Abstract
Algorithms for finding shortest paths and their numerous variants have been studied extensively over several decades in graph theory, computational geometry, and in operations research. Still, design of such algorithms poses newer challenges in various emerging areas of image analysis and computer vision. This mandates further investigation of application-specific shortest-path problems in the framework of digital geometry. We present here an efficient combinatorial algorithm for finding a shortest isothetic path (SIP) between two grid points in a digital object without any hole, such that the SIP lies entirely inside the object. Our algorithm first determines a maximum-area isothetic polygon that is inscribed within the object. Certain combinatorial rules are then used to construct the SIP on the basis of its constituent monotone sub-paths, the number of which is invariant regardless of the choice of SIP between two given grid points. For a given grid size, the proposed algorithm runs in \(O(n\log n)\) time, where n is the number of grid points appearing on the boundary of the inscribed polygon. Experimental results show the effectiveness of the algorithm and its further prospects in shape analysis.
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A preliminary version of this paper appeared in the Proc. IWCIA 2012 [16]
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Dutt, M., Biswas, A., Bhowmick, P. et al. On finding a shortest isothetic path and its monotonicity inside a digital object. Ann Math Artif Intell 75, 27–51 (2015). https://doi.org/10.1007/s10472-014-9421-y
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DOI: https://doi.org/10.1007/s10472-014-9421-y