IS this right or not about calculation of Total Variation (TV) for image y?

for a natural image it is difficult to calculate SNR so total variation (TV) will be calculated as an evaluation to noise.

for y(i,j)

TV=(sqrt(y(i,j)-y(i-1,j))^2+(y(i,j)-y(i+1,j))^2+(y(i,j)-y(i,j-1))^2+(y(i,j)-y(i,j+1))^2);

how can this implemented for a whole image ?

[VINSHI KK]

What indicates the variation of i and j .Is it image size?

[Image Analyst]

Yes, i and j range over the image dimensions. So i = 1 : rows and j = 1 : columns.

Answer 1

[Image Analyst]

You can calculate your TV image, and its mean and sum, like this:

clc;    % Clear the command window.
workspace;  % Make sure the workspace panel is showing.
fontSize = 20;

% Read in a standard MATLAB gray scale demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
baseFileName = 'cameraman.tif';
fullFileName = fullfile(folder, baseFileName);
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
if ~exist(fullFileName, 'file')
  % Didn't find it there.  Check the search path for it.
  fullFileName = baseFileName; % No path this time.
  if ~exist(fullFileName, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
grayImage = imread(fullFileName);
% Get the dimensions of the image.  numberOfColorBands should be = 1.
[rows columns numberOfColorBands] = size(grayImage);
% Display the original gray scale image.
subplot(2, 2, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]); % Maximize figure.
set(gcf,'name','Demo by ImageAnalyst','numbertitle','off') 

% Compute the differences between the middle pixel and the
% 4-connected neighbors.
kernel = [-1 1 0];
g = double(grayImage);
diffImageLeft = imfilter(g, kernel);
kernel = [0 1 -1];
diffImageRight = imfilter(g, kernel);
kernel = [-1 1 0]';
diffImageTop = imfilter(g, kernel);
kernel = [0 1 -1]';
diffImageBottom = imfilter(g, kernel);
TV_Image = sqrt(diffImageLeft.^2 + diffImageRight.^2 + diffImageTop.^2 + diffImageBottom.^2);
% Display the original gray scale image.
subplot(2, 2, 2);
imshow(TV_Image, []);
title('TV Image', 'FontSize', fontSize);

meanTV = mean(TV_Image(:));
sumTV = sum(TV_Image(:));
message = sprintf('The sum of the TV image pixels is %.1f\nThe mean of the TV pixels is %.5f',...
    sumTV, meanTV);
msgbox(message);

[mmm ssss]

can i kmow why you use these kernels , the calculation of the TV_image should be done to all pixels in grayImage and all results will be sum then.

also , i didnot understand this line

'The sum of the TV image pixels is %.1f\nThe mean of the TV pixels is %.5f',...

what this means?

Thanks

[Image Analyst]

I'm using imfilter to compute the difference between each pixel and the 4 neighbors, like you asked for. This creates another image of course since every x,y value will have a difference value. Now, we have 4 of those since you have 4 neighbors you're concerned about. It can't be done in one single call to imfilter because you're going to square them and add them together. Then I square those, sum them, and take the square root. This also gives another image. Then I add them all together or take the mean or sum.

The lines you asked about are simply stuffing the numerical values into a string. The '...' means the statement is continued on the next line. See sprintf() help for more info.

Answer 2

[David Young]

I don't know, but an easy initial check is to see whether it gives the same answer as

var(y(:))

or possibly

var(y(:), 1)

(See the documentation for var.)

Answer 3

[Image Analyst]

That's just the sum of the squares of a differences of a pixel value with its 3 nearest neighbors values plus the difference of one pair not squared. How is that a variance? Who says the center pixel is the mean of the 4 neighbors? Plus you didn't divide by (N-1) even if it were the mean. And I don't know what "Total" Variance is - how does it differ from the regular variance that everyone is familiar with? And your first term:

sqrt(y(i,j)-y(i-1,j))^2

is identical to y(i,j)-y(i-1,j) since you're just taking the square root and squaring it. So you're adding a linear term to two squared terms.

I think you need to think this through some more.