Topological hierarchy-contour tracing algorithm for nests of interconnected contours

As a simple meaningful external illustration, a group of boundary contours is commonly used for representing the physical appearance of an object of interest on a 2D plane (e.g., a part drawing, CT scan image, a sliced layer, tile pattern). The illustration is understood from the composition of the contours and their attributes that include their shapes, sizes, locations and relationships. Therefore, not only is geometrical information important for contours to be useful in subsequent operations but their topological hierarchy relationships also are essential. Presented in this paper is a topological hierarchy-contour tracing algorithm that is capable of tracing nests of interconnected contours often found in practice and of identifying their topological hierarchy relationships automatically during contour tracing. The algorithm organizes contours by family rather than by group or as individual. However, contours are traced across families generation by generation instead of going deep with one family branch at a time. The outputs of the algorithm are ordered sequences of boundary pixels representing all closed contours and their topological hierarchy relationships. The algorithm has been implemented on LabVIEW, and tested with several samples to illustrate its applications.