A linear time combinatorial algorithm to compute the relative orthogonal convex hull of digital objects

Abstract

A linear time combinatorial algorithm to construct the relative orthogonal convex hull of the inner isothetic cover of a digital object (hole-free) with respect to its outer isothetic cover is presented in this paper. The algorithm first constructs the inner and the outer isothetic covers of the digital object which is the input to the algorithm and then constructs the relative orthogonal convex hull from the inner isothetic cover and the outer isothetic cover. The algorithm can also be used to construct the relative orthogonal convex hull of one orthogonal polygon with respect to another orthogonal polygon which encloses the first polygon entirely where the input will be two orthogonal polygons one containing the other instead of the digital object. The proposed algorithm first finds the concavities of the inner polygon and checks for intruded concavities of the outer polygon. A combinatorial technique is used to obtain the relative orthogonal convex hull. The efficiency and the correctness of the algorithm are verified as it is tested on various types of digital objects.