1. Automatic thresholding for defect detection
Author: Hui-Fuang Ng
Source: Pattern Recognition Letters, vol. 27, pp , 2006.
Speaker: Shang-Chin Pai

2. Outline Introduction Otsu method Valley-emphasis method Experiments
Conclusion

3. Introduction After automatic thresholding process for image
Original Image

4. Introduction
Problem with the Otsu method in thresholding small defects
(a) Original image
(b) Desired threshold result
(c) Otsu threshold result
(d) Histogram and threshold values

5. Otsu method There are 100 pixels in the image Gary-level Amount Pi 2020
0.2 1 40
0.4 2 3 10
0.1 4 5
0.05
Gray level
Pi is the probability of gray-level i.
μT is average gray- level of the image.

6. Otsu method t W1(t) W2(t) μ1(t) μ2 (t) σ2B(t) 0.2 0.8 1.938 3.005 1
0.2
0.8
1.938
3.005 1
0.6
0.4
0.667
2.875
3.573 2
3.75
3.612 3
0.9
0.1
1.222
4.5
3.369 4
0.95
0.05
1.368 5
3.028
1.55
2.403
For M classes
W1(t) and W2(t) are probabilities of the two classes.
μ1(t) and μ2(t) are mean gray- level values of the two classes.
σB2(t) is between-class variance.
t* is optimal threshold.

7. Valley-emphasis method
Optimal threshold selection in gray-level histogram: (a) bimodal; (b) unimodal
The formulation for the valley-emphasis method is:
For M classes

8. Valley-emphasis methodPt
W1(t)
W2(t)
μ1(t)
μ2 (t)
σ2B(t)
σ2BV(t)
0.2
0.8
1.938
3.005
2.404 1
0.4
0.6
0.667
2.875
3.573
2.144 2
3.75
3.612
2.89 3
0.1
0.9
1.222
4.5
3.369
3.032 4
0.05
0.95
1.368 5
3.028
2.877
1.55
2.403
2.283

9. Experiments
Valley-emphasis and Otsu threshold results for contamination
detection: (a) image with no contaminant; (b) valley-emphasis threshold result; (c) Otsu threshold result and (d) histogram and threshold values.

10. Experiments
Valley-emphasis and Otsu threshold results for ceramic body
defect detection: (a) ceramic body image; (b) valley-emphasis threshold result; (c) Otsu threshold result; (d) histogram and threshold values.

11. Experiments
Valley-emphasis and Otsu threshold results for metal sheet scratch inspection: (a) metal sheet image; (b) valley-emphasis threshold result; (c) Otsu threshold result; (d) histogram and threshold values.

12. Experiments (Yasnoff et al., 1977)
BO and FO denote the background and foreground area pixels of the manually thresholded image.
BT and FT denote the background and foreground area pixels of the image that using automatic theresholding method.

13. Experiments
Valley-emphasis and Otsu threshold results for a part image: (a) part image; (b) valley-emphasis tri-level threshold result; (c) Otsu tri-level threshold result; (d) histogram and threshold values.

14. Conclusion
Valley-emphasis method is effective for selecting threshold values for defect detection applications.