Abstract

this paper is that, even when you throw out such specifics, there are commonalities in the statistics of images, striking regularities which can be captured. Our hope is that the models described here are only a start, that much more about the nature of the images we are used to seeing is contained in very simple low-level statistics. We can formulate this in a conjecture: there exist simply described stochastic models for images which a) assign high liklihood to any `natural' image of the world we live in and b) whose randon samples have the `look and feel' of natural images, i.e. make you look twice to see if you recognize something in them. For instance, no Gaussian probability measures on images have anything like the look and feel of the real world -- the best one can do is make them look like clouds (see below). The outline of this paper is as follows. In x2, we will introduce the precise mathematical formulation of the problem. In x3, we describe the most striking empirical phenomenon exhibited by the statistics of natural images: their apparent scale-invariance. In x4 we digress to show the problems that scale-invariance creates: there are no scale-invariant probability measures supported on image

Citations