The high complexity of the remotely sensed images and measurements provided by the last generations of sensors demand new techniques for scene understanding and analysis. The similarity of fractal and real world objects was observed and intensively studied from the very beginning. The fractal geometry became a tool for computer graphics and data visualisation in the simulation of the real world...

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several well-studied notions of fractal dimension for sets and measures in Euclidean space. We consider a definition of fractal dimension for finite metric spaces whic...

We consider completely invariant subsets A of weakly expanding piecewise monotonic transformations T on [0, 1]. It is shown that the upper box dimension of A is bounded by the minimum tA of all parameters t for which a t-conformal measure with support A exists. In particular, this implies equality of box dimension and Hausdorff dimension of A.

We measure the fractal dimension of islands during epitaxial thin-film growth. The fractal dimension appears to depend on the ratio of the diffusion-to-deposition rates D/F and on the coverage of adatoms. For sufficiently large D/F , i.e., D/F ≥ 10, and for sufficiently low coverages, the fractal dimension appears to be similar to that of the diffusion-limited aggregation (DLA) while for smalle...

A new method for estimating fractal dimension of tree crowns from digital images is presented. Three species of trees, Japanese yew (Taxus cuspidata Sieb & Zucc), Hicks yew (Taxus × media), and eastern white pine (Pinus strobus L.), were studied. Fractal dimensions of Japanese yew and Hicks yew range from 2.26 to 2.70. Fractal dimension of eastern white pine range from 2.14 to 2.43. The differe...