MATLAB: How do you perform a difference of Gaussian filter on an image,

Question

Hi guys

How do you perform a 3×3 difference of Gaussian filter on an image, where sigma1 = 5 and sigma2 = 2 and retain the positive values?

Your help is really appreciated!!!!!!!!!!!!

Thanks

Marcus

Answer 1

You can't. Try to visualize: what kind of Gaussian shape can you have when you just have one sample point on either side of the middle? Is that really a Gaussian? Now think of two Gaussians - so basically there's two numbers for that location (one pixel away from the center pixel). Now you subtract them and you still have one number. How do you know if that one number is the result of subtracting two Gaussians or is just one single Gaussian? You don't.

That said, you can do DOG filters with larger window sizes. See fspecial() for examples. See this demo I wrote just for you:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures.
clear;  % Erase all existing variables.
workspace;  % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;
% Read in a standard MATLAB gray scale demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
button = menu('Use which demo image?', 'CameraMan', 'Moon', 'Eight', 'Coins');
if button == 1
  baseFileName = 'cameraman.tif';
elseif button == 2
  baseFileName = 'moon.tif';
elseif button == 3
  baseFileName = 'eight.tif';
else
  baseFileName = 'coins.png';
end
% 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);
% 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]);
% 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, 2, 2); 
bar(pixelCount);
grid on;
title('Histogram of Original Image', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.
gaussian1 = fspecial('Gaussian', 21, 15);
gaussian2 = fspecial('Gaussian', 21, 20);
dog = gaussian1 - gaussian2;
dogFilterImage = conv2(double(grayImage), dog, 'same');
subplot(2, 2, 3); 
imshow(dogFilterImage, []);
title('DOG Filtered Image', 'FontSize', fontSize);
% Let's compute and display the histogram.
[pixelCount grayLevels] = hist(dogFilterImage(:));
subplot(2, 2, 4); 
bar(grayLevels, pixelCount);
grid on;
title('Histogram of DOG Filtered Image', 'FontSize', fontSize);