doi:10.1016/S0167-8655(03)00037-0
Copyright © 2003 Elsevier Science B.V. All rights reserved.
Threshold selection by clustering gray levels of boundary
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Lisheng Wang
, 
, and Jing Bai
Department of Biomedical Engineering, Institute of Biomedical Engineering, Tsinghua University, Beijing 100084, PR China
Received 12 July 2002;
revised 17 January 2003.
Available online 23 March 2003.
Abstract
In this paper, threshold selection is considered in the continuous image rather than in digital image. We prove that, for each given object within 2D image, its optimal threshold is determined by the mean of the gray values of the points lying on its continuous boundary. Thus, we try to deduce threshold from the gray values of the boundary rather from the gray values of the given discrete sampling points (pixels or edge pixels). By the scheme, we well overcome some disadvantages existing in the threshold methods based on the histogram of edge pixels. Besides, the proposed method has the ability to well handle the image whose histogram has very unequal peaks and broad valley.
Author Keywords: Threshold selection; Clustering algorithm; Image segmentation
Fig. 1. Step-like edge point (O) of 1D function.
Fig. 2. Each object has its two peaks in the histogram of “double responding” edge points. A represents edge points in the background and B represents edge points in the object.
Fig. 3. Histogram of gray levels of true boundary (solid curve) and histogram of “double responding” edge points (two dashed curves) of each object in 2D image.
Fig. 4. Regular grid of 2D image.
Fig. 5. 256-level gray images of the girl, the baboon and the goldhill.
Fig. 6. 256-level gray images of the characters, the nerve cell and the mouse nervous tissue.
Fig. 7. Histograms of images of the girl, the baboon and the goldhill, shown in Fig. 5.
Fig. 8. Histograms of images of the characters, the nerve cell and the mouse nervous tissue, shown in Fig. 6.
Fig. 9. Histograms of the discrete sampling points of the boundaries within images of the girl, the baboon and the goldhill, shown in Fig. 5.
Fig. 10. Histograms of the discrete sampling points of the boundaries within images of the characters, the nerve cell and the mouse nervous tissue, shown in Fig. 6.
Fig. 11. Binary images of the girl: (a) Otsu method (t=101); (b) Kapur, Sahoo and Wong method (t=139); (c) our method (t=90).
Fig. 12. Binary images of the baboon: (a) Otsu method (t=125); (b) Kapur, Sahoo and Wong method (t=142); (c) our method (t=122).
Fig. 13. Binary images of the goldhill: (a) Otsu method (t=113); (b) Kapur, Sahoo and Wong method (t=133); (c) our method (t=107).
Fig. 14. Binary images of the character: (a) Otsu method (t=147); (b) Kapur, Sahoo and Wong method (t=167); (c) our method (t=148).
Fig. 15. Binary images of the nerve cell: (a) Otsu method (t=67); (b) Kapur, Sahoo and Wong method (t=88); (c) our method (t=42).
Fig. 16. Binary images of the mouse nervous tissue: (a) Otsu method (t=205); (b) Kapur, Sahoo and Wong method (t=185); (c) our method (t=194).
Fig. 17. Histogram of discrete sampling points of boundaries within 2D image including three objects.
Fig. 18. CT image of leg with three different objects.
Fig. 19. Histogram of discrete sampling points of boundaries (above), histogram of 2D image (below).
Fig. 20. Different structures (white area) segmented from 2D CT image of leg by selecting multi-thresholds. (a) Background, (b) connective tissue, (c) muscle, (d) bone.
Fig. 21. CT image of head with three different structures.
Fig. 22. Histogram of discrete sampling points of boundaries (above), histogram of 2D image (below).
Fig. 23. Different structures (white area) segmented from 2D CT image of head by selecting multi-thresholds. (a) Background, (b) soft tissue, (c) bone.
Fig. 24. Binary image and its changed versions added the enlarged gaussian noise in turn.
Fig. 25. Histograms of the images shown in Fig. 24.
Fig. 26. Histograms of discrete sampling points of boundaries within the images in Fig. 24.
Fig. 27. Corresponding edge maps (a)–(c), histograms of the discrete sampling points of boundary (a1)–(c1), and segmentation results (a2)–(c2) of the image of girl when gradient threshold T selects three different values from low to high (from left-to-right), respectively.
Fig. 28. Corresponding edge maps (a)–(c), histograms of the discrete sampling points of boundary (a1)–(c1), and segmentation results (a2)–(c2) of the image of baboon when gradient threshold T selects three different values from low to high (from left-to-right), respectively.
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