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Discrepancy: Local/Global Shape Characterization with a Roundness Bias

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Abstract

Disk shape frequently appears as a reference in shape characterization applications. We propose a local measure of deviation from a disk as the local difference between numerical solution of a PDE on the shape and an analytical expression in the form of modified Bessel function. The deviation defined at each shape point defines a field over the shape. This field has useful properties, which we demonstrate via illustrative applications ranging from shape decomposition to shape characterization. Furthermore, we show that a global measure extracted from the field is capable of characterizing the body roundness and periphery thickness uniformity.

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References

  1. Aktas, M.A., Zunic, J.: A family of shape ellipticity measures for galaxy classification. SIAM J. Imaging Sci. 6(2), 765–781 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baseski, E., Erdem, A., Tari, S.: Dissimilarity between two skeletal trees in a context. Pattern Recognit. 42(3), 370–385 (2009)

    Article  MATH  Google Scholar 

  3. Genctav, M., Genctav, A., Tari, S.: Nonlocal via local-nonlinear via linear: a new part-coding distance field via screened poisson equation. J. Math. Imaging Vis. 55(2), 242–252 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Herrera-Navarro, A.M., Jimenez-Hernandez, H., Terol-Villalobos, I.R.: A probabilistic measure of circularity. In: Combinatorial Image Analysis, pp. 75–89. Springer (2012)

  5. Latecki, L., Lakamper, R., Eckhardt, T.: Shape descriptors for non-rigid shapes with a single closed contour. CVPR 1, 424–429 (2000)

    Google Scholar 

  6. Maurer, C.R., Qi, R., Raghavan, V.: A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 265–270 (2003)

    Article  Google Scholar 

  7. Misztal, K., Tabor, J.: Ellipticity and circularity measuring via Kullback–Leibler divergence. J. Math. Imaging Vis. 55(1), 136–150 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Montero, R.S., Bribiesca, E.: State of the art of compactness and circularity measures. Int. Math. Forum 4(27), 1305–1335 (2009)

    MathSciNet  MATH  Google Scholar 

  9. Rosin, P.L.: Measuring shape: ellipticity, rectangularity, and triangularity. Mach. Vis. Appl. 14(3), 172–184 (2003)

    Article  Google Scholar 

  10. Tari, S.: Hierarchical shape decomposition via level sets. In: ISMM, pp. 215–225. Springer (2009)

  11. Tari, S., Genctav, M.: From a non-local Ambrosio–Tortorelli phase field to a randomized part hierarchy tree. J. Math. Imaging Vis. 49(1), 69–86 (2014)

    Article  Google Scholar 

  12. van der Maaten, L., Hinton, G.: Visualizing high-dimensional data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605 (2008)

    MATH  Google Scholar 

  13. Zunic, J., Hirota, K., Rosin, P.L.: A Hu moment invariant as a shape circularity measure. Pattern Recognit. 43(1), 47–57 (2010)

    Article  MATH  Google Scholar 

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Acknowledgements

The work is funded by Turkish National Science Foundation TUBITAK under Grant 112E208.

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  1. Middle East Technical University, 06800, Ankara, Turkey

    Asli Genctav & Sibel Tari

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  1. Asli Genctav
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  2. Sibel Tari
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Correspondence to Sibel Tari.

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Genctav, A., Tari, S. Discrepancy: Local/Global Shape Characterization with a Roundness Bias. J Math Imaging Vis 61, 160–171 (2019). https://doi.org/10.1007/s10851-018-0851-8

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  • DOI: https://doi.org/10.1007/s10851-018-0851-8

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