Question: Use Matlab programming to solve the following questions.
1. Using eigshow, and the 2x2 matrices shown in the dropdown toolbar, answer the following questions
- Which matrices are singular?
- Which matrices have complex eigenvalues?
- Which matrices have double eigenvalues?-
- In each case answer why?
2. The NCM file imagesvd.m helps you investigate the use of PCA in digital image processing. If you have them available, use your own photographs. If you have access to the Matlab Image Processing Toolbox, you may want to use its advanced features. However, it is possible to do basic image processing without the toolbox. For an m-by-n color image in JPEG format, the statement X = imread('myphoto.jpg'); produces a three-dimensional m-by-n-by-3 array X with m-by-n integer subarrays for the red, green, and blue intensities. It would be possible to compute three separate m-by-n SVDs of the three colors. An alternative that requires less work involves altering the dimensions of X with X = reshape(X,m,3*n) and then computing one m-by-3n SVD.
(a) The primary computation in imagesvd is done by [V,S,U] = svd(X',0)
Eigenvalues and Singular Values How does this compare with [U,S,V] = svd(X,0)
(b) How does the choice of approximating rank affect the visual qualities of the images? There are no precise answers here. Your results will depend upon the images you choose and the judgments you make.