Fully parallel homological region adjacency graph via frontier recognition

Abstract

Relating image contours and regions and their attributes according to connectivity based on incidence or adjacency is a crucial task in numerous applications in the fields of image processing, computer vision and pattern recognition. In this paper, the crucial incidence topological information of 2-dimensional images is extracted in an efficient manner through the computation of a new structure called the HomDuRAG of an image; that is, the dual graph of the HomRAG (a topologically consistent extended version of the classical RAG). These representations are derived from the two traditional self-dual square grids (in which physical pixels play the role of 2-dimensional cells) and encapsulate the whole set of topological features and relations between the three types of objects embedded in a digital image: 2-dimensional (regions), 1-dimensional (contours) and 0-dimensional objects (crosses). Here, a first version of a fully parallel algorithm to compute this new representation is presented, whose timing complexity order (in the worst case and supposing one processing element per 0-cell) is