Question

MATLAB ONLY

Instructions: The following problems can be done interactively or by writing the commands iın an M-file (or by a combination of the two). In either case, record all MATLAB input commands and output in a text document and edit it according to the instructions of LAB 1 and LAB 2. For problem 2, include a picture of the rank-1 approximation. For problem 3, include a picture of the rank-10 approximation and for problem 4, include a picture of the lower rank approximation that, in your opinion, gives an acceptable approximation to the original picture. Crop and resize the pictures so that they do not take up too much space and paste them into ur lab report in the appropriate order. Step 1. Download the file gauss.jpg and save it to your working MATLAB directory Then load it into MATLAB with the command A inread('gauss.jpg'); % note the semicolon! The semicolon is necessary so that MATLAB does not print out many screenfuls of data The result is a matrix of grayscale values corresponding to a black and white picture of a dog. (The matrix has 252320 entries). Now, A is actually 380 x 664 x 3. To create an image from the matrix A, MATLAB uses the three values A(i, j,1 : 3) as the RGB values to use to color the pixel in the i-th row and j-th column. We have a black and white picture so A( : , : , 1) A(: , : ,2) = A(: , : ,3) and we only need to work with A(:,: ,1) Step 2. We need to do some initial processing. Type B double CA (:,:,1)); % don't forget the semicolon which converts A into the double-precision format that is needed for the singular value decomposition. Now type B-B/255; % semicolon! [USV] =svd(B); % semicolon! This decomposition is just Eq. (1) The gray scale goes from 0 to 255 in a black- and-white JPEG image. We divide B by 255 to obtain values between 0 and 1, which is required for MATLAB's image routines, which we will use later. PROBLEM 1. What are the dimensions of U, S, and V? (Find out by typing size(U) without the semicolon - and likewise for the others.)

gauss.jpg BELOW

Answer 1

As the rank of image increases, the resultant image goes to signal image, Images with rank above i.e 10, 20, 30 and 40 are good approximate the unean equare error (MSF) and peak signal to moise ration (PSNR) indicates the image quality Mage with rank 20 and above are very approximate image to that of the original one the matrix seript is given below: Close all clear all clc, subplotrow = 6: subplotcol = 2 % slep - 1 project path - pwd Image path - strcat (project path: \ frobenicesjpg) orig = imread (image path) subplot (subtrow, subplotcol,1) imshow(orig) fettle frobenius A = orig(: : ,1): subplot (subplot row, subplotcol) (A): tittle (original Frobenius imag -A (.;.: 1) % slep 2 B = double (A) B = B/255: [USV] svd (B): disp (size(4) =): size (4) disp (size(s) =): size(s) disp(size (V) =): size (V) % step 3 c = zero s (size (A)):