Abstract
In this paper we propose a new idea to design a measure for shape descriptors based on the concept of Q-convexity. The new measure extends the directional convexity measure defined in [2] to a two-dimensional convexity measure. The derived shape descriptors have the following features: (1) their values range from 0 to 1; (2) their values equal 1 if and only if the binary image is Q-convex; (3) they are invariant by reflection and point symmetry; (4) their computation can be easily and efficiently implemented.
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Balázs, P., Brunetti, S.: A measure of Q-Convexity. In: Normand, N., Guédon, J., Autrusseau, F. (eds.) DGCI 2016. LNCS, vol. 9647, pp. 219–230. Springer, Cham (2016). doi:10.1007/978-3-319-32360-2_17
Balázs, P., Ozsvár, Z., Tasi, T.S., Nyúl, L.G.: A measure of directional convexity inspired by binary tomography. Fundamenta Informaticae 141(2–3), 151–167 (2015)
Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R.: Medians of polyominoes: a property for the reconstruction. Int. J. Imag. Syst. Technol. 9, 69–77 (1998)
Boxter, L.: Computing deviations from convexity in polygons. Pattern Recogn. Lett. 14, 163–167 (1993)
Brunetti, S., Daurat, A.: An algorithm reconstructing convex lattice sets. Theor. Comput. Sci. 304(1–3), 35–57 (2003)
Brunetti, S., Daurat, A.: Reconstruction of convex lattice sets from tomographic projections in quartic time. Theor. Comput. Sci. 406(1–2), 55–62 (2008)
Brunetti, S., Del Lungo, A., Del Ristoro, F., Kuba, A., Nivat, M.: Reconstruction of 4- and 8-connected convex discrete sets from row and column projections. Linear Algebra Appl. 339, 37–57 (2001)
Chrobak, M., Dürr, C.: Reconstructing hv-convex polyominoes from orthogonal projections. Inform. Process. Lett. 69(6), 283–289 (1999)
Daurat, A.: Salient points of Q-convex sets. Int. J. Pattern Recogn. Artif. Intell. 15, 1023–1030 (2001)
Daurat, A., Nivat, M.: Salient and reentrant points of discrete sets. Electron. Notes Discrete Math. 12, 208–219 (2003)
Latecki, L.J., Lakamper, R.: Convexity rule for shape decomposition based on discrete contour evolution. Comput. Vis. Image Understand. 73(3), 441–454 (1999)
Nelson, M.R.: The Data Compression Book. M&T Books, Redwood City (1991)
Rahtu, E., Salo, M., Heikkila, J.: A new convexity measure based on a probabilistic interpretation of images. IEEE Trans. Pattern Anal. 28(9), 1501–1512 (2006)
Rosin, P.L., Zunic, J.: Probabilistic convexity measure. IET Image Process. 1(2), 182–188 (2007)
Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis, and Machine Vision, 3rd edn. Thomson Learning, Toronto (2008)
Stern, H.: Polygonal entropy: a convexity measure. Pattern Recogn. Lett. 10, 229–235 (1998)
Zunic, J., Rosin, P.L.: A new convexity measure for polygons. IEEE T. Pattern Anal. 26(7), 923–934 (2004)
Acknowledgements
The collaboration of the authors was supported by the COST Action MP1207 “EXTREMA: Enhanced X-ray Tomographic Reconstruction: Experiment, Modeling, and Algorithms”. The research of Péter Balázs and Péter Bodnár was supported by the NKFIH OTKA [grant number K112998]. The authors also thank the anonymous reviewers for their useful observations which enhanced the quality of the paper.
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Brunetti, S., Balázs, P., Bodnár, P. (2017). Extension of a One-Dimensional Convexity Measure to Two Dimensions. In: Brimkov, V., Barneva, R. (eds) Combinatorial Image Analysis. IWCIA 2017. Lecture Notes in Computer Science(), vol 10256. Springer, Cham. https://doi.org/10.1007/978-3-319-59108-7_9
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DOI: https://doi.org/10.1007/978-3-319-59108-7_9
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