Simplicial complexes of finite fuzzy sets Fabio Cuzzolin Dipartimento di Elettronica e Informazione – Politecnico di Milano Image and Sound Processing Group IPMU04, Perugia, 4-9 July 2004

today well be … 1 …introducing our research 2 …presenting the paper 3 …planning the future

… about the author PhD student, University of Padova, Department of Computer Science (NAVLAB laboratory) with Ruggero Frezza Visiting student, Washington University in St. Louis (ESSRL laboratory) Visiting student, UCLA, Los Angeles (VisionLab) with Stefano Soatto Image and Sound Processing Group, Politecnico di Milano

… the research research Computer vision object and body tracking data association gesture and action recognition Discrete mathematics linear independence on lattices Belief functions and imprecise probabilities geometric approach algebraic analysis total belief problem

2 Simplicial complexes of consonant b.f.

Probability and plausibility assignments belief functions or lower probabilities A B2B2 B1B1 plausibility functions or upper probabilities

Consonant belief functions

Belief space it has the shape of a simplex the space of all the belief functions on a given frame each subset A A-th coordinate s(A) in an Euclidean space

Condition for simplices

Simplicial complex

3 Open research

Geometric approximations