Edge Detection Using ICA

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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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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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Quick Tip of ICA

• X(k) AS(k)
• S mn, m independent signals length n
• X mn, m mixed signals length n
• A mm, each column of A is a basic vector
• S(k) WX(k)
• W mm, separating independent signals from
  mixed signals

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S (j,) average image?

• b Frame 55

• a Frame 50

• c 1 Component of ICA

• d Average Image

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Why?

• 2 images
• W -0.0549 0.0553 0.0083 0.0102
• gt c 0.45a0.55b
• Diff (c, d) lt 0.19
• 4 images
• Diff (c, d) lt 0.25

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Basic Vector(1)
Basic Vector is the main directions of the data.
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Basic Vector(2)

• A
• 9.988 54.280 -8.166 53.940

Conclusion One of basic vector is approximately
the diagonal.
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Basic Vector (3)
t is coordinate
T(t,t)
(a, b)
O

• K (b-t)/(a-t) gt t a(a-b)/(k-1), when k-1,
  t (ab)/2

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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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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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Locality of Image

• Locality is the similarity of neighbor pixels
• Edge is where locality is low.
• Locality can be represented by mn matrix

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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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Reshape the matrix
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One image gt Several Images

• To connect locality with ICA component, consider
  the reshaped vector as column of X
• If the size of the image is XY, we have
  (X-m1)(Y-n1) 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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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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This method vs. 33 Operators (1)

• 33 operators have pre-defined coefficients.
• This method has self-adaptive coefficients.
• What is the coefficient matrix?
• Let A A after removing Aj, AW is matrix.
• Theyre the optimal coefficients for a particular
  image.

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This method vs. 33 Operators (2)

• 33 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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Experiments (1)

• Original Images

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Experiments (2)

• Edge detection by 33 operator and ICA

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Experiments (3)

• Edge detection by 33 operator and ICA

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Experiments (4)
Original Image
By most of 33 operator
By this method
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Experiments (5)

• Original Image
  I plane after RGB2YIQ

• 33 Operator
  This method

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Conclusion

• ICA provides a solution for edge detection.
• The solution provides the more accurate
  coefficients, compared to 33 operators.
• It configures the locality window size flexibly.
• It can recognize some edges, unable to be done by
  33 operators.

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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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Reference

• Roberts and Everson, Independent Component
  Analysis Principles and Practice, Cambridge
  University Press, 2001
• Paper and software on http//www.cis.hut.fi/projec
  ts/ica/
• Comparison of edge detection methods on
  http//robotics.eecs.berkeley.edu/mayi/imgproc/
• Video Analysis using Principal Component Analysis
  http//knight.cis.temple.edu/video/VA/