Download Multifractal Analysis of Closed Contour Fluctuations Speaker

Title: Multifractal Analysis of Closed Contour Fluctuations
Speaker: Paulo Duarte-Neto
Affiliation: Departamento de Estatística e Informática - UFRPE
Abstract
In recent decades multifractal analysis has been successfully applied to characterize the complex
temporal and spatial organization of diverse natural phenomena such as heartbeat dynamics, the
dendritic shape of neurons, retinal vessels, rock fractures, etc. However, common methods of
multifractal analysis do not seem appropriate for analyzing quasi-onedimensional structures, with
complexity far from filling two dimensional space, but more complex than a line, such as the
contours of objects. For this reason, the characterization of multifractal properties of closed
contours has up to date remained rather elusive. A new, robust, technique, “The Traveling Observer”
Multifractal Detrended Fluctuation Analysis is presented, which bridges the gap between the
methods used for geometrical fractals and those used for temporal series, reducing the limitations
present in existing multifractal techniques to analyze contours. The procedure first maps the contour
onto a “time series” of distances from the central path (defined by harmonic term zero), as observed
by a virtual observer traveling along this path at constant angular speed. The fluctuations from the
central path of the contour perimeter are registered as a “time series”, and the MF-DFA is then
implemented to quantify the “temporal” correlations of this series. The relevance of studying the
fractal properties of the contour fluctuations is demonstrated through several applications to natural
and simulated data, highlighting the advantages of this new approach.