In various scientific fields from astrophysics to neuroimaging,
researchers observe entire images or functions rather than single
observations. The integral geometric properties, notably the Euler
characteristic of the level/excursion sets of these functions,
typically modelled as Gaussian random fields, have found some
interesting applications in these domains. In this talk, I will
describe some of the statistical applications of the integral
geometric properties of these random sets, particularly their
Lipschitz-Killing curvature measures. I will focus on describing the
results, and sketching some proofs for a class of non-Gaussian random
fields (but built up of Gaussians) and the relation (the so called
Gaussian Kinematic Formula) between their Lipschitz-Killing curvature
measures and the classical Kinematic Fundamental Formulae of integral geometry.
Audio (MP3 File, Podcast Ready)
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