Speaker
Description
During this lecture and workshop, we will introduce Fractal Space Curve Analysis (FSCA), a novel methodology for characterizing multidimensional data—particularly neuroimaging data—by examining their fractal properties. The core concept of FSCA is to transform multidimensional data (e.g., 2D, 3D, or 3+1D scans) into one-dimensional time series using space-filling curves (SFCs), primarily the Hilbert SFC. Detrended fluctuation analysis (DFA) is then applied to these series to quantify fractal features by extracting Hurst exponents.
To demonstrate the robustness of the method, we present FSCA tests conducted on artificially generated datasets, including two-dimensional fractional Brownian motion, Cantor sets, and Gaussian processes, as well as neuroimaging data. The results clearly show that FSCA effectively quantifies and distinguishes correlations in both stationary and dynamic two-dimensional images.
For neuroimaging data, we present results from the analysis of MRI scans, which include both healthy individuals and patients at various stages of dementia. A systematic decrease in the Hurst exponent was observed in Alzheimer's disease patients, particularly at longer scales, suggesting a reorganisation of brain structure toward greater variability as the disease progresses. Furthermore, FSCA-based features demonstrated promising performance when incorporated into machine learning classifiers for diagnostic tasks, such as distinguishing healthy controls from or AD patients and predicting mild cognitive impairment conversion to AD.
In the workshop portion practical information will be provided to enable participants to perform the analysis FSCA themselves.
Reference:
J. Grela, Z. Drogosz, J. Janarek, J.K. Ochab, I. Cifre, E. Gudowska-Nowak, M.A. Nowak, P. Oświęcimka, and D.R. Chialvo. Using space-filling curves and fractals to reveal spatial and temporal patterns in neuroimaging data. Journal of Neural Engineering 22 (2025) 016016.
