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A maximum likelihood local scale estimation principle is presented. An actual implementation of the estimation principle uses second order moments of multiple measurements at a fixed location in the image. These measurements consist of Gaussian derivatives possibly taken at several scales and/or having different derivative orders. Although the principle is applicable to a wide variety of image models, the main focus here is on the Brownian model and its use for scale selection in natural images. Furthermore, in the examples provided, the simplifying assumption is made that the behavior of the measurements is completely characterized by all moments up to second order. [ABSTRACT FROM AUTHOR]

This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part of the derivation, we introduce a blurring operator At that acts on jet space contrary to doing spatial filtering and a scaling operator Ss. The stochastic Brownian image model is an example of a class of functions which are scale invariant with respect to the operators At and Ss. This paper also includes empirical results where we estimate the scale invariant jet covariance of natural images and show that it resembles that of Brownian images. [ABSTRACT FROM AUTHOR]