I am recently learning about Computer Vision and I am having a trouble understanding Difference of Gaussian (DoG) algorithm. I get how the algorithm works in high level idea, but I am trying to implement my own and I am confused about some steps.

For instance, I am trying to create 5 blur level for each octave, and I am confused about which filter and sigma value applying to which image. Using Matlab, for the first octave, I created a filter and applied:

sigma = 0.5;
gauss = fspecial('gaussian', [5 5], sigma);
blur1 = imfilter(img, gauss, 'replicate');
dog1 = img - blur1;
%Next level
blur2 = imfilter(blur1, gauss, 'replicate');
dog2 = blur1 - blur2;

I am not so sure if this is how I need to apply? Do I apply gaussian filter to previously applied image? I also saw code using k*sigma. I am not sure what k means and how to apply? Oh and what value should I used for sigma? Is it in [0, 1] range or can be bigger than that? Could someone help me on this? Thank you very much.
Thank you so much!

  • $\begingroup$ If you have MATLAB version R2015a or later, there is an imgaussfilt function, that will save you the trouble of creating the filter. $\endgroup$
    – Dima
    Commented Nov 5, 2015 at 23:45

1 Answer 1


Difference of gaussian is the difference in the output of two Gaussian filters with different blur amounts (sigma).

Sigma is the size of the Gaussian filter. A bigger sigma gives you a bigger amount of blurring. A good way to think about it is a Gaussian filter with variance sigma is very roughly like averaging 3 x sigma samples wide (or 3 x 3 in an image)

e.g. from wikipedia:

enter image description here

Very Important when making a Gaussian filter in MATLAB make sure the size of the filter is at least 6 x sigma. In your above code you have 5 x 5 which is fine for sigma = 0.5, but for sigma = 1 you would want 6 x 6 or bigger.

The k is simply a multiplier for sigma.


sigma = 0.5;
gauss1 = fspecial('gaussian', round([10*sigma 10*sigma]), sigma);
sigma = 1;
gauss2 = fspecial('gaussian', round([10*sigma 10*sigma]), sigma);
blur1 = imfilter(img, gauss1, 'replicate', 'same');
blur2 = imfilter(img, gauss2, 'replicate', 'same');
dog2 = blur1 - blur2;

A more complete code example that allows you to set the number of octaves and the steps per octave:

%% Filter using DoG
stepsPerOctave = 5;
octaves = 4;
mult = nthroot(2,stepsPerOctave);

% Create blurry images
sigma = 0.5;
kernelSize = [10*sigma*2^(octaves),10*sigma*2^(octaves)]
for k = 1:octaves*stepsPerOctave+1
    disp(['Sigma is ' num2str(sigma)]);
    gauss = fspecial('gaussian', kernelSize, sigma);
    blur(:,:,k) = imfilter(I, gauss, 'replicate', 'same');
    imagesc(blur(:,:,k)); colorbar; title(['Gaussian ' num2str(k)]); pause;
    sigma = sigma * mult;

% Create DoG
for k = 1:octaves*stepsPerOctave
    dog(:,:,k) = blur(:,:,k+1) - blur(:,:,k);
    imagesc(dog(:,:,k)); colorbar; title(['DoG ' num2str(k)]); pause;
  • $\begingroup$ Thank you very much for your explanation and code! That definitely helps me understanding and clear all the confusion! Thank you very very much! $\endgroup$
    – user2168
    Commented Jul 6, 2015 at 0:24

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