Australasian Mathematical Psychology Conference 2019

Re-contextualisation of harmonic power for measuring local complexity (Good wholesome local fun with fractals and eFourier)

Erin I. Walsh
Centre for Research on Ageing, Health and Wellbeing, Australian National University
Tianqi Zhang
Centre for Research on Ageing, Health and Wellbeing, Australian National University
Nicolas Cherbuin
Centre for Research on Ageing, Health and Wellbeing, Australian National University

Local shape complexity can be biologically meaningful as a marker of disease, trauma, or change in brain structure over time. Fractal dimensionality (FD) is currently the dominant measure of local shape complexity used in neuroimaging but its limitations are not well understood. Elliptical Fourier (eFourier) has been applied in the neuroimaging literature to examine global shape. We propose a stopping rule applied to the number of harmonics can be re-interpreted as a measure of local complexity. In this brief talk we introduce these two measures and apply them to an example dataset of 807 contours.