Run-length chain coding and scalable computation of a shape's moments using reconfigurable optical buses

The main contribution of this paper is the design of several efficient algorithms for modified run-length chain coding and for computing a shape's moments on arrays with reconfigurable optical buses. The proposed algorithms are based on the boundary representation of an object. Instead of using chain code, the boundary can be represented by a modified run-length chain code, where each entity represents a line segment (two adjacent corner pixels). The sequential nature of the chain code makes it difficult to be parallelized. We first propose two constant time algorithms for boundary extraction and run-length chain coding. To the authors' knowledge, these are the most time efficient algorithms yet published. Based on the modified run-length chain coding, and the advantages of both optical transmission and electronic computation, a constant time parallel algorithm for computing a shape's moments using N x N processors is proposed. Additionally, instead of using N x N processors, a scalable moment algorithm using r x r processors is also derived, where r < N. Based on the product of time and the number of processors used, both proposed parallel algorithms are time and cost optimal.