Extensive numerical experiments indicate that images, in general, possess a considerable degree of self-similarity, that is, blocks are well approximated (in the L sense) by a number of other blocks – at the same or different scales – when affine greyscale transformations are employed. This paper outlines a simple model of affine image self-similarity which includes the method of fractal image ...

Many minimum distance estimators have the potential to provide parameter estimates which are both robust and efficient and yet, despite these highly desirable theoretical properties, they are rarely used in practice. This is because the performance of these estimators is rarely guaranteed per se but obtained by placing a suitable value on some tuning parameter. Hence there is a risk involved in...

We show that the total space of any affine C-bundle over CP with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.

We prove that generically, for a self-affine set in R, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.

Compass, power-spectral, and roughness-length estimates of fractal dimension are widely used to evaluate the fractal characteristics of geological and geophysical variables. These techniques reveal self-similar or self-affine fractal characteristics and are uniquely suited for certain analysis. Compass measurements establish the self-similarity of profile and can be used to classify profiles ba...

Let fi(x) = Aix + bi (1 ≤ i ≤ n) be affine maps of Euclidean space RN with each Ai nonsingular and each fi contractive. We prove that the self-affine set K of {f1, . . . , fn} is uniformly perfect if it is not a singleton.

We investigate a formula of Falconer which describes the typical value of the generalised Rényi dimension, or generalised q-dimension, of a self-affine measure in terms of the linear components of the affinities. We show that in contrast to a related formula for the Hausdorff dimension of a typical self-affine set, the value of the generalised q-dimension predicted by Falconer’s formula varies ...