A proposal of quantization theorem: How should an image's gray value be digitized?
Hiroyasu Koshimizu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
Mathematical basis for the digitization of gray value of the image is proposed. This can be called Oteru-Kochimizu's Quantization Theorem (OK-QT), just in the same meaning of Shannon's Sampling Theorem (Shannon-ST) for the digitization of the shape of the image. Inspired by the fact ST is the reconstruction theorem of the analog image from discrete image, OK-ST was modeled as the reconstruction theorem of the shape of the probability density function of gray value of the image. This is the novel and unique mathematical basis for the digitization of the gray scale of the image. This paper shows the outline of this theorem and shows also some experimental results to demonstrate its practical applicability. Through this, OK-QT gives a clue to the mathematical paradigm for the complete digitization basis, together with Shannon ST.