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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.
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.
Context Free Attentional Operators: the Generalized Symmetry Transform
 International Journal of Computer Vision
, 1995
"... Active vision systems, and especially foveated vision systems, depend on efficient attentional mechanisms. We propose that machine visual attention should consist of both high level, context dependent components, and low level, context free components. As a basis for the context free component, we p ..."
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Cited by 58 (6 self)
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Active vision systems, and especially foveated vision systems, depend on efficient attentional mechanisms. We propose that machine visual attention should consist of both high level, context dependent components, and low level, context free components. As a basis for the context free component, we present an attention operator based on the intuitive notion of symmetry, which generalizes many of the existing methods for detecting regions of interest. It is a low level operator that can be applied successfully without a priori knowledge of the world. The resulting symmetry edge map can be applied in various low, intermediate and high level tasks, such as extraction of interest points, grouping and object recognition. In particular, we have implemented an algorithm which locates interest points in real time, and can be incorporated in active and purposive vision systems. The results agree with some psychophysical findings concerning symmetry as well as evidence concerning selection of fixation points...
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...
Shape representation using a generalized potential field model
 IEEE TPAMI
, 1997
"... Abstract—This paper is concerned with efficient derivation of the medial axis transform of a twodimensional polygonal region. Instead of using the shortest distance to the region border, a potential field model is used for computational efficiency. The region border is assumed to be charged and the ..."
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Cited by 31 (0 self)
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Abstract—This paper is concerned with efficient derivation of the medial axis transform of a twodimensional polygonal region. Instead of using the shortest distance to the region border, a potential field model is used for computational efficiency. The region border is assumed to be charged and the valleys of the resulting potential field are used to estimate the axes for the medial axis transform. The potential valleys are found by following force field, thus, avoiding twodimensional search. The potential field is computed in closed form using the equations of the border segments. The simple Newtonian potential is shown to be inadequate for this purpose. A higher order potential is defined which decays faster with distance than as inverse of distance. It is shown that as the potential order becomes arbitrarily large, the axes approach those computed using the shortest distance to the border. Algorithms are given for the computation of axes, which can run in linear parallel time for part of the axes having initial guesses. Experimental results are presented for a number of examples. Index Terms—Generalized potential, Newtonian potential, topology, medial axis, symmetric axis transform, skeletonization, distance
Symmetry and Asymmetry from Local Phase
 Tenth Australian Joint Converence on Artificial Intelligence
, 1997
"... . Symmetry is an important mechanism by which we identify the structure of objects. Manmade objects, plants and animals are usually highly recognizable from the symmetry, or partial symmetries that they often exhibit. Two difficulties found in most symmetry detection algorithms are firstly, that ..."
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Cited by 28 (1 self)
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. Symmetry is an important mechanism by which we identify the structure of objects. Manmade objects, plants and animals are usually highly recognizable from the symmetry, or partial symmetries that they often exhibit. Two difficulties found in most symmetry detection algorithms are firstly, that they usually require objects to be segmented prior to any symmetry analysis, and secondly, that they do not provide any absolute measure of the degree of symmetry at any point in an image. This paper presents a new measure of symmetry that is based on the analysis of local frequency information. It is shown that points of symmetry and asymmetry give rise to easily recognized patterns of local phase. This phase information can be used to construct a contrast invariant measure of symmetry that does not require any prior recognition or segmentation of objects. Keywords: Computer Vision, Symmetry, Asymmetry, Local Phase, Quadrature Filters 1 Introduction Under the most general definiti...
Robot Localization using a Computer Vision Sextant
 In Proc. IEEE Intl. Conf. on Robotics and Automation
, 1995
"... This paper explores the possibility of using Sun altitude for localization of a robot in totally unknown territory. A set of Sun altitudes is obtained by processing a sequence of timeindexed images of the sky. Each altitude constrains the viewer to a circle on the surface of a celestial body, calle ..."
