AiRobots Lab., EE Dept., NCKU aiRobots Lab., EE Dept., NCKU 1 Chrominance edge preserving grayscale transformation with approximate first principal component.

1 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU

Chrominance edge preserving grayscale Chrominance edge preserving grayscale transformation with approximate first principal transformation with approximate first principal

component for color edge detectioncomponent 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.

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OutlineOutline

Abstract Grayscale conversion

• Principal component analysis

• Principal component vector computation

• Proposed method

• Computational complexity analysis

Results and discussion Conclusion

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AbstractAbstract

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

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ProblemProblem

Original Image Grayscale Image

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Principal Component AnalysisPrincipal Component Analysis

Principal component analysis (PCA)• De-correlate a data set

• Reduce the dimensionality of the data set

maximum-likelihood (ML) covariance matrix estimat

e is

• C is a 3× 3 real and symmetric matrix

• eigenvalues λ1, λ2, λ3

• eigenvectors v1, v2, v3

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Principal Component AnalysisPrincipal 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)

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Principal Component AnalysisPrincipal Component Analysis For a1=25, a2=62, a3=18

v1 =

-0.8143

0.5550

0.1697

k = 4V(k) =-0.83270.43040.3483

k = 5V(k) =-0.82940.48900.2701

k = 6V(k) =-0.82410.51970.2252

k = 1V(k) =-0.6119-0.07030.7878

k = 2V(k) =-0.75680.14070.6383

k = 3V(k) =-0.81990.32110.4740

…

k =15V(k) =-0.81440.55490.1699

k =16V(k) =-0.81440.55490.1698

k =17V(k) =-0.81440.55500.1697

k =18V(k) =-0.81440.55500.1697

k =19V(k) =-0.81440.55500.1697

k =20V(k) =-0.81440.55500.1697

V(0) =-0.3060-0.08820.9479

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Principal Component AnalysisPrincipal Component Analysis For a1=25, a2=62, a3=18

v1 =

-0.8143

0.5550

0.1697

k = 4V(k) =-0.83270.43040.3483

k = 5V(k) =-0.82940.48900.2701

k = 6V(k) =-0.82410.51970.2252

k = 1V(k) =-0.6119-0.07030.7878

k = 2V(k) =-0.75680.14070.6383

k = 3V(k) =-0.81990.32110.4740

…

k =15V(k) =-0.81440.55490.1699

k =16V(k) =-0.81440.55490.1698

k =17V(k) =-0.81440.55500.1697

k =18V(k) =-0.81440.55500.1697

k =19V(k) =-0.81440.55500.1697

k =20V(k) =-0.81440.55500.1697

V(0) =-0.3060-0.08820.9479

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Grayscale conversionGrayscale conversion

The data is projected along the directions where it varies most

v1 = Ckv(0)

Using (3) for i = 1

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussion

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Results and discussionResults and discussionOriginal Image General Grayscale Grayscale (The Proposed Method)

RGB Edge Map General Grayscale Edge Map Edge Map (The Proposed Method)

Original Image General Grayscale Grayscale (The Proposed Method)

RGB Edge Map General Grayscale Edge Map Edge Map (The Proposed Method)

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Results and discussionResults and discussion

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ConclusionConclusion

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

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Thank you for your attention!Thank you for your attention!

aiRobots Laboratory, Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C.