# Mirror Image

## Fast Fourier Transform for P2P networking

Very unusual application of FFT in this arxiv paper. Butterfly diagrams for radix-n FFT allow building P2P network with maximum diversity, reliability and flexibility and minimum complexity.

19, October, 2009 Posted by | Uncategorized | , | Comments Off on Fast Fourier Transform for P2P networking

## Some phase correlation tricks

Then doing phase correlation on low-resolution, or extreme low-resolution (like below 32×32) images, the noise could become a serious problem, up to making result completely useless. Fortunately there are some tricks, which help in this situation. Some of them I stumbled upon myself, and some picked up in relevant papers.
First is obvious – pass image through the smoothing filter. Pretty simple window filter from integral image can help here.
Second – check consistency of result. Histogram of cross-power specter can help here. Here there is the wheel within the wheel, which I have found out the hard way – discard lower and right sectors of cross-power specter for histogram, they are produced from high-frequency parts of the specter and almost always are noise, even if cross-power specter itself quite sane.
$\frac{F_{1}\cdot F_{2}^{*}} {\left| F_{1}\cdot F_{2} \right|}$
$\frac{F_{1}\cdot F_{2}^{*}} {a + \left| F_{1}\cdot F_{2} \right|}$
where $a$ is a small positive parameter