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Hessian matrix based saddle point detection for granules segmentation in 2D image

  • Published:
Journal of Electronics (China)

Abstract

Segmenting the touching objects in an image has been remaining as a hot subject due to the problematic complexities, and a vast number of algorithms designed to tackle this issue have come into being since a decade ago. In this paper, a new granule segmentation algorithm is developed using saddle point as the cutting point. The image is binarized and then sequentially eroded to form a gray-scale topographic counterpart, followed by using Hessian matrix computation to search for the saddle point. The segmentation is performed by cutting through the saddle point and along the maximal gradient path on the topographic surface. The results of the algorithm test on the given real images indicate certain superiorities in both the segmenting robustness and execution time to the referenced methods.

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References

  1. Ken Chen, Larry E. Banta, and Jiang Gangyi. 2-D Image-based volumetric modeling for particles of random shape. Journal of Electronics (China), 23 (2006)6, 877–881.

    Article  Google Scholar 

  2. Ken Chen, John Zaniewski, Pan Zhao, and Rener Yang. 2D Image based sieving for particle aggregate gradation. Journal of Electronics (China), 25(2008)2, 277–282.

    Article  Google Scholar 

  3. Zhao Rongchun, Chi Yaobin, and Zhu Chongguang. Evolution of image segmentation technology. Journal of Stereology and Image Analysis, 3(1998)2, 121–128 (in Chinese). 赵荣椿, 迟耀斌, 朱重光. 图像分割技术进展, 中国体视学与图像分析, 3(1998)2, 121–128.

    Google Scholar 

  4. L. Vincent and P. Soille. Watersheds in digital spaces: An efficient algorithm based on immersion simulation. IEEE Trans. on Pattern Anal. Machine Intell., 13 (1991)6, 583–598.

    Article  Google Scholar 

  5. Vincent Tariel, Dominique Juelin, et al. 3D Multiscale segmentation of granular materials. Image Anal Stereol, 27(2008), 23–28.

    Article  Google Scholar 

  6. Yang Huadong and Han Miaofu. The segmentation algorithm of particle image based on grayscale morphological reconstruction. Journal of Nanjing University of Technology, 27(2005)3, 98–102 (in Chinese). 杨华东, 简淼夫. 基于灰度形态重构的颗粒图像分割方法. 南京工业大学学报, 27(2005)3, 98–102.

    Google Scholar 

  7. Ken Chen, Larry E. Banta, and Jiang Gangyi. Saddle-point based separation of touched objects in 2-D image. Journal of Electronics (China), 23(2006)3, 452–456.

    Article  Google Scholar 

  8. Ken Cheng. Optical Gradation for Crushed Limestone Aggregates. [Ph.D. Dissertation], Evansdale Library of West Virginia University, USA, 2000.

    Google Scholar 

  9. G. Strang. Linear Algebra and Its Applications. 2nd ed, New York, Academic Press, 1980, 304–321.

    MATH  Google Scholar 

  10. Edward R. Dougherty. An introduction to morphological image processing. Bellingham, SPIE Optical Engineering Press, 1992, vol.TT9, ch.1.

    Google Scholar 

  11. R.A. Olsen, G. J. Kroes, et al. Comparison of methods for finding saddle points without knowledge of the states. Journal of Chemical Physics, 121(2004)20, 9776–9787.

    Article  Google Scholar 

  12. P. Culot, G. Dive, et al. A quasi-Newton algorithm for first-order saddle-point location. Theor. Chim. Acta, 82(1992)3/4, 189–205.

    Article  Google Scholar 

  13. G. Henkelman and H. Jonsson. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. Journal of Chemical Physics, 111(1999)15, 7010–7022.

    Article  Google Scholar 

  14. I. V. Ionova and E. A. Carter. Ridge method for finding saddle points on potential energy surfaces. Journal of Chemical Physics, 98(1993)8, 6377–6386.

    Article  Google Scholar 

  15. A. Kuijper. On detecting all saddle points in 2D images. Pattern Recognition Letters, 25(2004)15, 1665–1672.

    Article  Google Scholar 

  16. M. Hirsch and L. Quapp. Improved RGF method to find saddle points. J. Comput. Chem., 23(2002)9, 887–894.

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Information Science and Engineering, Ningbo University, Zhejiang, 315211, China

    Ken Chen, Yicong Wang & Rener Yang

Authors
  1. Ken Chen
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  2. Yicong Wang
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  3. Rener Yang
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Corresponding author

Correspondence to Ken Chen.

Additional information

Funded by Ningbo Natural Science Foundation (No.2006A610016), and Foundation of the Ministry of Education Ministry for Returned Overseas Students & Scholars (SRF for ROCS, SEM. No.2006699).

Communication author: Chen Ken, born in 1962, male, Ph.D., Associate Professor.

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Chen, K., Wang, Y. & Yang, R. Hessian matrix based saddle point detection for granules segmentation in 2D image. J. Electron.(China) 25, 728–736 (2008). https://doi.org/10.1007/s11767-008-0038-3

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  • DOI: https://doi.org/10.1007/s11767-008-0038-3

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