Optimal requantization of deep grayscale images and Lloyd-Max quantization

The classic signal quantization problem was introduced by Lloyd. We formulate another, similar problem: The optimal mapping of digital fine grayscale images (such as 9-13 bits-per-pixel medical images) to a coarser scale (e.g., 8 bits per pixel on conventional computer monitors). While the former problem is defined basically in the real signal domain with smoothly distributed noise, the latter refers to an essentially digital domain. As we show in this paper, it is this difference that makes the classic quantization methods virtually inapplicable in typical cases of requantization of the already digitized images. We found experimentally that an algorithm based on dynamic programming provides significantly better results than Lloyd´s method.