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Free Edge Lengths in Plane Graphs
"... We study the impact of metric constraints on the realizability of planar graphs. Let G be a subgraph of a planar graphH (whereH is the “host ” ofG). The graphG is free inH if for every choice of positive lengths for the edges of G, the host H has a planar straightline embedding that realizes these ..."
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We study the impact of metric constraints on the realizability of planar graphs. Let G be a subgraph of a planar graphH (whereH is the “host ” ofG). The graphG is free inH if for every choice of positive lengths for the edges of G, the host H has a planar straightline embedding that realizes
An Inequality on the Edge Lengths of Triangular Meshes ∗
"... We give a short proof of the following geometric inequality: for any two triangular meshes A and B of the same polygon C, if the number of vertices in A is at most the number of vertices in B, then the maximum length of an edge in A is at least the minimum distance between two vertices in B. Here th ..."
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We give a short proof of the following geometric inequality: for any two triangular meshes A and B of the same polygon C, if the number of vertices in A is at most the number of vertices in B, then the maximum length of an edge in A is at least the minimum distance between two vertices in B. Here
The Steiner problems with edge lengths 1 and 2
 INFORMATION PROCESSING LETTERS
, 1989
"... The Steiner problem on networks asks for a shortest subgraph spanning a given subset of distinguished vertices. We give a 4/3approximation algorithm for the special case in which the underlying network is complete and all edge lengths are either 1 or 2. We also relate the Steiner problem to a compl ..."
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Cited by 85 (1 self)
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The Steiner problem on networks asks for a shortest subgraph spanning a given subset of distinguished vertices. We give a 4/3approximation algorithm for the special case in which the underlying network is complete and all edge lengths are either 1 or 2. We also relate the Steiner problem to a
Inverse pMedian Problems with Variable Edge Lengths
, 2009
"... The inverse pmedian problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a pmedian with respect to the new edge lengths. The problem is shown to be strongly N ..."
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The inverse pmedian problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a pmedian with respect to the new edge lengths. The problem is shown to be strongly N
Graph topologies induced by edge lengths
, 2009
"... Let G be a graph each edge e of which is given a length ℓ(e). This naturally induces a distance dℓ(x, y) between any two vertices x, y, and we let Gℓ denote the completion of the corresponding metric space. It turns out that several well studied topologies on infinite graphs are special cases of  ..."
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Cited by 12 (7 self)
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Let G be a graph each edge e of which is given a length ℓ(e). This naturally induces a distance dℓ(x, y) between any two vertices x, y, and we let Gℓ denote the completion of the corresponding metric space. It turns out that several well studied topologies on infinite graphs are special cases
Graph Drawings with Relative Edge Length Specifications
 ´CCCG
, 2014
"... We study plane straightline embeddings of graphs where certain edges are specified to be longer than other edges. We analyze which graphs are universal in the sense that they allow a plane embedding for any total, strict order on the edge lengths. In addition, we also briefly consider circular arc ..."
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We study plane straightline embeddings of graphs where certain edges are specified to be longer than other edges. We analyze which graphs are universal in the sense that they allow a plane embedding for any total, strict order on the edge lengths. In addition, we also briefly consider circular arc
Cauchy’s Theorem and Edge Lengths of Convex Polyhedra
, 2007
"... In this paper we explore, from an algorithmic point of view, the extent to which the facial angles and combinatorial structure of a convex polyhedron determine the polyhedron—in particular the edge lengths and dihedral angles of the polyhedron. Cauchy’s rigidity theorem of 1813 states that the dihe ..."
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In this paper we explore, from an algorithmic point of view, the extent to which the facial angles and combinatorial structure of a convex polyhedron determine the polyhedron—in particular the edge lengths and dihedral angles of the polyhedron. Cauchy’s rigidity theorem of 1813 states
Active Contours without Edges
, 2001
"... In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy ..."
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Cited by 1188 (37 self)
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In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "meancurvature flow"like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We will give a numerical algorithm using finite differences. Finally, we will present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.
On Hamiltonian Paths with Prescribed edge lengths in the Complete Graph
 Bull. Inst. Combin. Appl
, 2010
"... Marco Buratti has conjectured that given p a prime and a multiset S containing p 1 nonzero elements from Zp, there exists a Hamiltonian path in Kp where the multiset of edge lengths is S. In this paper we completely solve this conjecture when S contains at most two distinct values. 1 ..."
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Cited by 5 (0 self)
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Marco Buratti has conjectured that given p a prime and a multiset S containing p 1 nonzero elements from Zp, there exists a Hamiltonian path in Kp where the multiset of edge lengths is S. In this paper we completely solve this conjecture when S contains at most two distinct values. 1
A computational approach to edge detection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1986
"... AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal ..."
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Cited by 4621 (0 self)
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AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal
Results 1  10
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