In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fra...

Medical images typically have irregular and fragmented contours. This is a strong motivation to use fractal geometry, rather than Euclidian geometry, for their description and characterization. In this paper we analyse a set of 100 images of melanoma and non-melanoma moles. The moles have their contours extracted with several tools and then the contours have their fractal dimension computed wit...

Some man-made objects are geometrically simple in that they resemble idealized forms such as lines, planes, cubes, or polyhedra. Ever since Euclid invented geometry, people have been content with the idea that all objects can be classified as compositions of regular geometric shapes. The architecture found inspiration by the Euclidean geometry and by the properties of the symmetry. The analogy ...

The natural complexity of the brain, its hierarchical structure, and the sophisticated topological architecture of the neurons organized in micronetworks and macronetworks are all factors contributing to the limits of the application of Euclidean geometry and linear dynamics to the neurosciences. The introduction of fractal geometry for the quantitative analysis and description of the geometric...