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57
A Survey of Shape Analysis Techniques
 Pattern Recognition
, 1998
"... This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems. ..."
Abstract

Cited by 200 (2 self)
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This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.
Hierarchic Voronoi Skeletons
, 1995
"... Robust and timeefficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape's boundary points, i.e., by removal of noisesensitive parts of the tessellation and then by estab ..."
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Cited by 122 (3 self)
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Robust and timeefficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape's boundary points, i.e., by removal of noisesensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents. Each component of the VD is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise. The second processing step, a hierarchic clustering of skeleton branches, leads to a multiresolution representation of the skeleton, termed skeleton pyramid.
HamiltonJacobi Skeletons
, 1999
"... The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shapefromshading and for recent dynamic theories of shape. Its numerical simulation can be delicate, ..."
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Cited by 119 (12 self)
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The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shapefromshading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front and is typically based on level set methods. However, there are more classical approaches rooted in Hamiltonian physics which have yet to be widely used by the computer vision community. In this paper we review the Hamiltonian formulation, which offers specific advantages when it comes to the detection of singularities or shocks. We specialize to the case of Blum's grass fire flow and measure the average outward ux of the vector field that underlies the Hamiltonian system. This measure has very different limiting behaviors depending upon whether the region over which it is computed shrinks to a singular point or a nonsingular one. Hence, it is an effective way to distinguish between these two cases. We combine the ux measurement with a homotopy preserving thinning process applied in a discrete lattice. This leads to a robust and accurate algorithm for computing skeletons in 2D as well as 3D, which has low computational complexity. We illustrate the approach with several computational examples.
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.
Voronoi Skeletons: Theory and Applications
 in Proc. Conf. on Computer Vision and Pattern Recognition
, 1992
"... The paper presents a novel method of robust skeletonization based on the Voronoi diagram (VD) of boundary points, which is characterized by correct Euclidean metrics and inherent preservation of connectivity. The regularization of the Voronoi medial axis (VMA) in the sense of Blum's prairie fire ana ..."
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Cited by 57 (6 self)
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The paper presents a novel method of robust skeletonization based on the Voronoi diagram (VD) of boundary points, which is characterized by correct Euclidean metrics and inherent preservation of connectivity. The regularization of the Voronoi medial axis (VMA) in the sense of Blum's prairie fire analogy is done by attributing each component of the VMA with a measure of prominence and stability. The resulting Voronoi skeletons (VSK) appear largely invariant with respect to typical noise conditions in the image and geometric transformations. Hierarchical clustering of the skeleton branches, the socalled skeleton pyramid, leads to further simplification of the skeleton. Several applications demonstrate the suitability of the Voronoi skeleton to higher order tasks such as object recognition. 1 Introduction During the last decades, skeletonization or thinning has been a constant research topic. The concept of skeletonization denotes a process, which transforms a 2D object into a 1D lin...
A Fast Level Set based Algorithm for TopologyIndependent Shape Modeling
 Journal of Mathematical Imaging and Vision, special issue on Topology and
"... Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains the most attractive features of existing methods, and overco ..."
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Cited by 33 (1 self)
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Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains the most attractive features of existing methods, and overcomes their prominent limitations. Our technique can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object's topology is made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher & Sethian to model propagating solid/liquid interfaces with curvaturedependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature...
Flux Invariants for Shape
 In CVPR
, 2003
"... We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, ..."
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Cited by 28 (3 self)
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We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, this measure has very different behaviours at medial points than at nonmedial ones, providing a theoretical justification for its use in the HamiltonJacobi skeletonization algorithm of [7]. We then specialize to the case of shrinking circular neighborhoods and show that the average outward flux measure also reveals the object angle at skeletal points. Hence, formulae for obtaining the boundary curves, their curvatures, and other geometric quantities of interest, can be written in terms of the average outward flux limit values at skeletal points. Thus this measure can be viewed as a Euclidean invariant for shape description: it can be used to both detect the skeleton from the Euclidean distance function, as well as to explicitly reconstruct the boundary from it. We illustrate our results with several numerical simulations. 1.
Computing hierarchical curveskeletons of 3d objects
 The Visual Computer
, 2005
"... A curveskeleton of a 3D object is a sticklike figure or centerline representation of that object. It is used for diverse applications, including virtual colonoscopy and animation. In this paper we introduce the concept of hierarchical curveskeleton and describe a general and robust methodology wh ..."
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Cited by 28 (1 self)
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A curveskeleton of a 3D object is a sticklike figure or centerline representation of that object. It is used for diverse applications, including virtual colonoscopy and animation. In this paper we introduce the concept of hierarchical curveskeleton and describe a general and robust methodology which computes a family of increasingly detailed curveskeletons. The algorithm is based upon computing a repulsive force field over a discretization of the 3D object and using topological characteristics of the resulting vector field, such as critical points and critical curves, to extract the curveskeleton. We demonstrate this method on many different types of 3D objects (volumetric, polygonal and scattered point sets) and discuss various extensions of this approach.
Skeletonization via Distance Maps and Level Sets
 Computer Vision and Image Understanding
, 1995
"... The medial axis transform (MAT) of a shape, better known as its skeleton, is frequently used in shape analysis and related areas. In this paper a new approach for determining the skeleton of an object, is presented. The boundary is segmented at points of maximal positive curvature and a distance map ..."
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Cited by 23 (1 self)
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The medial axis transform (MAT) of a shape, better known as its skeleton, is frequently used in shape analysis and related areas. In this paper a new approach for determining the skeleton of an object, is presented. The boundary is segmented at points of maximal positive curvature and a distance map from each of the segments is calculated. The skeleton is then located by applying simple rules to the zero sets of distance maps differences. A framework is proposed for numerical approximation of distance maps that is consistent with the continuous case, hence does not suffer from digitization bias due to metrication errors of the implementation on the grid. Subpixel accuracy in distance map calculation is obtained by using gray level information along the boundary of the shape in the numerical scheme. The accuracy of the resulting efficient skeletonization algorithm is demonstrated by several examples. Keywords: Differential Geometry, Distance Map, Medial Axis Transform, Shape Analysis, S...
Skeleton Extraction of 3D Objects with Radial Basis Functions
 Proceedings of Shape Modeling International 2003
, 2003
"... Skeleton is a lower dimensional shape description of an object. The requirements of a skeleton di#er with applications. For example, object recognition requires primitive features to make similarity comparison. On the other hand, detailed geometry descriptions are essential to reduce the approximati ..."
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Cited by 21 (3 self)
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Skeleton is a lower dimensional shape description of an object. The requirements of a skeleton di#er with applications. For example, object recognition requires primitive features to make similarity comparison. On the other hand, detailed geometry descriptions are essential to reduce the approximation error for surface reconstruction. Whereas many previous works have been done, most of these methods are time consuming and sensitive to noise, or restricted to specific 3D models.