In this paper we revisit the Mumford-Shah functional, one of the most studied variational approaches to image segmentation. The contribution of this work is to propose a modification of the Mumford-Shah functional that includes Fractal Analysis to improve the segmentation of images with fractal or semifractal objects. Here we show how the fractal dimension is calculated and embedded in the func...

Fractal dimensions have been frequently applied to generalize the complexity and drainage of particular stream networks. Certain techniques to calculate dimension have become particularly popular, specifically the Divider method, functional-box counting, and as a function between bifurcation and length ratios. The frequency and variability with which these techniques are applied creates discrep...

Fractal measures like fractal dimension and lacunarity are widely-used for the analysis of textures, or any images with self-similar content. However, all the existing approaches are defined for one dimensional signals or binary images with extension to grey-scale images. We propose a colour approach, derived from the existing probabilistic algorithm for the computation of the fractal dimension...

The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters. This was done in the context of a preliminary analysis of a small dataset, via a novel way to partition the wavelet-transform space-scale skeleton. For the first time, the estimat...

BACKGROUND: This study presents an analysis of trabecular bone structure in standard radiographs using Fourier transforms and principal components analysis (PCA) to identify contributions to hip fracture risk. METHODS: Radiographs were obtained from 26 hip fracture patients and 24 controls. They were digitised and five regions of interest (ROI) were identified from the femoral head and neck for...

In our recent papers we applied fractal methods to extract the earthquake precursory signatures from scaling characteristics of the ULF geomagnetic data, obtained in a seismic active region of Guam Island during the large earthquake of 8 August 1993. We found specific dynamics of their fractal characteristics (spectral exponents and fractal dimensions) before the earthquake: appearance of the f...

Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth anal...

Objective: The notion that artistic capability increases with dementia is both novel and largely unsupported by available literature. Recent research has suggested an emergence of artistic capabilities to be a by-product of involuntary behaviour seen with dementia, as opposed to a progression in original thinking (de Souza, et al., 2010). A far more complementary explanation comes from Hanneman...

abstract purpose - the aim of this paper is to describe the population ecology theory through fractal thinking, an emergent human operating system that is creative, adaptive, healthy, and evolutionary; furthermore, a parallel is drawn between the population ecology model and the fractal structure. top-down hierarchies are typically characterized by command and control systems of the authority t...

BACKGROUND AND PURPOSE Alzheimer disease (AD) and vascular dementia (VaD) are the two major diseases that cause dementia, and early diagnosis is important. Single photon emission CT (SPECT) of cerebral blood flow (CBF) is used for the early detection of dementia and as an auxiliary method for follow-up. AD shows reduced posterior blood flow and VaD manifests reduced anterior blood flow on CBF S...