adaptive filter with mask 5*5 for an image with noise

how can mplement this adaptive filter with mask 5*5 for an image with noise :

f(x,y) = g(x,y) - ( (ση)^2 / (σL)^2 ) * ( g(x,y)-mL ))

where :

g(x,y) : is the value of the pixel (x,y) in the noisy image

ση : is the variance of the noise corrupting f(x,y)

σL : is the local variance for the pixels in Sxy

mL: the local mean for the pixels in Sxy

Answer 1

[Image Analyst]

This looks like the Wallis Filter. See http://www.dtic.mil/dtic/tr/fulltext/u2/a248301.pdf. It does a localized contrast stretch where is sets the mean and standard deviation of every window equal to some specified values. There is no built-in MATLAB function to do the Wallis filter. You should be able to do this using stdfilt() and conv2(). Give that a try and come back if you can't figure it out.

[Maria]

i'm tierd of trying that , may u can help me

f(x,y) = g(x,y) - ( (ση)^2 / (σL)^2 ) * ( g(x,y)-mL ))

where :

g(x,y) : is the value of the pixel (x,y) in the noisy image

ση : is the variance of the noise corrupting f(x,y)

σL : is the local variance for the pixels in Sxy

mL: the local mean for the pixels in Sxy

Assumptions of Operation

If is zero, the filter should return the value of g(x,y). This is the trivial case in which there is no noise in the image

If the local variance is high relative to , the filter should return a value close to g(x,y) since high local variance is usually associated with edges and these have to be preserved

If the two variances are equal, the filter should return the mean value of the pixels in Sxy. This situation correspond to the case when the local area has similar properties as the overall image, and local noise is to be removed by averaging.

[Image Analyst]

What is Sxy? Is it an image? Do we need it or can we just work with ση and σL that you specify values for? Or do those need to be calculated from Sxy somehow?

[Maria]

Sxy is the pixels at each location on which the filter window is centerd

The mean gives the average intensity in the region while variance is a measure of contrast

The filter under discussion uses four different values to perform filtering in a certain neighborhood

ση is measured by assumption , all of remaining values can be computed from Sxy

this technique called (adaptive local noise reduction) its a techniques found in gonzales book (image processing) in image restoration cahpter

[Image Analyst]

Do you mean "tired of trying"? Well if you're exhausted of trying different things to program it up, then perhaps this will be enough to kick start your efforts:

% Script to compute the locally adaptive filter:
% f(x,y) = g(x,y) - ( (ση)^2 / (σL)^2 ) * ( g(x,y)-mL ))

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures if you have the Image Processing Toolbox.
clearvars;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 15;

% Check that user has the Image Processing Toolbox installed.
hasIPT = license('test', 'image_toolbox');
if ~hasIPT
  % User does not have the toolbox installed.
  message = sprintf('Sorry, but you do not seem to have the Image Processing Toolbox.\nDo you want to try to continue anyway?');
  reply = questdlg(message, 'Toolbox missing', 'Yes', 'No', 'Yes');
  if strcmpi(reply, 'No')
    % User said No, so exit.
    return;
  end
end

% Read in a standard MATLAB gray scale demo image.
button = menu('Use which demo image?', 'CameraMan', 'Moon', 'Eight', 'Coins', 'Pout');
if button == 1
  baseFileName = 'cameraman.tif';
elseif button == 2
  baseFileName = 'moon.tif';
elseif button == 3
  baseFileName = 'eight.tif';
elseif button == 4
  baseFileName = 'coins.png';
else
  baseFileName = 'pout.tif';
end

% Read in a standard MATLAB gray scale demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % File doesn't exist -- 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 in the search path folders.', 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);
if numberOfColorBands > 1
  % It's not really gray scale like we expected - it's color.
  % Convert it to gray scale by taking only the green channel.
  grayImage = grayImage(:, :, 2); % Take green channel.
end
% Display the original gray scale image.
subplot(2, 4, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Give a name to the title bar.
set(gcf,'name','Demo by ImageAnalyst','numbertitle','off') 

% Let's compute and display the histogram.
[pixelCount, grayLevels] = imhist(grayImage);
subplot(2, 4, 5); 
bar(pixelCount);
grid on;
title('Histogram of Original Grayscale Image', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.

% Get the local mean image
windowSize = 5;
kernel = ones(windowSize)/windowSize^2;
meanImage = conv2(double(grayImage), kernel, 'same');
% Display the local mean image.
subplot(2, 4, 2);
imshow(meanImage, []);
title('Local Mean Image', 'FontSize', fontSize);

% Let's compute and display the histogram.
[pixelCount, grayLevels] = hist(meanImage(:), 100);
subplot(2, 4, 6); 
bar(grayLevels, pixelCount);
grid on;
title('Histogram of Local Mean image', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.

% Get the standard deviation of the image
nHood = ones(windowSize);
sdImage = stdfilt(grayImage, nHood);
% Display the image.
subplot(2, 4, 3);
imshow(sdImage, []);
title('Standard Deviation Image', 'FontSize', fontSize);

% Let's compute and display the histogram.
[pixelCount, grayLevels] = hist(sdImage(:), 100);
subplot(2, 4, 7); 
bar(grayLevels, pixelCount);
grid on;
title('Histogram of Standard Deviation image', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.

% Compute the output image
% f(x,y) = g(x,y) - ( (ση)^2 / (σL)^2 ) * ( g(x,y)-mL ))
sn = 4;
sL = 3;
outputImage = double(grayImage) - (sn^2/sL^2) * (double(grayImage) - meanImage);
% Display the image.
subplot(2, 4, 4);
imshow(outputImage, []);
title('Output Image', 'FontSize', fontSize);

% Let's compute and display the histogram.
[pixelCount, grayLevels] = hist(outputImage(:), 100);
subplot(2, 4, 8); 
bar(grayLevels, pixelCount);
grid on;
title('Histogram of Output Image', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.