Hold Holes Countable in Binary Images

Given a 2D binary image it is sometimes of interest to determine invariant topological properties, such as Euler number and holes which can reflect directly the complexity of a binary image. Counting the number of holes of binary images is an important problem arising in medical image processing, phototypesetting, petroleum exploration, earthquake prediction, and pattern recognition. In this paper, we propose and prove a new formula to detect and count the number of holes of binary images. A local labeling algorithm is proposed to make detecting holes more efficient. It is demonstrated that holes, as one important property of a binary image, are locally countable.