Three aspects of texture are considered by the fractal geometry: Fractal Dimension (FD), Lacunarity and Succolarity. Fractal Dimension has been well studied; a great number of approaches have been presented to extract it from images. It can be computed from black-white to multi-band image. There are many approaches also, from the simple Box-Dimension to the most complex Hausdorff Dimension. The...

In this paper we present some new properties of the metric dimension defined by Bouligand in 1928 and prove the following new projection theorem: Let dimb(A − A) denote the Bouligand dimension of the set A − A of differences between elements of A. Given any compact set A ⊆ R such that dimb(A−A) < m, then almost every orthogonal projection P of A of rank m is injective on A and P |A has Lipschit...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

The present paper generalises results by Lutz and Ryabko. We prove a martingale characterisation of exact Hausdorff dimension. On this base we introduce the notion of exact constructive dimension of (sets of) infinite strings. Furthermore, we generalise Ryabko’s result on the Hausdorff dimension of the set of strings having asymptotic Kolmogorov complexity ≤ α to the case of exact dimension. Th...

this paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by topsis method. topsis method is technique for order preference by similarity to ideal solution. topsis is one of the renowned methods for classical multi-criteria decision-making (mcdm) problems that defines the positive ideal solution and negative ideal solution...

We analyze ‘Distribution to Distribution regression’ where one is regressing a mapping where both the covariate (inputs) and response (outputs) are distributions. No parameters on the input or output distributions are assumed, nor are any strong assumptions made on the measure from which input distributions are drawn from. We develop an estimator and derive an upper bound for the L2 risk; also,...