A novel and fast connected component count algorithm based on graph theory

Abstract

A fast component-counting algorithm is proposed based on graph theory in this paper. We derived a formulation to count faces in a plane given only the vertices based on Euler polyhedron formula. Vertices with degree no more than two are ineffective in counting components. With the derived formula, a graph component counting algorithm is constructed based only on searching cross points whose degree are no less than three. When applied to a two-dimensional binary image, the proposed method divides an image into patches of same size and decides which of them will be used in counting by searching the circumferential pixels of each patch. If the number of component edges within the circumferential pixels of a patch is no less than three, then the patch will be used in counting. After determining all the vertices with degree no less than three, the number of components can be calculated by the formula. Because only a small number of pixels are investigated in the process, the computational time is very fast. The disconnection of edges in an image is one of the main reasons which causes miscounts for scanning-based algorithms. The difficulty, however, can be naturally overcome by the proposed algorithm because disconnected points will be identified as futile pixels in the algorithm. Experimental results show the algorithm is more efficient than existing methods. When applied to images with disconnected edges, the counted number given by scanning-based algorithms is much smaller than the correct number whereas the proposed algorithm obtains satisfactory results.