Edge Detection Using ICA Supervisor: Dr. Longin Jan Latecki Presenter: Guoqiang Shan Class: CIS 601 Computer Graphics and Image Processing Date: December 6, 2004 2019/4/22

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 2019/4/22

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 2019/4/22

S (j,:) = average image? b: Frame 55 a: Frame 50 c: 1 Component of ICA 2019/4/22 d: Average Image

Why? 2 images: W = [-0.0549 0.0553; 0.0083 0.0102]; => c = 0.45a+0.55b Diff (c, d) < 0.19% 4 images: Diff (c, d) < 0.25% 2019/4/22

Basic Vector(1) Basic Vector is the main directions of the data. 2019/4/22

Basic Vector(2) A = [9.988 54.280 -8.166 53.940]; Conclusion: One of basic vector is approximately the diagonal. 2019/4/22

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 2019/4/22

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 2019/4/22

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. 2019/4/22

Locality of Image Locality is the similarity of neighbor pixels Edge is where locality is low. Locality can be represented by m*n matrix 2019/4/22

Locality vs. one component of ICA Locality is similarity One component shows common features among corresponding pixels They can be connected! 2019/4/22

Reshape the matrix 2019/4/22

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. 2019/4/22

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. 2019/4/22

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. 2019/4/22

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. 2019/4/22

Experiments (1) Original Images 2019/4/22

Experiments (2) Edge detection by 3*3 operator and ICA 2019/4/22

Experiments (3) Edge detection by 3*3 operator and ICA 2019/4/22

Experiments (4) Original Image By most of 3*3 operator By this method 2019/4/22

Experiments (5) Original Image I plane after RGB2YIQ 2019/4/22 3*3 Operator This method

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. 2019/4/22

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? 2019/4/22

Reference Roberts and Everson, Independent Component Analysis – Principles and Practice, Cambridge University Press, 2001 Paper and software on http://www.cis.hut.fi/projects/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/ 2019/4/22