Computer Science – Computational Geometry
Scientific paper
2012-01-16
Computer Science
Computational Geometry
Presented at: Workshop on Computational Topology, November 7-11, 2011, Fields Institute
Scientific paper
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of multidimensional persistence have been proved to hold when topological spaces are filtered by continuous functions, i.e. for continuous data. This paper aims to provide a bridge between the continuous setting, where stability properties hold, and the discrete setting, where actual computations are carried out. More precisely, a stability preserving method is developed to compare rank invariants of vector functions obtained from discrete data. These advances confirm that multidimensional persistent homology is an appropriate tool for shape comparison in computer vision and computer graphics applications. The results are supported by numerical tests.
Cavazza Niccolò
Ethier Marc
Frosini Patrizio
Kaczynski Tomasz
Landi Claudia
No associations
LandOfFree
Comparison of Persistent Homologies for Vector Functions: from continuous to discrete and back does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Comparison of Persistent Homologies for Vector Functions: from continuous to discrete and back, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Comparison of Persistent Homologies for Vector Functions: from continuous to discrete and back will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-409841