Seminars

My first example will be galaxies from the Sloan Digital Sky Survey, the second will be multiple sclerosis lesions and its relation to cortical thickness, and the third will be the 'bubbles' task, in which the subject is asked to discriminate between images that are revealed only through arandom set of small windows or 'bubbles'. In all three examples we shall model the smoothed points as random fields. The key tool used in the analysis is the Euler characteristic of the excursion set. An exact expression for its expectation is found using new results in random field theory involving Lipschitz-Killing curvatures and Jonathan Taylor's Gaussian Kinematic Formula. We use this to make statistical inference about large-scale structure in the universe, "functional" fiber tracts, and which parts of the brain are activated by which parts of an image.