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Fast Circular Arc Segmentation Based on Approximate Circularity and Cuboid Graph

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Abstract

A fast and efficient algorithm for circular arc segmentation is presented. The algorithm is marked by several novel features including approximate circularity for arc detection, cuboid graph defined by the detected arcs in the 3D parameter space, and resolving all delimited cliques in the cuboid graph to form larger arcs. As circular arcs present in a digitized document often deviate from the ideal conditions of digital circularity, we have loosened their radius intervals and center locations depending on an adaptive tolerance so as to detect the arcs by approximate circularity. The notion of approximate circularity is realized by modifying certain number-theoretic properties of digital circularity, which ensures that the isothetic deviation of each point in an input curve segment from the reported circle does not exceed the specified tolerance. Owing to integer computation and judiciousness of delimited cliques, the algorithm runs significantly fast even for very large images. Exhaustive experimentation with benchmark datasets demonstrate its speed, efficiency, and robustness.

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Notes

  1. A run is defined by a stretch of equi-abscissa or equi-ordinate pixels of maximal length. A sequence of pixels defining a circular arc is equivalently and succinctly expressed as a sequence of run-lengths.

  2. The dataset was available in the website mentioned in [23] till 2007.

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Acknowledgements

The authors deeply acknowledge the anonymous reviewers for their insightful and thorough review works, which helped enhancing the content and quality of the paper.

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  1. Indian Institute of Technology, Kharagpur, Kharagpur, West Bengal, India

    Partha Bhowmick & Shyamosree Pal

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  1. Partha Bhowmick
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Bhowmick, P., Pal, S. Fast Circular Arc Segmentation Based on Approximate Circularity and Cuboid Graph. J Math Imaging Vis 49, 98–122 (2014). https://doi.org/10.1007/s10851-013-0444-5

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