Posts Tagged ‘filtering’

No, that’s not a Gaussian filter

Friday, February 6th, 2015

I recently got a question from a reader regarding Gaussian filtering, in which he says:

I have seen some codes use 3×3 Gaussian kernel like

    h1 = [1, 2, 1]/4

to do the separate filtering.

The paper by Burt and Adelson (The Laplacian Pyramid as a Compact Image Code, IEEE Transactions on Communication, 31:532-540, 1983) seems to use 5×5 Gaussian kernel like

    h1 = [1/4 - a/2, 1/4, a, 1/4, 1/4-a/2],

and a is between 0.3-0.6. A typical value of a may be 0.375, thus the Gaussian kernel is:

    h1 = [0.0625, 0.25, 0.375, 0.25, 0.0625]

or

    h1 = [1, 4, 6, 4, 1]/16.

I have written previously about Gaussian filtering, but neither of those posts make it clear what a Gaussian filter kernel looks like.

(more…)

On interpolation

Saturday, January 4th, 2014

Last month I asked the following question in an exam for the advanced image analysis course we teach here: “Given that interpolation is a convolution, describe how you would compute an interpolation using the Fourier Transform.” Unfortunately I can count on one finger the number of students that did not simply answer with something in the order of “convolution can be computed by multiplication in the Fourier domain.” And the one student that did not give this answer didn’t give an answer at all… Apparently this question is too difficult, though I thought it was interesting and only mildly challenging. In this post I’ll discuss interpolation and in passing give the correct answer to this question.

(more…)