What is the "do-nothing" convolution kernel

Question

If I am trying to do a convolution kernel in Frequency space - what is the "do-nothing" kernel. In other words, if I view the image after applying the kernel, and normalizing it in Frequency space, I just want to see the raw Fourier transform

Is it the identity matrix? my kernel is 3x3

Thanks

Cordi

Answer 1

A do-nothing 3x3 kernel will be:

0 0 0
0 1 0
0 0 0

I hope I understood your question correctly - I'm not sure why you would want such a kernel, when it's much easier to just skip the convolution entirely.

Biggs

I am trying to test some functions from the CUDA FFT libraries that do the matrix multiplication AND normalization all in one step. So assuming I ran the FFT of an image, using this kernel in your answer, my FT image should be the true image FT, as if no filter applied, right? – Cordi

@Derek, right I think. I don't know what the convolution will do at the image boundaries so I can't say for sure. – Biggs

There is no reason a kernel must be 3x3. You can lea e out all those 0’s, and make a 1x1 kernel. – Proa

@CrisLuengo that's true. But the question specifically asked for a 3x3. – Biggs

Answer 2

The "do-nothing" convolution kernel is the Dirac delta function: "δ(x)".

The solution mark-ransom shared is just that! Any signal convolved with the Dirac delta is identical to the original signal. This applies to convolution in any n-dimension.

The Dirac delta has many other interesting properties:

• δ can be discrete or continuous in nature
• δ(0) = ∞
• The laplace transform of δ(x) equals 1
• The indefinite integral of δ(x) equals 1
• see Wikipedia for more

Also see how to create δ convolutional neural network layer

Leges

Thanks! I updated the answer to be more relevant. – Leges