# Fourier Mellin Transform

I'm working on a Fourier-Mellin transform on images to find angle and scale.

In most cases when I have scaled and rotated an image, the Fourier-Mellin transform gives me the almost exact angle and scale.

When I have a moiré pattern on my original image or some corrupted area of the original image, the Fourier-Mellin transform does not give a meaningful result.

I especially want to solve moiré pattern case.

• What does exactly affect on the Fourier-Mellin transform?
• What can I do to the image before the transform to enhance the result?

## 1 Answer

Moiré patterns in sampled imaging are usually effects of aliasing.

As usual, with aliasing, it's most visible in high-frequency bins, as that's where low-frequency energy gets aliased to. It's also the case that high-frequency energy gets aliased to low frequencies.

So, the first approach would be to compare the spectra (absolute of the Fourier transform) of images with and without Moiré patterns. You'll probably see more energy at higher frequencies. Note the rough ratio of how much of the overall Nyquist bandwidth is affected. (For example, if the top 10% of frequencies contain more energy in pictures with Moiré patterns, note 0.1)

Then design a real 1D bandpass FIR filter to pass through everything in frequency that is higher than that ratio, and lower than (1-ratio). Make a circularly symmettric 2D kernel from that, and convolve your image with it. (details on how to deal with edge effects will depend on what you're doing with the results later on, so you'll have to figure out for yourself what is appropriate – padding, cutting or circular repetition.)

With the Moire patterns out of the way, try your Mellin transform.