1. Edge Detection Using ICA
Supervisor: Dr. Longin Jan Latecki
Presenter: Guoqiang Shan
Class: CIS 601 Computer Graphics and Image Processing
Date: December 6, 2004
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2. Basic Idea
Consider the difference of the corresponding pixels between images
A pixel is independent from each other
Pros: Limit the scope of any condition
Cons: No relation among neighbor pixels
Similar as letter detection & motion detection
Representing locality is important
Locality: neighbor pixels tend same value
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3. Quick Tip of ICA X(k) = A*S(k) S: m*n, m independent signals length n
X: m*n, m mixed signals length n
A: m*m, each column of A is a basic vector
S(k) = W*X(k)
W: m*m, separating independent signals from mixed signals
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4. S (j,:) = average image? b: Frame 55 a: Frame 50 c: 1 Component of ICA
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d: Average Image

5. Why?
2 images:
W = [ ; ];
=> c = 0.45a+0.55b
Diff (c, d) < 0.19%
4 images:
Diff (c, d) < 0.25%
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6. Basic Vector(1) Basic Vector is the main directions of the data.
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7. Basic Vector(2)
A =
[ ];
Conclusion: One of basic vector is approximately the diagonal.
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8. Basic Vector (3) t is coordinate
T(t,t)
(a, b) O
K = (b-t)/(a-t) => t = a+(a-b)/(k-1), when k=-1, t = (a+b)/2
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9. Sense on ICA
One basic vector of ICA is the diagonal, or say, one component shows the common feature among images, if:
the mixed images are similar enough
# of images is not large
Other components of ICA show the difference among images
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10. Average Image as substitute?
No!
For the points changing a lot among images, average image can not give a good result. The points are just the points we need care more about.
My proof is to obtain sense, not for simplifying the calculation.
ICA calculation is still necessary.
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11. Locality of Image Locality is the similarity of neighbor pixels
Edge is where locality is low.
Locality can be represented by m*n matrix
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12. Locality vs. one component of ICA
Locality is similarity
One component shows common features among corresponding pixels
They can be connected!
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13. Reshape the matrix
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14. One image => Several Images
To connect locality with ICA component, consider the reshaped vector as column of X
If the size of the image is X*Y, we have (X-m+1)*(Y-n+1) vectors. They consist of X.
X is the overlap of the original image.
Each image starts at (1..m, 1..n). Different image starts differently.
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15. Remove component Sj X is ready, run ICA.
Sj = locality, thus remove Sj and the corresponding basic vector Aj.
Reconstruct one of the overlapped images by other signals and other basic vectors.
The image will show only low locality, edges.
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16. This method vs. 3*3 Operators (1)
3*3 operators have pre-defined coefficients.
This method has self-adaptive coefficients.
What is the coefficient matrix?
Let A’ = A after removing Aj, A’*W is matrix.
They’re the optimal coefficients for a particular image.
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17. This method vs. 3*3 Operators (2)
3*3 operators have pre-defined number of coefficients.
This method has a flexible number of coefficients.
The flexibility provides a better choice if the edges are mainly vertical or horizontal.
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18. Experiments (1)
Original Images
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19. Experiments (2)
Edge detection by 3*3 operator and ICA
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20. Experiments (3)
Edge detection by 3*3 operator and ICA
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21. Experiments (4) Original Image By most of 3*3 operator By this method
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22. Experiments (5) Original Image I plane after RGB2YIQ
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3*3 Operator This method

23. Conclusion ICA provides a solution for edge detection.
The solution provides the more accurate coefficients, compared to 3*3 operators.
It configures the locality window size flexibly.
It can recognize some edges, unable to be done by 3*3 operators.
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24. Future work Pre-processing on the image for edge detection
Post- processing on result by this method
Find the best locality window not by try
Find what kind of images it is proper to use and what kind is improper.
How to use ICA more efficiently?
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25. Reference
Roberts and Everson, Independent Component Analysis – Principles and Practice, Cambridge University Press, 2001
Paper and software on
Comparison of edge detection methods on
Video Analysis using Principal Component Analysis
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