A novel O(1) time algorithm for 3D block-based medial axis transform by peeling corner shells

نویسنده

  • Yuh-Rau Wang
چکیده

0167-8191/$ see front matter 2008 Elsevier B.V doi:10.1016/j.parco.2008.10.003 * Tel.: +886 2 28013131x6774; fax: +886 2 2801 E-mail address: [email protected] The block-based medial axis transform (BB_MAT, for short) of a 3D (2D) binary image, denoted 3D_BB_MAT (2D_BB_MAT), is defined as the problem to find a minimal set of upright 1-cubes (1-squares) whose union corresponds exactly to the 1-voxels (1-pixels) in the binary image. Many parallel algorithms have been proposed for computing the 2D_BB_MAT, almost all proposed approaches are unable to extend to a solution of the 3D_BB_MAT problem. In this paper, we first propose a novel Oð1Þ time algorithm for solving the 3D_BB_MAT (2D_BB_MAT) problem of a binary image of size N N N (N N) on a linear array with a reconfigurable pipelined bus system (LARPBS, for short) by peeling the 3D (2D) corner shell of each 1-voxel (1-pixel) of the image and revealing some properties of the 3D_BB_MAT (2D_BB_MAT). The 3D (2D) chessboard distance transform problem, denoted 3D_CDT (2D_CDT), is the problem for each 0-voxel (0-pixel) of a 3D (2D) binary image to find its nearest 1-voxel (1-pixel) in the binary image based on chessboard distance metric. In this paper, we also solve the 3D_CDT (2D_CDT) based on the computed 3D_BB_MAT (2D_BB_MAT). All the proposed algorithms are very innovative although they look like ‘‘straightforward”. To the best of our knowledge, the proposed 2D_BB_MAT (2D_CDT) algorithm is the first algorithm that can extend to a solution of the 3D_BB_MAT (3D_CDT) problem in parallel, and the 3D_BB_MAT (3D_CDT) algorithm is the first parallel algorithm proposed for solving the 3D_BB_MAT (3D_CDT) problem. 2008 Elsevier B.V. All rights reserved.

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عنوان ژورنال:
  • Parallel Computing

دوره 35  شماره 

صفحات  -

تاریخ انتشار 2009