Quantization

  In its original meaning, quantization is the step of passing from a continuous to a discrete variable, like in analogue-to-digital signal conversion. More generally, the term can be used for any method decreasing the precision of representation by eliminating part of the information. Applied to image compaction ( [Jain89]), quantization describes a step of eliminating or reducing the relevance of coefficients that carry little information (a different, analogous quantization is found in the thresholding of coefficients in principal component analysis). A typical compression step used for images transforms a (sub-)image, e.g. an pixel matrix, by a discrete cosine transform, then uses a quantization step which consists of a suitable linear combination of the transformed pixels (i.e. in the ``frequency domain''), and then uses Huffman coding for the resulting information. Except for quantization, these steps have a clearly defined inversion, so that in the definition of the quantization matrix the key criterion is the quality difference between the original and the encoded/decoded image.