TL;DR
This paper introduces a mathematical model for images based on multi-scale observations, providing bounds on image smoothness that serve as a baseline for natural images.
Contribution
It presents a scale-based mathematical model of images and derives quantitative bounds on smoothness without environmental assumptions.
Findings
Provides bounds on image smoothness as a function of available scales.
Serves as a baseline for comparing natural image smoothness.
Models images using multi-scale zoom levels.
Abstract
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.
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Taxonomy
TopicsImage and Signal Denoising Methods · Medical Image Segmentation Techniques · Advanced Image Fusion Techniques