Algorithms for extracting the medial axis transform of 2D images

Ching-Shoei Chiang

doi:10.1117/12.206651

21 April 1995 Algorithms for extracting the medial axis transform of 2D images

Ching-Shoei Chiang

Proceedings Volume 2501, Visual Communications and Image Processing '95; (1995) https://doi.org/10.1117/12.206651
Event: Visual Communications and Image Processing '95, 1995, Taipei, Taiwan

Abstract

We describe 5 algorithms for finding the MAT for 2D regions in this paper. There are Danielson's algorithm, Rosenfeld and Pfaltz's algorithm, interpolation/extrapolation algorithm, Newton and march algorithm and grid edge interpolation algorithm. The Rosenfeld and Pfaltz's, Danielson's, and interpolation/extrapolation methods are based on the maximal disc criterion. Whether the grid point (i,j) with distance amplitudes (a,b) to the boundary of the regions is a MA point is decided by its grid neighbors. If the discrete circle associated with the gird point (i,j) is not contained in one of the 8 discrete circles associated with its neighbors, then it is a MA point. The Newton and march and the grid edge interpolation methods are based on the equal distance criterion. Given the boundary of a region, we compute the distance transform for the discretized region as preprocessing step. With every grid point we associate the index of a nearest edge or a concave vertex, and the direction and distance to that edge or concave vertex. The main purpose of these steps is to solve the proximity problem. A system of equations will be generated and Newton method will be used to trace the MAT. If we add one more equation, such as the equation for a grid line, instead of marching MAT step by step, we can find the MA point square by square under some assumptions, this is the idea of grid interpolation method.

Citation Download Citation

Ching-Shoei Chiang "Algorithms for extracting the medial axis transform of 2D images", Proc. SPIE 2501, Visual Communications and Image Processing '95, (21 April 1995); https://doi.org/10.1117/12.206651

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