ...
Efficient and Robust Computation of an Approximated Medial Axis
 In Proceedings of the ACM Symposium on Solid Modeling and Applications
, 2004
"... The medial axis can be viewed as a compact representation for an arbitrary model; it is an essential geometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding up its computation and at addressing its instabilities. In this paper we pro ..."
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Cited by 7 (1 self)
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The medial axis can be viewed as a compact representation for an arbitrary model; it is an essential geometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding up its computation and at addressing its instabilities. In this paper we propose a new algorithm to compute the medial axis with arbitrary precision. It exhibits several desirable properties not previously combined in a practical and efficient algorithm. First, it allows for a tradeoff between computation time and accuracy, making it wellsuited for applications in which an approximation of the medial axis suffices, but computational efficiency is of particular concern. Second, it is output sensitive: the computation complexity of the algorithm does not depend on the size of the representation of a model, but on the size of the representation of the resulting medial axis. Third, the densities of the approximated medial axis points in different areas are adaptive to local free space volumes, based on the assumption that a coarser approximation in wide open area can still suffice the requirements of the applications. We present theoretical results, bounding the error introduced by the approximation process. The algorithm has been implemented and experimental results are presented that illustrate its computational efficiency and robustness.
2D Shape Decomposition And The Automatic Generation Of Hierarchical Representations
"... This paper presents a ..."
Discrete Medial Axis Transform for Discrete Objects
, 1998
"... this report, a Discrete Medial Axis definition is proposed as a direct extension of Blum's definition in order to achieve a complete and compressed model representation of discrete objects which retains the significant features of the object without introducing distorsions of its own. Moreover, it p ..."
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Cited by 4 (2 self)
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this report, a Discrete Medial Axis definition is proposed as a direct extension of Blum's definition in order to achieve a complete and compressed model representation of discrete objects which retains the significant features of the object without introducing distorsions of its own. Moreover, it preserves the axis connectivity and it is based on local properties of the Distance Map which enable to design a seed algorithm for its construction whose cost is linear with the size of the object.