Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously.
In signal processing, quantization is the process of approximating a continuous signal by a set of discrete symbols or integer values.
In imaging software, quantization is the process of reducing the number of colors used to represent an image.
In music software, quantization is the altering of the times and durations of notes so they fit the beat or subbeat perfectly.
In physics, quantization is either the taking of discrete rather than continuous values for some physical quantities; or the procedure to construct a quantum theory from its classical limit.
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Note that the quantization tables generated from a save within Photoshop CS are concatenated together into a single quantization table of length 132 instead of the 2 x 67 that we see in other software programs and the digital camera itself.
The only case in which you can mathematically figure out the quantization tables from the quality setting is in programs such as Irfanview and other IJG-based JPEG encoders, where the quantization table is scaled by the quality setting (according to the function shown in the comment posted on 2006-03-07).
Given that the quantization table coefficients are up to the encoder to specify, one should be able to select a set based off of the JPEG Annex's suggested matrix.
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