One of my most hated subtopics of all math subjects are the Fourier series and transforms chapters. I can never understand the concepts and the formulas always look like a bunch of gibberish to me. This could be attributed to my laziness of weeding through thick blocks of texts conveying the concepts, and soon enough it became a spanking brand new fear for me.
When I passed my math papers, I thought that’s it. No more Fourier. That was true for the next three years, because most of the subjects during that two years were powerpacked with theories about computers and networking and software designing and programming algorithms… you know, the really IT kinda knowledge. Knowledge that you can really apply when you use your home PC.
Right now, it seemed like I’ve taken most of my theory subjects and one Final Year Project (FYP) waiting for me. Everything was fine and Fourierless until today. The new ruling of the university demands each student undertaking their FYPs to have unique titles and if there was a group working on a similar title before, the group has to split and each member will select a part of the research as their subtopic. The subtopic will narrow the scope of my research, but that’s fine with me, as long as it doesn’t go too narrow.
I was given the choices of Image Enhancement, Image Restoration, Morphological Image Processing, and Image Segmentation. I went through each of the chapters and they all still seem alien to me, even though I have been using Photoshop for months. The concepts are pretty easy to describe if you want a layman version, but if you go into the details I’m as lost as… the characters on Lost.
The chapter that interests me most is Image Restoration. You see all those banks and speedtraps, they apply the knowledge of Image Restoration to catch criminals, by manipulating the image in such a way that the pixels of the images are restored from noise and filtering. There are examples everywhere on the Internet, but I find the following pair best describes the function of Image Restoration in real life.
This is a picture of a car, but is degraded by film-grain noise. After restoration with adaptive window median filter, the image turns out like this.
See the difference? In the second picture you can read the number plate better, hence maybe catching the culprit who has been parking in the middle of the road under harsh weather circumstances (that might have caused the noise).
Why all this in the Fourierphobia post? Because almost every website I Googled for, uses Fourier transforms for their techniques. I think it’s back to the textbooks for me again. *sniff*
Images shamelessly leeched from http://www.cs.uoi.gr/~galatsanos/IMAGE%20RESTORATION.htm
