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Persistent homology in the cubical setting: theory, implementations and applications
2007 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The Theory of persistent homology, as developed by Gunnar Carlsson at Stanford and others, is based on simplicial homology. In this thesis we explore the possibility of basing persistent homology on cubical homology. We managed to achieve this to some extent and have created a working set of prototype procedures able to calculate the persistent homology of a filtered cubical complex in 2D, and in part 3D, with mod 2 coefficients. We also propose a path that should transform our embryo to a set of procedures capable of handling real applications, in e.g. digital image processing, involving large amounts of data. Extensions to arbitrary finite dimension, orientation, spaces with torsion, PID coefficients and more are also included in the plan for the future.

Place, publisher, year, edition, pages
Keyword [en]
Physics Chemistry Maths, mathematics, computational mathematics, algebraic topology, homology
Keyword [sv]
Fysik, Kemi, Matematik
URN: urn:nbn:se:ltu:diva-45820ISRN: LTU-EX--07/124--SELocal ID: 37bd863b-6c8f-432f-990a-eae21ce9dbc0OAI: diva2:1019117
Subject / course
Student thesis, at least 30 credits
Educational program
Engineering Physics, master's level
Validerat; 20101217 (root)Available from: 2016-10-04 Created: 2016-10-04Bibliographically approved

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