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Cited by 22 (2 self)
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This paper explores the possibility of using Sun altitude for localization of a robot in totally unknown territory. A set of Sun altitudes is obtained by processing a sequence of timeindexed images of the sky. Each altitude constrains the viewer to a circle on the surface of a celestial body, called the circle of equal altitude. A set of circles of equal altitude can be intersected to yield viewer position. We use this principle to obtain position on Earth. Since altitude measurements are corrupted by noise, a leastsquare estimate is numerically calculated from the sequence of altitudes. The paper discusses the necessary theory for Sunbased localization, the technical issues of camera calibration and image processing, and presents preliminary results with real data. 1 Introduction This work addresses the problem of robot localization: how can a robot make precise measurements of position in totally unknown territory? We focus on the use of celestial cues in order to obtain localiza...
Skeleton Graph Generation for Feature Shape Description
 IN JOINT EUROGRAPHICS–IEEE TCVG SYMPOSIUM ON VISUALIZATION
, 2000
"... An essential step in feature extraction is the calculation of attribute sets describing the characteristics of a feature. Often, attribute sets include the position, size, and orientation of the feature. These attributes are very important, but they do not provide a good approximation of the sh ..."
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Cited by 15 (2 self)
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An essential step in feature extraction is the calculation of attribute sets describing the characteristics of a feature. Often, attribute sets include the position, size, and orientation of the feature. These attributes are very important, but they do not provide a good approximation of the shape of a feature. For better shape description, a more sophisticated method is needed. This paper describes a method that extracts a binary skeleton of a feature, and transforms it into a graphical representation: the skeletongraph. This graph represents the original skeleton with controlled precision, and contains the essential topology and geometry of the skeleton. In addition, distance information is used to generate a simplified reconstruction of the original 3D feature shape, which can also be used as an iconic object for visualization.
Finding Shape Axes using Magnetic Fields
, 1998
"... In this paper we present a novel method for obtaining the axes of shapes. The method is based on directional information of the shape's boundary. By simulating a parallel algorithm, we are able to generate the inner as well as the outer axes (axes of concavities) of the shape. The preprocessing phas ..."
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Cited by 7 (1 self)
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In this paper we present a novel method for obtaining the axes of shapes. The method is based on directional information of the shape's boundary. By simulating a parallel algorithm, we are able to generate the inner as well as the outer axes (axes of concavities) of the shape. The preprocessing phase for this algorithm involves obtaining the shape's gradient. Each point of the gradient is substituted by a minute magnetic dipole. The cumulative magnetic field due to these dipoles is accumulated at all points in the image in a onepass algorithm. The magnitude of the final magnetic vector field has valleys that are created from mutual and directionally balanced cancellations of opposing boundary segments. These valleys signify the axes of the shape. The axes are obtained by performing a valley search. Our algorithm has the advantage over previous approaches since it utilizes not only the location information of the boundary, but also its directional information. INDEX TERMS: shape axes, ...
FeatureBased Visualization of TimeDependent Data
, 2001
"... L. Lagendijk, Technische Universiteit Delft Prof.dr.ir. F.T.M. Nieuwstadt, Technische Universiteit Delft Prof.dr.ir. F.C.A. Groen, Universiteit van Amsterdam Prof.dr. D. Silver, Rutgers University Dr.H.J.W.Spoelder, VrijeUniversiteitAmsterdam Preface The research described in this thesis was c ..."
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Cited by 6 (0 self)
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L. Lagendijk, Technische Universiteit Delft Prof.dr.ir. F.T.M. Nieuwstadt, Technische Universiteit Delft Prof.dr.ir. F.C.A. Groen, Universiteit van Amsterdam Prof.dr. D. Silver, Rutgers University Dr.H.J.W.Spoelder, VrijeUniversiteitAmsterdam Preface The research described in this thesis was carried out at the Computer Graphics & CAD/CAM group of Delft University of Technology. It is the fifth PhD project in a series of projects on visualization. The project was supervised by Frits Post (TU Delft) and Hans Spoelder (VU Amsterdam), and was supported by the Netherlands Computer Science Research Foundation (SION), with financial support of the Netherlands Organization for Scientific Research (NWO). The research concentrated on featurebased visualization techniques. Feature based visualization is particularly suited to visualize large data sets, such as timedependent data. It directs the attention to interesting phenomena (features) in the data; the objective is to extract, quan