A linear-time combinatorial algorithm to find the orthogonal hull of an object on the digital plane

Authors:
Arindam Biswas;Partha Bhowmick;Moumita Sarkar;Bhargab B. Bhattacharya
Affiliations:
Department of Information Technology, Bengal Engineering and Science University, Howrah 711 103, India;Computer Science and Engineering Department, Indian Institute of Technology, Kharagpur 721 302, India;Department of Information Technology, Bengal Engineering and Science University, Howrah 711 103, India;Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata 700 108, India
Venue:
Information Sciences: an International Journal
Year:
2012

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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 size, 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 is linear on the object perimeter instead of the object area. For a larger grid size, 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.