Finding the orthogonal hull of a digital object: A combinatorial approach

Abstract

A combinatorial algorithm to compute the orthogonal hull of a digital object imposed on a background grid is presented in this paper. The resolution and complexity of the orthogonal hull can be controlled by varying the grid spacing, which may be used for a multiresolution analysis of a given object. Existing algorithms on finding the convex hull are based on divide and conquer strategy, sweepline approach, etc., whereas the proposed algorithm is combinatorial in nature whose time complexity depends on the object perimeter instead of the object area. For a larger grid spacing, the perimeter of an object decreases in length in terms of grid units, and hence the runtime of the algorithm reduces significantly. The algorithm uses only comparison and addition in the integer domain, thereby making it amenable to usage in real-world applications where speed is a prime factor. Experimental results including the CPU time demonstrate the elegance and efficacy of the proposed algorithm. © 2008 Springer-Verlag Berlin Heidelberg.