Combinatorial Construction of the Orthogonal Concavity Tree of a Digital Object

A novel two-stage algorithm for constructing the orthogonal concavity tree (OCT) of a digital object is proposed. In Stage I, it derives the minimum-area orthogonal cover of the object. In Stage II, it constructs the orthogonal hull from the ortho-cover, and while doing so, extracts the orthogonal concavities in an iterative manner. Nested concavities, if any, are obtained by considering each concavity and its ortho-hull, and the resultant concavities can be used to prepare the OCT. A smaller grid size captures the finer concavities of the underlying object, whereas a larger grid size results in fewer and coarser concavities. Experimental results demonstrate the efficacy and elegance of the proposed algorithm.