Abstract The Three-Dimensional (3-D) Otsu’s method is an effective improvement on the traditional Otsu’s method. However, it not only has high computational complexity, but also needs to improve its anti-noise ability. This paper presents a new Otsu’s method based on 3-D histogram. This method transforms 3-D histogram into a 1-D histogram by a plane that is perpendicular to the main diagonal of the 3-D histogram, and designs a new maximum variance criterion for threshold selection. In order to enhance its anti-noise ability, a method based on geometric analysis, which can correct noise, is used for image segmentation. Simulation experiments show that this method has stronger anti-noise ability and less time consumption, comparing with the conventional 3-D Otsu’s method, the recursive 3-D Otsu’s method, the 3-D Otsu’s method with SFLA, the equivalent 3-D Otsu’s method and the improved 3-D Otsu’s method.

References

[1] AlSaeed D., Bouridane A., and El-Zaart A., “A Novel Fast Otsu Digital Image Segmentation Method,” The International Arab Journal of Information Technology, vol. 13, no. 4, pp. 427- 433, 2016.

[2] Fan J., Wang Q., Luo H., and Yuan N., “Fast Iterative Algorithm for Segmentation Based on An Improved Three-Dimensional Otsu,” in Proceedings of National Conference on Materials for Modern World, Hefei, pp. 1936-1940, 2015.

[3] Fan J. and Zhao F., “Two-Dimensional Otsu’s Curve Thresholding Segmentation Method for Gray-Level Images,” Acta Electronica Sinica, vol. 35, no. 4, pp. 751-755, 2007.

[4] Fan J., Zhao F., and Zhang X., “Recursive Algorithm for Three-Dimensional Otsu’s Thresholding Segmentation Method,” Acta Electronica Sinica, vol. 35, no. 7, pp. 1398-1402, 2007.

[5] Jianzhuang L. and Wenqing L., “The Automatic Thresholding of Gray-Level Pictures Via Two Dimensional Otsu Method,” Acta Automatica Sinica, vol. 19, no. 1, pp. 101-105, 1993.

[6] Jing X., Li J., and Liu Y., “Image Segmentation Based on 3-D Maximum Between-Cluster Variance,” Acta Electronica Sinica, vol. 31, no. 9, pp. 1281-1285, 2003.

[7] Khairuzzaman A. and Chaudhury S., “Multilevel Thresholding Using Grey Wolf Optimizer for Image Segmentation,” Expert Systems with Applications, vol. 86, no. 15, pp. 64-76, 2017.

[8] Li Y. and Feng X., “A Multiscale Image Segmentation Method,” Pattern Recognition, vol. 52, pp. 332-345, 2016.

[9] Liu L., Yang N., Lan J., and Li J., “Image Segmentation Based on Gray Stretch and Threshold Algorithm,” Optik, vol. 126, no. 6, pp. 626-629, 2015.

[10] Manikandan S., Ramar K., Iruthayarajan M., and Srinivasagan K., “Multilevel Thresholding for Segmentation of Medical Brain Images Using Real Coded Genetic Algorithm,” Measurement, vol. 47, no. 1, pp. 558-568, 2014.

[11] Nie F., Wang Y., Pan M., Peng G., and Zhang P., “Two-Dimensional Extension of Variance-based Thresholding for Image Segmentation,” Multidimensional Systems and Signal Processing, vol. 24, no. 3, pp. 485-501, 2013.

[12] Sahoo P., Slaaf D., and Thomas A., “Thresholding Selection Using a Minimal Histogram Entropy Difference,” Optical Engineering, vol. 36, no. 7, pp. 1976-1981, 1997.

[13] Sthitpattanapongsa P. and Srinark T., “An Equivalent 3-D Otsu’s Thresholding Method,” in Proceedings of 5th Pacific-Rim Symposium on Image and Video Technology, Gwangju, pp. 358-369, 2011.

[14] Sures S. and Lal S., “Multilevel Thresholding Based on Chaotic Darwinian Particle Swarm Optimization for Segmentation of Satellite Images,” Applied Soft Computing, vol. 55, pp. 503-522, 2017.

[15] Truong B. and Lee B., “Automatic Multithresholds Selection for Image Segmentation Based on Evolutionary Approach,” International Journal of Control, Automation and Systems, vol. 11, no. 4, pp. 834- 844, 2013.

[16] Wang N., Li X., and Chen X., “Fast Three- Dimensional Otsu Thresholding with Shuffled Frog-Leaping Algorithm,” Pattern Recognition Letters, vol. 31, no. 13, pp. 1809-1815, 2010.

[17] Wu Y., Pan Z., and Wu W., “Image Thresholding Based on Two-Dimensional Histogram Oblique Segmentation and Its Fast Recurring Algorithm,” Journal on Communications, vol. 29, no. 4, pp. 77-83, 2008.

[18] Yu H., Zhi X., and Fan J., “Image Segmentation Based on Weak Fuzzy Partition Entropy,” Neurocomputing, vol. 168, no. 30, pp. 994-1010, 2015.

[19] Zhi-yong H., Li-ning S., Huang W., and Li-guo C., “Thresholding Segmentation Algorithm Based on Otsu Criterion and Line Intercept Histogram,” Optics and Precision Engineering, vol. 20, no. 10, pp. 2315-2323, 2012. Otsu’s Thresholding Method Based on Plane Intercept Histogram and Geometric Analysis 701 Leyi Xiao received her M.S. degree form Hunan Normal University in 2012, and received her Ph.D. degree form Hunan University in 2020. She is currently a lecturer in the School of Computer Science, Xiangtan University. Her currently research interest includes intelligent information processing, pattern recognition and artificial intelligence. Honglin Ouyang received the M.S. degree from Huazhong University of Science and Technology, Wuhan, China, in 1992. And he received the Ph.D. degree in Control Theory and Control Engineering from Hunan University in 2005. Now he is a professor in Automation at Hunan University. His research interests include intelligent control, computer vision, and pattern recognition. Chaodong Fan (Corresponding author, received his B.S. degree form Hainan University in 2008, and received his M.S. and Ph.D. degree both form Hunan University in 2011 and 2014. He is currently a lecturer in the School of Computer Science, Xiangtan University. His currently research interest includes intelligent information processing, smart grid, pattern recognition and artificial intelligence.