Parallel algorithms for determining k-width- connectivity in binary images

The authors consider a new form of connectivity in binary images, called k-width-connectivity. Two pixels a and b of value `1' are in the same k-width-component if and only if there exists a path of width k such that a is one of the k start pixels and b is one of the k end pixels of this path. The authors present characterisations of the k-width-components and show how to determine the k-width-components of an n× n image in O(n) and O(log² n) time on a mesh of processors and hypercube, respectively, when the image is stored with one pixel per processor. The methods use a reduction of the k-width-connectivity problem to the 1-width-connectivity problem. A distributed, space-efficient encoding of the k-width-components of small size allows the solution to be represented using O(l) registers per processor. The hypercube algorithm also implies an algorithm for the shuffle-exchange network