3.3 Quantisation of dct coefficients

For our discussion of the 2-D DCT we assumed a quantiser step size of 15 to allow direct comparison ofentropies with the Haar transform. But what step size do we really need?

(a) and (b) show images reconstructed from the $8\times 8$ DCT of Lenna (see subfigure (c) ), when all the DCT coefficients are quantised with step sizes of 15 and 30respectively. It is difficult to see quantising artefacts in (a) ( $Q_{\mathrm{step}}=15$ ) but they are quite noticeable in (b) ( $Q_{\mathrm{step}}=30$ ).

The visibility of the $8\times 8$ DCT basis functions of subfigure (a) in our discussion of the 2-D DCT has been measured (for a $720\times 576$ image viewed from 6 times the image width) and the minimum quantiser steps have been determined which will giveartefacts just at the threshold of visibility. The matrices (JPEG Book, p37) for the luminance and chrominance thresholdstep sizes are:

shows the entropies of the 64 quantised subimages used to reconstruct each of the fourimages in . Also given on each plot is the mean entropy (giving the bits/pel for theimage) and the rms quantising error between the quantised image and the original.

We see that (c) has about the same mean entropy and rms error as (b), but that its quantising artefacts are much less visible. (d) has similar visibility of artefacts to (b), but has significantly lower entropy and hence greater compression (similarly for (c) versus (a)).

This shows the distinct advantages of subjectively weighted quantisation , and also that it is unwise to rely too much on the rms error as a measure of image quality.