2 years ago

Lode's Computer Graphics Tutorial Fourier Transform

Lode's Computer Graphics Tutorial Fourier Transform

ow shows the spectrum

ow shows the spectrum with a low pass filter applied to it: only the low frequency components remain.The bottom row shows the result of the Inverse FT on the new spectrum: all high frequencycomponents of the image are removed, and the image becomes blurred.Here's another example, which shows what happens if you set the imaginary part of the spectrum to 0.To get this, first press space and then press the b key in the program.More on different types of filters follows in the next sections.The DC ComponentThe center of the spectrum is the DC component of the picture, and represents the average color of thepicture: if you calculate the IDFT of a spectrum with only the DC component left, you get a flat imagewith only one color: the average of the original image. In the program for which the code was givenabove, first accept the image by pressing space, and then you can add or remove the DC component byusing the arrow keys, get the full spectrum again by pressing the a key (or the q key on azertykeyboards), and make the spectrum zero by pressing the m key (the , key on azerty keyboards). To getonly the DC component, first press m to remove the spectrum, then the up arrow to get only the DC

component back.This is the original image (the bright blue line in the spectrum probably comes from the sharp edgesfrom the cooling fin):Here's the same image with the DC component removed (note the black dot in the center of thespectrum). You can't see the whole story in fact, all the parts of the image that look black are actuallynegative, since this picture represents the original image with the average color substracted from it. Onthe right is the amplitude of the image instead, which reveals the negative parts.And here below only the DC component is left. Only a single dot remains in the spectrum. It lookswhite on the computer screen, but in reality it are 3 large floating point numbers that contain the DCcolor information. The DC component of an image's spectrum is usually very large, it contains the most"energy": as you could see on the previous image, removing this single dot from the spectrum makesthe image a whole lot darker. Energy has to be understood in terms of Information here.This is the average color of the image, you can call it the ultimate blur, what you'd see if you werestanding very far away from the image, or what you'd get if you took the sum of the color of all pixels,and divided the result though the total number of pixels.Low Pass Filters: BlurringLow frequencies in an audio represent the bass of the music, but in pictures, it represents the blurriestparts and gradients. Sharp edges and lines have high frequencies.

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