CODEWITHSUNDEEP
image-processingcompressionjpegfftdct
user5469190
user5469190

Reputation:

Fourier Transform and Image Compression

I'm getting all pixels' RGB values into

R=[], G=[], B=[]

arrays from the picture. They are 8 bits [0-255] values containing arrays. And I need to use Fourier Transform to compress image with a lossy method.

Blockquote Fourier Transform

N will be the pixel numbers. n is i for array. What will be the k and imaginary j?

Can I implement this equation into a programming language and get the compressed image file?

Or I need to use the transformation equation to a different value instead of RGB?

Upvotes: 1

Views: 2709

Answers (1)

Mark Adler
Mark Adler

Reputation: 112617

First off, yes, you should convert from RGB to a luminance space, such as YCbCr. The human eye has higher resolution in luminance (Y) than in the color channels, so you can decimate the colors much more than the luminance for the same level of loss. It is common to begin by reducing the resolution of the Cb and Cr channels by a factor of two in both directions, reducing the size of the color channels by a factor of four. (Look up Chroma Subsampling.)

Second, you should use a discrete cosine transform (DCT), which is effectively the real part of the discrete Fourier transform of the samples shifted over one-half step. What is done in JPEG is to break the image up into 8x8 blocks for each channel, and doing a DCT on every column and row of each block. Then the DC component is in the upper left corner, and the AC components increase in frequency as you go down and to the left. You can use whatever block size you like, though the overall computation time of the DCT will go up with the size, and the artifacts from the lossy step will have a broader reach.

Now you can make it lossy by quantizing the resulting coefficients, more so in the higher frequencies. The result will generally have lots of small and zero coefficients, which is then highly compressible with run-length and Huffman coding.

Upvotes: 7

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