Abstract
A computational method is presented which efficiently segments digital grayscale images by directly applying the Q-state Ising (or Potts) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems (i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to partitioning the system into regions of four classes of magnetism. This direct Potts segmentation technique is demonstrated on photographic, medical, and acoustic images.
[1] D. L. Pham, C. Xu, J. L. Prince, Annu. Rev. Biomed. Eng. 2, 315 (2000) http://dx.doi.org/10.1146/annurev.bioeng.2.1.31510.1146/annurev.bioeng.2.1.315Search in Google Scholar
[2] Y. H. Yang, M. J. Buckley, S. Dudoit, T. P. Speed, J. Comput. Graph. Stat. 11, 108 (2002) http://dx.doi.org/10.1198/10618600231737564010.1198/106186002317375640Search in Google Scholar
[3] S. Peng, B. Urbanc, L. Cruz, B. T. Hyman, H. E. Stanley, P. Natl. Acad. Sci. USA 100, 3847 (2003) http://dx.doi.org/10.1073/pnas.023049010010.1073/pnas.0230490100Search in Google Scholar
[4] V. Grau, A. U. J. Mewes, M. Alcañiz, IEEE T. Med. Imaging 23, 447 (2004) http://dx.doi.org/10.1109/TMI.2004.82422410.1109/TMI.2004.824224Search in Google Scholar
[5] S. Hadjidemetriou, C. Studholme, S. Mueller, M. Weiner, N. Schuff, Med. Image Anal. 13, 36–48 (2009) http://dx.doi.org/10.1016/j.media.2008.05.00310.1016/j.media.2008.05.003Search in Google Scholar
[6] X. Descombes, M. Moctezuma, H. Maître, J.-P. Rudant, Signal Process. 55, 123–132 (1996) http://dx.doi.org/10.1016/S0165-1684(96)00125-910.1016/S0165-1684(96)00125-9Search in Google Scholar
[7] F. W. Bentrem, W. E. Avera, J. Sample, Sea Technol. 47, 37 (2006) Search in Google Scholar
[8] T. Asano, D. Z. Chen, N. Katoh, T. Tokuyama, Int. J. Comput. Geom. Ap. 11, 145 (2001) http://dx.doi.org/10.1142/S021819590100042010.1142/S0218195901000420Search in Google Scholar
[9] E. Ising, Z. Phys. 31, 253 (1925) http://dx.doi.org/10.1007/BF0298057710.1007/BF02980577Search in Google Scholar
[10] R. B. Potts, P. Camb. Philos. Soc. 48, 106 (1952) http://dx.doi.org/10.1017/S030500410002741910.1017/S0305004100027419Search in Google Scholar
[11] F. W. Bentrem, Provisional Patent Application, Navy Case No. 99, 755 (2009) Search in Google Scholar
[12] K. Tanaka, J. Phys. A-Math. Gen. 35, R81 (2002) http://dx.doi.org/10.1088/0305-4470/35/37/20110.1088/0305-4470/35/37/201Search in Google Scholar
[13] J. P. Neirotti, S. M. Kurcbart, N. Caticha, Phys. Rev. E 68, 031911 (2003) http://dx.doi.org/10.1103/PhysRevE.68.03191110.1103/PhysRevE.68.031911Search in Google Scholar PubMed
[14] M. Blatt, S. Wiseman, E. Domany, Phys. Rev. Lett. 76, 3251 (1996) http://dx.doi.org/10.1103/PhysRevLett.76.325110.1103/PhysRevLett.76.3251Search in Google Scholar PubMed
[15] M. Blatt, S. Wiseman, E. Domany, Neural Computation 9, 1805 (1997) http://dx.doi.org/10.1162/neco.1997.9.8.180510.1162/neco.1997.9.8.1805Search in Google Scholar
[16] S. Wiseman, M. Blatt, E. Domany, Phys. Rev. E 57, 3767 (1998) http://dx.doi.org/10.1103/PhysRevE.57.376710.1103/PhysRevE.57.3767Search in Google Scholar
[17] K. Tanaka, H. Shouno, M. Okadak, D. M. Titterington, J. Phys. A-Math. Gen. 37, 8675 (2004) http://dx.doi.org/10.1088/0305-4470/37/36/00710.1088/0305-4470/37/36/007Search in Google Scholar
[18] E. Sharon, A. Brandt, R. Basriy, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, Hilton Head Island, 2000) 1, 70 Search in Google Scholar
[19] P. F. Felzenszwalb, D. P. Huttenlocher, Int. J. Comput. Vision 59, 167 (2004) http://dx.doi.org/10.1023/B:VISI.0000022288.19776.7710.1023/B:VISI.0000022288.19776.77Search in Google Scholar
[20] A. X. Falcão, P. A. V. Miranda, A. Rocha, Lect. Notes Comp. Sci. 4179/2006, 138 (2006) http://dx.doi.org/10.1007/11864349_1310.1007/11864349_13Search in Google Scholar
[21] D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987) Search in Google Scholar
[22] J. C. Lee Thermal Physics: Entropy and Free Energies (World Scientific Publishing Company, Singapore, 2002) 10.1142/4898Search in Google Scholar
[23] L. Onsager, Phys. Rev. 65, 117 (1944) http://dx.doi.org/10.1103/PhysRev.65.11710.1103/PhysRev.65.117Search in Google Scholar
[24] D. Martin, C. Fowlkes, D. Tal, J. Malik, Proceedings of the 8th International Conference on Computer Vision 2, 416 (2001) Search in Google Scholar
[25] F. W. Bentrem, J. Sample, M. T. Kalcic, M. E. Duncan, Proceedings of Oceans 2002 (MTS/IEEE, Biloxi) 1, 7 (2002) Search in Google Scholar
[26] F. W. Bentrem, J. T. Sample, M. M. Harris, Scientific Computing 25, 30 (2008) Search in Google Scholar
[27] R. A. Bagnold, The Physics of Blown Sand and Desert Dunes (Methuen, London, 1941) Search in Google Scholar
[28] L. Kang, L. Guo, Phys. Lett. A 330, 198 (2004) http://dx.doi.org/10.1016/j.physleta.2004.07.06110.1016/j.physleta.2004.07.061Search in Google Scholar
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