The fundamental problem of local scale selection is addressed by
means of a novel principle, which is based on maximum likelihood
estimation. The principle is generally applicable to a broad
variety of image models and descriptors, and provides a generic
scale estimation methodology.

The focus in this work is on applying this selection principle
under a Brownian image model. This image model provides a simple
scale invariant prior for natural images and we provide
illustrative examples of the behavior of our scale estimation on
such images. In these illustrative examples, estimation is based
on second order moments of multiple measurements outputs at a
fixed location. These measurements, which reflect local image
structure, consist in the cases considered here of Gaussian
derivatives taken at several scales and/or having different
derivative orders.