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While learning an image denoising technique based on bilateral filter, I encountered this tutorial which provides with full lists of arguments used to run OpenCV's bilateralFilter function. What I see, it's slightly confusing, because there is no explanation about a mathematical rule to alter the diameter value by manipulating both the sigma arguments. So, if picking some specific arguments to pass into that function, I realize hardly what diameter corresponds with a particular couple of sigma values.

Does there exist a dependency between both deviations and the diameter? If my inference is correct, what equation (may be, introduced in OpenCV documentation) is to be referred if applying bilateral filter in a program-based solution?

Cris Luengo
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mission_code_now
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2 Answers2

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According to the documentation, the bilateralFilter function in OpenCV takes a parameter d, the neighborhood diameter, as well as a parameter sigmaSpace, the spatial sigma. They can be selected separately, but if d "is non-positive, it is computed from sigmaSpace." For more details we need to look at the source code:

    if( d <= 0 )
        radius = cvRound(sigma_space*1.5);
    else
        radius = d/2;
    radius = MAX(radius, 1);
    d = radius*2 + 1;

That is, if d is not positive, then it is taken as 3 times sigmaSpace. d is also always forced to be odd, so that there is a central pixel in the neighborhood.

Note that the other sigma, sigmaColor, is unrelated to the spatial size of the filter.

In general, if one chooses a sigmaSpace that is too large for the given d, then the Gaussian kernel will be cut off in a way that makes it not appear like a Gaussian, and loose its nice filtering properties (see for example here for an explanation). If it is taken too small for the given d, then many pixels in the neighborhood will always have a near-zero weight, meaning that computational work is wasted. The default value is rather small (one typically uses a radius of 3 times sigma for Gaussian filtering), but is still quite reasonable given the computational cost of the bilateral filter (a smaller neighborhood is cheaper).

Cris Luengo
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These two value (d and sigma) are totally unrelated to each other. Sigma determines the values of the pixels of the kernel, but d determines the size of the kernel.

For example consider this Gaussian filter with sigma=1:

enter image description here

It's a filter kernel and and as you can see the pixel values of the kernel only depends on sigma (the 3*3 matrix in the middle is equal in both kernel), but reducing the size of the kernel (or reducing the diameter) will make the outer pixels ineffective without effecting the values of the middle pixels.

And now if you change the sigma, (with k=3) the kernel is still 3*3 but the pixels' values would be different.

MeiH
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