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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.
2 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
OutlineOutline
Abstract Grayscale conversion
• Principal component analysis
• Principal component vector computation
• Proposed method
• Computational complexity analysis
Results and discussion Conclusion
3 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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
4 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
ProblemProblem
Original Image Grayscale Image
5 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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
6 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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)
7 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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
8 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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
9 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Grayscale conversionGrayscale conversion
The data is projected along the directions where it varies most
v1 = Ckv(0)
Using (3) for i = 1
10 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
11 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
12 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
13 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
14 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
15 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
16 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
17 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
18 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
19 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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)
20 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
Results and discussionResults and discussion
21 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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
22 aiRobots Lab., EE Dept., NCKUaiRobots Lab., EE Dept., NCKU
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.