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Interpreting and comparing shapes are challenging issues in computer vision, computer graphics and pattern recognition. Persistent homology allows us to describe shapes by means of suitable shape descriptors, the persistence diagrams. They capture both geometrical and topological features of an object by recording the homological changes and their longevity in the lower level sets of a real valued function (called a filtering function) defined on a topological space associated with the object. This seminar provides an overview of some of the most relevant results in persistent homology, the main properties of persistence diagrams and the principal aspects in the generalization to multivalued filtering functions that allow the description of shape properties with an intrinsically multidimensional nature.
Is shape just geometric similarity? Surely not; on the other hand, the main topological type of equivalence, i.e., homeomorphism, is much too far from the human idea of "having the same shape". Still, this does not mean that we have to avoi
3 avril 2015 54 min
Musicians* use notes and chords as words of their personal dictionary to create musical phrases. Quite often, these phrases are shaped as tension patterns over time, drawing the attention of the listener to particular moments thanks to spec
3 avril 2015 42 min
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