Fig. 1. Multi-scale product effect in the vertical direction （（a） show the original image and its gray level histogram， （b）-（f） show the corresponding MPT image Zv and its gray level histogram when ω is 1， 2， 3， 4 and 5.）

Fig. 2. Schematic diagram of left and right division of gray

Fig. 3. MPT images Zθ and ωθ values corresponding to five wavelets

Fig. 4. Several key steps in the construction of objective function. The gray level histogram Ht is truncated at the frequency 200 for more clearly showing the frequency of gray level in the range 0,255.

Fig. 5. Selected thresholds and the segmentation results of the EREM method on synthetic images with unbalanced target and background sizes

Fig. 6. Selected thresholds and the segmentation results of the EREM method on synthetic images with relatively balanced target and background sizes

Fig. 7. Selected thresholds of the 5 threshold segmentation methods on 4 representative synthetic images

Fig. 8. Segmentation results of 9 methods on 4 synthetic images in Fig. 7（a）-（d）

Fig. 9. Selected thresholds of the 5 threshold segmentation methods on 4 real-world images

Fig. 10. Segmentation results of 9 methods on 4 real-world images in Fig. 9（a）-（d）

Fig. 11. MCC values of 9 segmentation methods on 50 real-world images

Fig. 12. Statistical result of average MCC value for different α