k × k thinning

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.