Image Technology Design: A Perceptual Approach by Jean-Bernard Martens is an essential reference for both academic and professional researchers in the fields of image technology, image processing and coding, image display, and image quality.
This is what it says on the back flap. However, even though as an industrial designer we deal with the processing of images and data all the time. I don’t think this book was written for people without a mathematical or physics background. I started reading but pretty soon the terminology and advanced mathematical concepts became hard to understand and I stranded in researching all the new terms and formulas.
Here I will try and explain some of the concepts that I found interesting.
Banach Space: A Banach space is a term in mathematics for a complete vector space, with means that it describes a surface area that is not infinite (as opposed to vectors that describe infinite space, like two diverging lines). More about what a vector space is here on Wikipedia. A real in-depth course on Banach space can be found here. A Banach space is basically any complete vector space that was described by the Polish mathematician Stefan Banach.
Multidimensional models of image quality: When judging the quality of images, people usually agree on aspects like colorfulness, brightness and contrast. However, the aesthetical quality of an image is harder to agree on. In the book there are some examples worked out on how to map the quality of an image, like putting Quality, Blur and Noise in one graph. This way we can see that Blur appears to have a more direct negative influence on the quality of the image, than Noise (in the example below).