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581
Computing Geodesic Paths on Manifolds
 Proc. Natl. Acad. Sci. USA
, 1998
"... The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. A ..."
Abstract

Cited by 294 (28 self)
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. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds. 1 Introduction Sethian`s Fast Marching Method [8], is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M
Sparse Geodesic Paths
, 2009
"... In this paper we propose a new distance metric for signals that admit a sparse representation in a known basis or dictionary. The metric is derived as the length of the sparse geodesic path between two points, by which we mean the shortest path between the points that is itself sparse. We show that ..."
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Cited by 1 (1 self)
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In this paper we propose a new distance metric for signals that admit a sparse representation in a known basis or dictionary. The metric is derived as the length of the sparse geodesic path between two points, by which we mean the shortest path between the points that is itself sparse. We show
Geodesic paths on triangular meshes
 In Proc. of SIBGRAPI/SIACG
, 2004
"... Abstract. We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian’s Fast Marching Method and Polthier’s Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex and no ..."
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Cited by 6 (0 self)
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Abstract. We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian’s Fast Marching Method and Polthier’s Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex
Geodesic Paths on Triangular Meshes
 In Proc. of SIBGRAPI/SIACG
, 2004
"... We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian's Fast Marching Method and Polthier's Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex and no ..."
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We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian's Fast Marching Method and Polthier's Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex
on Geodesic Paths in Skeleton Graphs
"... any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI ..."
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any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress CataloginginPublication Data Graphbased methods in computer vision: developments and applications / Xiao Bai, Jian Cheng, and Edwin Hancock, editors. p. cm. Includes bibliographical references and index.
Curves matching using geodesic paths
 IEEE Proc. of Computer Vision and Pattern Recognition
, 1998
"... We present a method for matching curves which accommodates large and small deformation. The method preserves geometric similarities in the case of small deformation, and loosens these geometric constraints when large deformations occur. The approach is based on the computation of a set of geodesic p ..."
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Cited by 18 (6 self)
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We present a method for matching curves which accommodates large and small deformation. The method preserves geometric similarities in the case of small deformation, and loosens these geometric constraints when large deformations occur. The approach is based on the computation of a set of geodesic
A Survey of Geodesic Paths on 3D Surfaces
, 2011
"... This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on threedimensional surfaces. The survey focuses on threedimensional polyhedral surfaces. The goal of this survey is to identify the most relevant open problems, both the ..."
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Cited by 6 (2 self)
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This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on threedimensional surfaces. The survey focuses on threedimensional polyhedral surfaces. The goal of this survey is to identify the most relevant open problems, both
ESTIMATION OF TORTUOSITY AND RECONSTRUCTION OF GEODESIC PATHS IN 3D
, 2012
"... The morphological tortuosity of a geodesic path in a medium can be defined as the ratio between its geodesic length and the Euclidean distance between its two extremities. Thus, the minimum tortuosity of all the geodesic paths into a medium in 2D or in 3D can be estimated by image processing methods ..."
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The morphological tortuosity of a geodesic path in a medium can be defined as the ratio between its geodesic length and the Euclidean distance between its two extremities. Thus, the minimum tortuosity of all the geodesic paths into a medium in 2D or in 3D can be estimated by image processing
Visibility in Discrete Geometry: an application to discrete geodesic paths
, 2002
"... In this article, we present a discrete definition of the classical visibility in computational geometry. We present algorithms to compute the set of pixels in a nonconvex domain that are visible from a source pixel. Based on these definitions, we define discrete geodesic paths in discrete domain ..."
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Cited by 2 (0 self)
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In this article, we present a discrete definition of the classical visibility in computational geometry. We present algorithms to compute the set of pixels in a nonconvex domain that are visible from a source pixel. Based on these definitions, we define discrete geodesic paths in discrete domain
Heuristically driven front propagation for geodesic paths extraction
 In Proceedings of VLSM’05
"... Abstract. In this paper we present a simple modification of the Fast Marching algorithm to speed up the computation using a heuristic. This modification leads to an algorithm that is similar in spirit to the A ∗ algorithm used in artificial intelligence. Using a heuristic allows to extract geodesics ..."
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Cited by 4 (0 self)
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geodesics from a single source to a single goal very quickly and with a low memory requirement. Any application that needs to compute a lot of geodesic paths can gain benefits from our algorithm. The computational saving is even more important for 3D medical images with tubular structures and for higher
Results 1  10
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