Approximate partitioning of 2D objects into orthogonally convex components

Abstract

A fast and efficient algorithm to obtain an orthogonally convex decomposition of a digital object is presented. The algorithm reports a sub-optimal solution and runs in O(nlogn) time for a hole-free object whose boundary consists of n pixels. The decomposition algorithm can, in fact, be applied on any hole-free orthogonal polygon; in our work, it is applied on the inner isothetic cover of the concerned digital object. The approximate/rough decomposition of the object is achieved by partitioning the inner cover (an orthogonal polygon) of the object into a set of orthogonal convex components. A set of rules is formulated based on the combinatorial cases and the decomposition is obtained by applying these rules while considering the concavities of the inner cover. The rule formulation is based on certain theoretical properties apropos the arrangement of concavities, which are also explained in this paper. Experimental results on different shapes have been presented to demonstrate the efficacy, elegance, and robustness of the proposed technique.