3D edge detection by separable recursive filtering and edge closing

1. 3D edge detection by separable recursive filtering and edge closing Author: Monga, O.; Deriche, R.; Malandain, G.; Cocquerez, J.P. Source: Pattern Recognition, 1990. Proceedings., 10th International Conference , Page(s): 652 - 654 Student: Jia – Hong Chen Advisor: Ku – Yaw Chang

2. Outline • Introduction • A 3D edge detection scheme • Closing 3D edges • Conclusion

3. Introduction • 3D edge detectors are issued • a generalization in 3D of 2D edge detectors • we propose an unified formalism for 3D edge detection • recursive filters • tracking/closing algorithm

4. Outline • Introduction • A 3D edge detection scheme • Closing 3D edges • Conclusion

5. A 3D edge detection scheme • Canny演算法 • Step1: smoothing,降低雜訊 • Step2:找邊緣,求梯度的強度 • Step3: hysteresis

6. A 3D edge detection scheme • Step1: smoothing • 使用Gaussian filter,在Gaussian filter函式中使用到variance來調整Gaussian filter的值

7. A 3D edge detection scheme

8. A 3D edge detection scheme

9. A 3D edge detection scheme

10. A 3D edge detection scheme • Step2:找邊緣,求梯度的強度 • 使用Sobel method找出邊緣,他會先計算出每一個像素的值再利用求出梯度 • 另外利用求出梯度方向

11. A 3D edge detection scheme • 1st Derivative (Gradient)

12. A 3D edge detection scheme

13. A 3D edge detection scheme

14. A 3D edge detection scheme

15. A 3D edge detection scheme

16. A 3D edge detection scheme • Step3: hysteresis • 設定2個門檻值T1和T2,由G得到的結果,任何像素如果大於T1則被認定為邊緣像素,而在這個邊緣像素鄰近的點如果有大於T2也會被認定為邊緣像素.

17. Outline • Introduction • A 3D edge detection scheme • Closing 3D edges • Conclusion

18. Closing 3D edges • It is often very difficult • select adequate thresholds for the thresholding stage • High thresholds allows to remove noisy edge points but also true edge points • low thresholds allow to obtain all true edge points but also noisy edge points

19. Closing 3D edges • Generally it is easier • extend uncompleted contours thanvalidate true contours in a noisy edge image • choose high thresholds • remove false edge points • use atracking/closing algorithm

20. Closing 3D edges • Deriche and Cocquerez • 2D edge closing method proposed • supposes that it is possible to recognize endpoints of contours • Examination of a neighbourhood 3 x 3 of an edge point • The implementation of this algorithm is easy • if an edge point is identified as an extremity the algorithm is applied recursively to the involved extremity until a stop condition is verified

21. Closing 3D edges • The 3D extension of this algorithm • applying it on each plane XY, YZ, ZX • adding the three edge images obtained • This can be justified by the assumption • the intersection of a 3D surface by at least one plane among XY,YZ and ZX

22. Closing 3D edges • it remains some localized information lacks • cause holes of width 1 along X,Y or Z • To solve this problem • select the codes corresponding to holes of width 1 • 2D implementation consists in scanning the image • fill up each identified hole

23. Outline • Introduction • A 3D edge detection scheme • Closing 3D edges • Conclusion

24. Conclusion • We have proposed a 3D edge detection scheme • saving in computational effort is of great interest • Currently we investigate true 3D closing edge methods

25. The End