JPEG Image Compression
We may think of the color of each pixel as represented by a three-dimensional vector (R,G,B) consisting of its red, green, and blue components. In a typical image, there is a significant amount of correlation between these components. For this reason, we will use a color space transform to produce a new vector whose components represent luminance, Y, and blue and red chrominance, Cb and Cr.
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As is typical, the luminance shows more variation than the the chrominance. For this reason, greater compression ratios are sometimes achieved by assuming the chrominance values are constant on 2 by 2 blocks, thereby recording fewer of these values.
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Now we come to the heart of the compression algorithm. Our expectation is that, over an 8 by 8 block, the changes in the components of the (Y, Cb, Cr) vector are rather mild, as demonstrated by the example above. Instead of recording the individual values of the components, we could record, say, the average values and how much each pixel differs from this average value. In many cases, we would expect the differences from the average to be rather small and hence safely ignored. This is the essence of the Discrete Cosine Transform (DCT), which will now be explained.
He also explains the improvements in JPEG 2000.
Update (2024-08-09): DefenderOfBasic:
one of the most popular tools I ever made was this thing to explain how JPEG images are created out of these mathematical patterns
