Towards a certified computation of homology groups for digital images

Jónathan Heras 1 Maxime Dénès 2 Gadea Mata 1 Anders Mörtberg 3 María Poza 1 Vincent Siles 3
1 Department of Mathematics and Computer Science - Departamento de Matematicas y Computacion
2 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
3 CSE - Department of Computer Science and Engineering [Göteborg]
Abstract : In this paper we report on a project to obtain a verified computation of homology groups of digital images. The methodology is based on program- ming and executing inside the COQ proof assistant. Though more research is needed to integrate and make efficient more processing tools, we present some examples partially computed in COQ from real biomedical images.
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Submitted on : Sunday, June 24, 2012 - 4:27:26 PM
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Jónathan Heras, Maxime Dénès, Gadea Mata, Anders Mörtberg, María Poza, et al.. Towards a certified computation of homology groups for digital images. CTIC - Computational Topology in Image Context - 2012, May 2012, Bertinoro, Italy. pp.49-57, ⟨10.1007/978-3-642-30238-1_6⟩. ⟨hal-00711385⟩

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