Lode's Computer Graphics Tutorial Fourier Transform

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It can be seen that only the high frequency parts of the image are left: subtle gradients and colorchanges are gone, only the edges of objects and especially the cooling fin are still recognisable.Photoshop, instead of adding the DC component, adds grey to the image to make all pixels positive, sothe result of the High Pass filter in Photoshop is something like this:If we use a higher radius for the removed circle, only the very highest frequencies remain, only thecooling fin still looks pretty nice:A high pass filter can also be done by first blurring the image, and then substracting the blurred imagefrom the original.After seeing those pictures you might wonder if there is actually something useful that can be donewith a High Pass Filter? Well, it can for example be used to make better tillable textures, take forexample this grass texture:If you tile it, it looks like this:
It looks pretty ugly, because there are obvious bright and dark spots in the image, and these look veryrepetitive. These large areas of bright and darker color are very low frequency components, so they canbe removed with a subtle High Pass Filter!Let's process the image to our program, apply a High Pass filter with a very small radius to it, and bringthe DC component back: the DC component is the lowest frequency of all, just a flat color, so it can'tlook repetitive, and is very important because it contains the green color of the grass. As you can see onthe third row on the right in the screenshot, a very small circular section of the spectrum is removed,and in the centre of the circle is a single white point which is the DC component.At the bottom row a new version of the grass texture appeared, that looks already much better whentiled if you take a certain distance from it:
Page 1 and 2: Lode's Computer Graphics TutorialFo
Page 3 and 4: would have a single peak. A spectru
Page 5 and 6: The spectrum is positive everywhere
Page 7 and 8: This looks already much more progra
Page 9 and 10: that remains at fixed position, whi
Page 11 and 12: It takes 4 arrays as parameters: *g
Page 13 and 14: FFT, which uses only O(n*logn) oper
Page 15 and 16: FiltersIn the Fourier Domain, it's
Page 17 and 18: Now the keys all change the spectru
Page 19 and 20: A HP FilterHere, the same is done w
Page 21 and 22: The main function first loads an im
Page 23 and 24: And here's the Fast Fourier Transfo
Page 25 and 26: left corner at xpos,yPos. The shift
Page 27 and 28: would have only 2 color channels, o
Page 29 and 30: The sloped lines in the spectrum he
Page 31 and 32: shown here, the code for all keys i
Page 33 and 34: }calculateAmp(N, M, fAmp[0][0], fRe
Page 35 and 36: component back.This is the original
Page 37: In the above images, a circular sec
Page 41 and 42: And here's the result of a much thi

Lode's Computer Graphics Tutorial Fourier Transform

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