Fig. 1. Regions in 2D histogram. (a) Histogram method; (b) line interpret histogram method

Fig. 2. Directions about a pixel. (a) Eight directions of center pixel; (b) NW direction of edge of SW-NE direction

Fig. 3. Algorithm segmentation results. (a) Original image; (b) result obtained by Otsu; (c) result obtained by directional fuzzy derivative; (d) fusion result

Fig. 4. Algorithm segmentation results. (a) Original image 1; (b) Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method

Fig. 5. Algorithm segmentation results. (a) Original image 2; (b) Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method

Fig. 6. Algorithm segmentation results. (a) Original image 3; (b)Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method

Fig. 7. Fuzzy derivative segmentation results. (a) Segmentation result of Fig. 4(a); (b) segmentation result of Fig. 5(a); (c) segmentation result of Fig. 6(a)

Fig. 8. Algorithm segmentation results of image 1. (a) Original image; (b) Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method

Fig. 9. Algorithm segmentation results of image 2. (a) Original image; (b) Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method

Fig. 10. Algorithm segmentation results of image 3. (a) Original image; (b) Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method

Fig. 11. Algorithm segmentation results of image 4. (a) Original image; (b) Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method

Fig. 12. Algorithm segmentation results of image 5. (a) Original image; (b) Otsu; (c) 2D maximum entropy; (d) algorithm in Ref. [18]; (e) algorithm in Ref. [23]; (f) proposed method