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.

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

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

Problem Original Image Grayscale Image

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

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)

Principal Component Analysis For a1=25, a2=62, a3=18 v1 = -0.8143 0.5550 0.1697 k = 1 V(k) = -0.6119 -0.0703 0.7878 k = 2 -0.7568 0.1407 0.6383 k = 3 -0.8199 0.3211 0.4740 k = 4 V(k) = -0.8327 0.4304 0.3483 k = 5 -0.8294 0.4890 0.2701 k = 6 -0.8241 0.5197 0.2252 k =15 V(k) = -0.8144 0.5549 0.1699 k =16 0.1698 k =17 0.5550 0.1697 k =18 V(k) = -0.8144 0.5550 0.1697 k =19 k =20 … V(0) = -0.3060 -0.0882 0.9479

Principal Component Analysis For a1=25, a2=62, a3=18 v1 = -0.8143 0.5550 0.1697 k = 1 V(k) = -0.6119 -0.0703 0.7878 k = 2 -0.7568 0.1407 0.6383 k = 3 -0.8199 0.3211 0.4740 k = 4 V(k) = -0.8327 0.4304 0.3483 k = 5 -0.8294 0.4890 0.2701 k = 6 -0.8241 0.5197 0.2252 k =15 V(k) = -0.8144 0.5549 0.1699 k =16 0.1698 k =17 0.5550 0.1697 k =18 V(k) = -0.8144 0.5550 0.1697 k =19 k =20 … V(0) = -0.3060 -0.0882 0.9479

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

Results and discussion

Results and discussion

Results and discussion

Results and discussion

Results and discussion

Results and discussion

Results and discussion

Results and discussion

Results and discussion

Results and discussion

Results and discussion

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

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