1. IEEE Transactions on Consumer Electronics, Vol. 45, No. 1, AUGUST 1999 Muhammad Bilal Ahmad and Tae-Sun Choi, Senior Member,IEEE

2. Outline  Introduction  Overview  Method - Thresholding - Boolean Functions - False Edge Rremoval  Experimental Results  Conclusion  Q & A

3. Introduction (1/2)  The edge detection methods can be classified into two types, namely, directional operators, and non-directional operators. - two masks, convolutions vs single masks, convolutions. - zero-crossing vs gradient-based  The popular gradient operators are that of Sobel,Prewitt, Robert, Laplacian, etc.

4. Introduction (2/2)  The operator based on derivatives of Gaussian is Laplacian of Gaussian. Gradient based operators use thresholding for edge detection. - less than the threshold set to black(0), otherwise set to white(1). Threshold 128

5. Overview (1/2)  Two types thresholding - (a) local techniques - (b) global techniques  The algorithm is based on local operations, global operations, and Boolean algebra. - Thresholding (Local operation) - Boolean Functions (Local operation) - False Edge Rremoval (Global Thresholding)

6. Overview (2/2) Local Global

7. Method Local Global

8. Method  Take window of size (3x3) of the original gray- level image.  Local threshold is found on the basis of local mean value. - converts the gray-level image into binary image.  Use Boolean functions in the cross-correlation of the image window. - true edges as well as false edges.

9. Method  The global threshold is preselected, considering the presence of noise in the image. - remove false edges  The resulting intermediate edge map is logically ANDed with the intermediate edge map from local threshold.

10. Method (Thresholding)  Common types - T L = Mean - T L = Median - T L = (Max+Min) / 2 - T L = (Max-Min) / 2  Use the mean value approach.

11. Method (Thresholding 1/2)  Formula Mean μ = where N=3, Local threshold shown below T L (X,Y) = (μ - C), where C is a constant(preselected).

12. Method (Thresholding 2/2)  W L (X,Y) = 1 if W(X,Y) > T L (X,Y) W L (X,Y) = 0 otherwise  1 set to white, 0 set to black. - binary image  W L is the binary image(0,1) and then we can get the edge we find. - Boolean operation.

13. Method (Boolean Functions 1/2) [2] M A. Sid-Ahmed, “Image Processing”, McGraw-Hill, Inc. Sixteen patterns Prewitt compass masks

14. Method (Boolean Functions 2/2)  For edge finding, the window W L (x,y) is cross- correlated with sixteen edge like patterns.  Any pattern which matches the window W L (x,y) is called an edge at the center of the window W(x,y).  B0 = !B(0,0) ×B(0,1) × B(0,2) ×!B(1,0) × B(1,1) × B(1,2) ×!B(2,0) × B(2,1) × B(2,2)

15. Method (False Edge Rremoval 1/2)  False edges are detected due to the presence of noise.  We take a new threshold T N (preselected), whose value is related with the noise level in the image.  We calculate as variance value.

16. Method (False Edge Rremoval)  Formula where g(x,y) is the intensity value of the window W(x,y), μ is the mean of the neighbors (3x3) at (x,y) position, and NxN is the window size. B (X,Y) = 1 if > T N (X,Y) B (X,Y) = 0 otherwise

17. Method  The two resulting images are logically ANDed to get the final edge map.

18. Experimental Results

21. Conclusions  The global threshold(T N ) and the constent C in Mean value approach are preselected.  The proposed method detects edges in two processes. - (local)image is locally thresholded and using Boolean algebra(true and false edge) - (global)detects the true edges only.  Minimizes the noise, and also edge lines are thinner.

22. Q & A