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www.cim.mcgill.ca
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, shape-from-shading and for recent dynamic theories of shape....
Kaleem Siddiqi, Sylvain Bouix, Allen Tannenbaum, Steven W. Zucker
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ICCV - 1999
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www4.ncsu.edu
"A computational study of the Fast Marching and the Fast Sweeping methods for the Eikonal equation is given. It is shown that even though Fast Sweeping requires asymptotically less operations than Fast Marching, the latter method is faster than the former for the problems under consideration and for realistic grid sizes....
Pierre A. Gremaud and Christopher M. Kuster
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www2.imm.dtu.dk
This technical report discusses Sethian's Fast Marching Method and its higher accuracy variant. Both methods may be used to compute the arrival times at the points of a discrete lattice of a front which is monotonously expanding. Applications of the method include arrival time computation and the construction of distance fields for 2D or 3D objects....
Jakob Andreas Bærentzen
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mecca.louisville.edu
Detailed explanation of the Fast Marching Methods, which can be used to efficiently solve the Eikonal equation that models moving interfaces whose motion is either monotonically increasing or decreasing....
M. Sabry Hassouna
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50
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mecca.louisville.edu
In this paper, we present a novel framework for computing centerlines for both 2D and 3D shape analysis. The framework works as follows: an object centerline point is selected automatically as the point of global maximum Euclidean distance from the boundary, and is considered a point source (PS) that transmits a wave front that evolves over time and traverses the object domain....
M. Sabry Hassouna
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24
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mecca.louisville.edu
In this paper, we present a novel framework for computing centerlines for both 2D and 3D shape analysis. The framework works as follows: an object centerline point is
selected automatically as the point of global maximum Euclidean distance from the boundary, and is considered a point source (PS) that transmits a wave front that evolves over time and traverses the object domain....
M. Sabry Hassouna, Aly A. Farag
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mecca.louisville.edu
A wide range of computer vision applications such as distance field computation, shape from shading, and shape representation require an accurate solution of a particular
Hamilton-Jacobi (HJ) equation, known as the Eikonal equation....
M. Sabry Hassouna, Aly A. Farag
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mecca.louisville.edu
In this paper, we propose a new variational framework for computing continuous curve skeletons from discrete objects that are suitable for structural shape representation.
We have derived a new energy function, which is proportional to some medialness function, such that the minimum cost path between any two medial voxels in the shape is a curve skeleton....
M. Sabry Hassouna, Aly A. Farag
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mecca.louisville.edu
A wide range of computer vision applications require an accurate solution of a particular Hamilton-Jacobi (HJ) equation known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains....
M. Sabry Hassouna, Aly A. Farag
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mecca.louisville.edu
Representing a 3D shape by a set of one-dimensional curves that are locally
symmetric with respect to its boundary (i.e., curve skeletons) is of importance
in several machine intelligence tasks. This paper presents a fast, automatic, and robust variational framework for computing continuous, sub-voxel accurate curve skeletons from volumetric objects....
M. Sabry Hassouna, Aly A. Farag
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