Why are images smooth?
This work addresses a fundamental question in image processing and computer vision about the smoothness of natural images, offering a theoretical framework for researchers in these fields.
The paper tackles the problem of explaining why natural images are smooth by proposing a mathematical model that assumes images can be taken at different scales, without environmental assumptions, and provides quantitative bounds on smoothness as a function of available scales, which can serve as a baseline for comparison.
It is a well observed phenomenon that natural images are smooth, in the sense that nearby pixels tend to have similar values. We describe a mathematical model of images that makes no assumptions on the nature of the environment that images depict. It only assumes that images can be taken at different scales (zoom levels). We provide quantitative bounds on the smoothness of a typical image in our model, as a function of the number of available scales. These bounds can serve as a baseline against which to compare the observed smoothness of natural images.