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We are given a finite set of points sampled from an object, e.g. atoms of a protein, or points on a surface provided by a laser scanner. The goal is to reconstruct the shape of the object, and analyze and manipulate the hole system of the resulting model.
First, I will introduce the 'Alpha complex', which often gives a good reconstruction in the form of a triangulated shape. Allowing the scale parameter to vary, we get a nested sequence of such discrete shapes. The hole system of this sequence is best described with 'persistent homology' and best visualized with the persistence diagram.
In many cases, holes are important for the functionality of an object. Therefore, we are intersted in operations to manipulate the holes of the reconstructed shape. We define operations to open and close holes, while preserving dependences between them.*

Mittwoch, den 12. Juni 2019 um 14.30 Uhr, in Mathematicon, INF 205, Konferenzraum, 5. Stock Mittwoch, den 12. Juni 2019 at 14.30, in Mathematicon, INF 205, Konferenzraum, 5. Stock

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers