Quantisation

Thresholding a greyscale image to a binary image is a particular case of reducing the range of levels. There are many applications where a reduction in the range has advantages. Quantisation over the greyscale is particularly important in image processing associated with compressing the image into fewer bits. A common technique of image compression is to first do a Discrete Cosine Transform of the image, which is just the even part of a Fourier Transform, and then take the resulting new image and quantise it judiciously. Then this quantised DCT image is stored. When the inverse DCT is performed, the original image is restored to quite high approximations, since the eye is relatively insensitive to very high and very low spatial frequencies. The same technique can, of course, be regarded as a measurement method.

Since one wants to make regions of the image which are close both in space and in grey level more likely to be assigned the same quantised value than regions of the image which are separate in either space or in grey level, it is convenient to work in the space of the graph of the function, as with Fig.2.11.

Again, this is more likely to be treated in a good book on image processing than one on Pattern Recognition, but the issue must be mentioned.