I'm surprised that 10 years later, the article still teaches an incorrect conceptual understanding of "quantization".

The context heavily implies that quantization is "discarding information" generally (e.g. clipping, masking). The wikipedia article he links in the footnote disagrees, and so do I:

> quantization is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements.

Quantization is a function over values, or the image itself. Clipping and masking, by contrast, are functions over the space/frequency dimensions, i.e. the pixel indices ("preimage"). A rule like "apply a circular mask" or "drop the first quadrant" does not depend on the values!

The most extreme example of quantization is a threshold filter. Regardless of location, output "1" if the pixel is brighter than X, or "0" otherwise. This depends only on the value, not on the location. He also misses the opportunity to point out that chroma subsampling is another application of quantization, this time to chroma values (drop the low-order bits).

Codecs like H.264 and JPEG use spatially-varying quantization rules to effectively discard more information at high frequencies, so his explanation of H.264 is spot on, but a non-expert encountering quantization for the first time would probably come away with the wrong idea. For an article explicitly targeted to non-experts that goes out of its way to introduce the term, it's a pretty important oversight.

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solarkraft 5 hours ago | parent | next [-]

Consider me confused. Isn’t quantizing a value, e.g. reducing the number of bits in an int, a form of discarding information from that value? Isn’t your comparison just about discarding information on another level (discarding entire values)?

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edflsafoiewq 2 hours ago | parent [-]

I think the GP's point is, if you don't know what quantization is, the article gives the impression it consists of discarding some of the values, which is where the compression comes from. This is a good "0-th order" intuition, but quantization is a softening of this; instead of fully retaining or fully discarding a value, there is a sliding scale of how much information to discard. If you already know what quantization is, it's easy to see how discarding is a special case, but the article gives the impression discarding = quantization.

	▲	dizzant 38 minutes ago \| parent [-]
		Exactly correct. Quantizing is like rounding. This is the same notion as in quantum mechanics: the values aren’t any real number (a huge input space), but rather integer multiples of some constant (a small output space). Quantization is “rounding” to the nearest allowed output. To build on the example used in the article, you could quantize an image by dropping the lower half of the bits of every pixel value. This discards half the information by mapping the larger input image space (e.g. 8 bits per pixel) to a smaller output image space (e.g. 4 bits per pixel), effectively scaling/rounding the original values. The fact that higher frequencies can be quantized more intensely with relatively little image quality loss is a completely separate idea from quantization itself. In this context, high frequency masking as described in the article could be accurately described as a spatially dependent quantization to zero-bit output values. But the quantization part is the mapping, not the shape of the mask, and I think the article is misleading about the distinction. In real codecs, there usually isn’t a hard boundary like a mask, but instead an empirical table of how many bits to keep based on the perceptual value of the information at each frequency.

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CharlesW 5 hours ago | parent | prev [-]

The definition you quoted explains why quantization discards information: multiple distinct input values map to the same output value. Once that happens, you can no longer determine the original input from the output alone. The distinctions between those inputs are the information that has been lost.

	▲	dizzant 2 hours ago \| parent [-]
		I’m not saying that quantization doesn’t lose information. Instead, I’m saying that every step to lose information is not quantization. Functions on the preimage (clipping, masking) are not quantization.