This paper introduces amodified formula for the fractal box counting dimension. Themethod is based on utilization of the probability distribution formula in the fractal box count. The purpose of this method is to use it for the discrimination of oil spill areas from the surrounding features, e.g., sea surface and lookalikes in RADARSAT-1 SAR Wide beam mode (W1) and Standard beam mode (S2) data ...

The box counting method for fractal dimension estimation had not been applied to large or colour images thus far due to the processing time required. In this letter we present a fast, easy to implement and very easily expandable to any number of dimensions variation, the box merging method. It is applied here in RGB images which are considered as sets in 5-D space.

Economic diversification is crucial for the socio-economic sustainability of single-industry communities in the Russian North. The single-industry towns in the Russian North were formed during the Soviet era under an ideology, which promoted large-scale resource extraction in the peripheries (Blakkisrud 2006, p. 39). However, in the contemporary era, the extraction of new deposits in the Russia...

Osteoporosis is a condition of decreased bone mass. This leads to fragile bones which are at an increased risk for fractures, more often, it affects postmenopausal women. In this paper we propose a study of osteoporosis with the fractal dimension. After an introduction to the theory and fractal dimension, we use the box counting method for the segmentation of radiographic images, the study of t...

This paper presents a multiply connected neural network designed to estimate the fractal dimension (Df) using the Box-counting method (BCM). Fractal analysis is a powerful shape recognition tool and has been applied to many pattern recognition problems. Additionally, the Box-Counting Method is one of the most popular methods for estimating Df. However, traditional methods used to estimate Df ar...

The Carathéodory and Kobayashi metrics have proved to be important tools in the function theory of several complex variables. But they are less familiar in the context of one complex variable. Our purpose here is to gather in one place the basic ideas about these important invariant metrics for domains in the plane and to provide some illuminating examples and applications. 0 Prefatory Thoughts...

Let A be the collection of groups which can be assembled from infinite cyclic groups using the binary operations free and direct product. These groups can be described in several ways by graphs. The group (Z ∗Z)×(Z ∗Z) has been shown by [1] to have a rich subgroup structure. In this article we examine subgroups of A–groups. DefineA to be the smallest class of groups which contains the infinite ...

Under conditions where an object is inside another object and only a single face is visible, is there a bias to assume smooth continuation of the surface straight back into the object? To examine the ability to estimate how features progress into a volume, participants viewed 16 pictures of everyday objects (rocks, food, wood) presented with only a single face visible (see Figure 1). Participan...