Normal vector and winding number in 2D digital images with application for hole detection

Digital topology has been extensively investigated in the past [1]. Fundamental topology concepts such as connectivity and component have been widely applied in pattern recognition. For instance, preserving the connectivity of objects is a key issue for thinning; in order to identify objects in images, we need to detect connected components. Theoretically, a connected component is entirely enclosed and determined by its external and hole contours. If we can detect all contours of a component and differentiate external with hole contours, the extraction of the component is straightforward. However, distinguishing external and internal contours is not a trivial task as it appears.