Speaker: Jaehyoek Shin

Abstract: In this talk, I will review some of basic concepts in the random closed set theory. Specifically, I will give a brief review of two intuitive definitions of expectations of random closed sets – the Vorob’ev expectation and the ODF expectation. The former minimizes the expected measure of the symmetric difference between the random set and its expectation. I will discuss how one might possibly use this property to construct a representative, non-random predictive region from observed random predictive regions. The latter has some attractive properties for shape and boundary estimation problem. These properties include inclusion relations, convexity preservation, and equivariance with respect to rigid motions.

References: 1. Molchanov, Ilya. Theory of random sets. Springer Science & Business Media, 2006; 2. Jankowski, Hanna K., and Larissa I. Stanberry. "Expectations of random sets and their boundaries using oriented distance functions." Journal of Mathematical Imaging and Vision 36.3 (2010): 291-303.