1. Chrominance edge preserving grayscale transformation with approximate first principal component for color edge detection
Professor: 連震杰 教授
Reporter: 第17組
郭秉寰、鄭凱中、王德凱、洪慈欣
aiRobots Laboratory, Department of Electrical Engineering,
National Cheng Kung University, Tainan, Taiwan, R.O.C.

2. Outline Abstract Grayscale conversion Results and discussion
Principal component analysis
Principal component vector computation
Proposed method
Computational complexity analysis
Results and discussion
Conclusion

3. Abstract Color edge detection Image edge analysis PCA
New set of luminance coefficients
Propose a transformation that preserves chrominance edges
Reduce the dimensionality of color space

4. Problem
Original Image
Grayscale Image

5. Principal Component Analysis
Principal component analysis (PCA)
De-correlate a data set
Reduce the dimensionality of the data set
maximum-likelihood (ML) covariance matrix estimate is
C is a 3× 3 real and symmetric matrix
eigenvalues λ1, λ2, λ3
eigenvectors v1, v2, v3

6. Principal Component Analysis
Let v(0) be a normalized vector not orthogonal to v1
Where k ≥ 0 As k→∞, v(k) → v1
v(k+1) = Ck+1v(0)

7. Principal Component Analysis
For a1=25, a2=62, a3=18
v1 =
0.5550
0.1697
k = 1
V(k) =
0.7878
k = 2
0.1407
0.6383
k = 3
0.3211
0.4740
k = 4
V(k) =
0.4304
0.3483
k = 5
0.4890
0.2701
k = 6
0.5197
0.2252
k =15
V(k) =
0.5549
0.1699
k =16
0.1698
k =17
0.5550
0.1697
k =18
V(k) =
0.5550
0.1697
k =19
k =20 …
V(0) =
0.9479

8. Principal Component Analysis
For a1=25, a2=62, a3=18
v1 =
0.5550
0.1697
k = 1
V(k) =
0.7878
k = 2
0.1407
0.6383
k = 3
0.3211
0.4740
k = 4
V(k) =
0.4304
0.3483
k = 5
0.4890
0.2701
k = 6
0.5197
0.2252
k =15
V(k) =
0.5549
0.1699
k =16
0.1698
k =17
0.5550
0.1697
k =18
V(k) =
0.5550
0.1697
k =19
k =20 …
V(0) =
0.9479

9. Grayscale conversion
The data is projected along the directions where it varies most
v1 = Ckv(0)
Using (3) for i = 1

10. Results and discussion

11. Results and discussion

12. Results and discussion

13. Results and discussion

14. Results and discussion

15. Results and discussion

16. Results and discussion

17. Results and discussion

18. Results and discussion

19. Results and discussion

20. Results and discussion

21. Conclusion Save computation time Data compression
The conversion enables the edge detector to detect some edges of the grayscale image that are not detected using regular grayscale image

22. Thank you for your attention!
aiRobots Laboratory, Department of Electrical Engineering,
National Cheng Kung University, Tainan, Taiwan, R.O.C.