Distance Solutions for Medial Axis Transform
Xia, Hao and Paul G. Tucker
Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.247-265, October 25-28 2009
18th International Meshing Roundtable
Salt Lake City, UT, USA.
October 25-28, 2009
Whittle Laboratory, Department of Engineering, University of Cambridge,
JJ Thomson Ave, Camridge, CB3 0DY, England
A method towards robust and efficient medial axis transform (MAT)
of arbitrary domains using distance solutions is presented. The distance field, d,
is calculated by solving the hyperbolic-natured Eikonal (or Level Set) equation.
The solution is obtained on Cartesian grids. Both the fast-marching method and
fast-sweeping method are used to calculate d. Medial axis point clouds are then
extracted based on the distance solution via a simple criteria: the Laplacian or the
Hessian determinant of d. These point clouds in 2D-pixel and 3D-voxel space are
further thinned to curves and surfaces through binary image thinning algorithms.
This results in an overall hybrid approach. As an alternative to other methods,
the current d-MAT procedure bypasses difficulties that are usually encountered by
pure geometric methods (e.g. the Voronoi approach), especially in 3D, and provides
better accuracy than pure thinning methods. It is also shown that the d-MAT
approach provides the potential to sculpt/control the MAT form for specialized
solution purposes. Various examples are given to demonstrate the current approach.
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