JPEG

A real JPEG splits the image into colour and brightness, and most encoders then keep one colour sample for each two-by-two group of brightness samples before the transform starts, because an eye is worse at colour than at brightness. That is 4:2:0, and it is a common choice rather than part of the format: 4:4:4 keeps every colour sample and the standard’s own reference software supports it. Then this runs on every 8 by 8 block, and the result is Huffman-coded with the coefficients read in a zigzag so the zeros end up together. None of that is here. What is here is the one step where information is actually lost, on one block, and the compression that follows it is what turns those zeros into a smaller file.

Each of the 64 coefficients is worked out by summing over all 64 samples, which is 4,096 cosines per block and about as slow as it can be made. Real encoders use a fast algorithm that gets the same answer in a fraction of the work. Slow and exactly right was the correct trade here, because it means the sum written on this page is the sum in the code rather than an optimisation of it.

The table is the example luminance table from Annex K of ITU-T T.81. It is not normative — the standard offers it as one that has been found to work — and it is what almost everything uses. It is a memorised table, which is exactly the kind of thing that rots quietly, so the claims test compares all 64 entries against libjpeg-turbo's independent copy rather than trusting this file. The standard's own PDF is not machine-readable from the archive, and a second implementation is the better witness anyway: it would catch two rows exchanged, which a structural check would not.

It is tempting to say JPEG discards high frequencies, and the fine stripes here show why that is wrong: they are the finest pattern the block can hold and they come back nearly intact, because their coefficient is enormous. What the quantiser removes is anything small relative to its divisor. A faint texture at the same frequency disappears completely; a bold one at that frequency survives.

The quality setting guarantees one thing and it is not the one people assume: no divisor in the table ever gets larger as quality rises, and that holds for all 64 entries at every step. What it does NOT guarantee is that any particular block comes out closer. A finer divisor can round a coefficient the other way, and on the gradient here the error rises slightly three times on the way from 5 to 100 before ending at zero. Over a whole photograph this averages out; on one block it does not, and the sweep on this page is one block.

The panel above used to say the rounding was the only lossy step in the whole format. On this page it is, because this page is one block of brightness with no colour in it. In a file encoded 4:2:0 the colour was thrown away before the transform ever ran, and that is lossy too. An outside reader caught the overclaim. The distinction worth keeping is between the mechanism this page demonstrates and the encoding choices it does not.