k × k thinning

doi:10.1016/0734-189X(90)90030-Y

Computer Vision, Graphics, and Image Processing

Volume 51, Issue 2, August 1990, Pages 195-215

Computer Vision, Gra...

https://doi.org/10.1016/0734-189X(90)90030-Y Get rights and content

Abstract

A commonly used method for thinning regions in binary images consists of examining windows of 3 × 3 pixels throughout an image, and erasing the center pixel if the thinning criteria are met. Thek × k thinning method is a generalization of the 3 × 3 method, wherek × k sized windows are examined and a center core of(k − 2) × (k − 2) pixels is erased if the criteria are met. The advantage ofk × k thinning is that, by peeling thicker layers from the boundaries of image regions, fewer iterations are required to reach the thinned result. For largerk, this is often at the cost of an increase in the coarseness of the result. Criteria are given by which thek × k method thins to minimally 8-connected lines while retaining connectivity and endpoints. Sequential and parallel algorithms are given. A procedure to obtain line widths in the course of thinning is described. Examples are shown illustrating the reduction in iterations with increase ofk, and the trade-off between size ofk and the coarseness of the result. Because of the highly repetitive, and local operations of the algorithm, it is straightforwardly mapped into VLSI hardware, and an example of this is given.

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This extraction is based not on polygon digitization but on automatic extraction provided by the software TLALOC_V2 (Parrot, 2015) that defines local hypsometric slices. Then, the skeleton of the mask of the drainage network segment is obtained by means of a thinning method (O’Gorman, 1990). Endpoints of this skeleton are used to calculate the altitude of all the successive pixels that describe the one-pixel- width skeleton of the river.
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The improvement of producing skeletons that preserve the significant geometric features of patterns is of great importance. One of feasible approaches is to develop a method embedded in a known parallel algorithm to produce bias-reduced skeletons since a bias skeleton usually degrades the preservation of significant geometric features of patterns. From our observations, bias skeletons always appear in the junction of lines which form an angle less than or near equal to 90°. In this paper, thehidden deletable pixel(HDP) which influences the speed of deleting the boundary pixels on a concave side is newly defined. Based on the comparable performance of our pseudo 1-subcycle parallel thinning algorithm (CH), a reduced form of larger support (twoL-pixel vectors, which is not the form ofk×ksupport) operated by an intermediate vector analysis about the deleted pixels in each thinning iteration is developed for HDP detection to obtain bias-reduced skeletons, which can be purchased by a reasonable computation cost. HDP restoration and parallel implementation are further considered to formulate an improved algorithm (CYS), where the connectivity preservation is guaranteed by the use ofCH's operators and HDP restoration. A set of synthetic images are used to quantify the skeleton from the geometry viewpoint and investigate the skeleton variations of using different (L)s. Based on the analyzing results, 3 ≤L≤ 9 are suggested for the current algorithm ofCYS.CYSis evaluated in comparison with two small support algorithms (AFP3andCH) and one larger support algorithm (VRCT) using the same patterns. Performances are reported by the number of iterations (NI), CPU time (TC), and number of unmatched pixels (N_unmatchfor bias-reduced measure). Results show that on the measure ofTC,CYSis approximately 2 to 3 times slower than the others, while on the measure ofNI, the four algorithms have approximately identical performance. On the measure ofN_unmatch,CYSis approximately 2 to 3 times less than the others. One-pixel boundary noise is also considered for exploring the noise immunity. The results suggest that the noise immunity ofCYSandCHis identical and is better than that ofAFP3. As a result, the better bias-reduced skeletons produced byCYSmay be purchased by a reasonable computation cost.
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A variety of approaches to parallel thinning using operators with small supports are reviewed, with emphasis on how one may preserve, and prove one has preserved, connec- tivity. Tests are demonstrated for verifying connectivity preservation; and for fundamental classes of parallel thinning algorithms, including fully parallel, two-subiteration, and two- subfield, conditions are identified using these tests which are sufficient for preservation of connectivity. Thus“design spaces” for connectivity preserving algorithms belonging to these classes are identified. Some fundamental limitations on parallel thinning operators for images with 8-4 connectivity are also reviewed, including constraints on support size and shape. Parallel computation time issues are addressed and it is shown that existing fully parallel thinning algorithms are nearly optimally fast.

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View full text

k × k thinning

Abstract

Comput. Graphics Image Process.

Pattern Recognit.

Comput. Vision Graphics Image Process.

Pattern Recognit.

Comput. Vision Graphics Image Process.

Comput. Vision Graphics Image Process.

Pattern recognition

J. Roy. Statist. Soc.

Linear skeletons from square cupboards

Mach. Intell.

Some parallel thinning algorithms for digital pictures

J. Assoc. Comput. Mach.

Thinning algorithms on rectangular, hexagonal, and triangular arrays

Commun. ACM