Are Natural Images of Bounded Variation?

The bounded variation assumption is the starting point of many methods in image analysis and processing. However, one common drawback of these methods is their inability to handle textures and small structures properly. Here we precisely show why natural images are incompletely represented by BV functions. Through an experimental study of the distribution of bilevels of natural images, we show that their total variation blows up to infinity with the increasing of resolution. To reach these conclusions, we compute bounds on the total variation, and we model convolution and sampling under quite general assumptions.