Fast equal and biased distance fields for medial axis transform with meshing in mind

Xia, Hao and Tucker, Paul G (2011) Fast equal and biased distance fields for medial axis transform with meshing in mind. Applied Mathematical Modelling, 35 (12). pp. 5804-5819. ISSN 0307-904X

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A method for robust and efficient medial axis transform (MAT) of arbitrary domains using distance solutions (or level sets) is presented. The distance field, d, is calculated by solving the hyperbolic-natured eikonal equation. The solution is obtained on Cartesian grids. Both the fast-marching method (FMM) and fast-sweeping method (FSM) are used to calculate d. Medial axis point clouds are then extracted based on the distance solution via a simple criterion: the Laplacian or the Hessian determinant of d(x). These point clouds in the pixel/voxel space are further thinned to single pixel wide so that medial axis curves or surfaces can be connected and splined. 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 three dimensions, 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.

Item Type: Article
Additional Information: Eikonal equation; Wall distance; Medial axis transform; Pixel/voxel thinning
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Hao Xia
Date Deposited: 06 Feb 2012 18:15
Last Modified: 04 Mar 2013 08:21
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