Article

Verifying an algorithm computing discrete vector fields for digital imaging

Authors:

Jónathan Heras,

Julio RubioAuthors Info & Claims

CICM'12: Proceedings of the 11th international conference on Intelligent Computer Mathematics

Pages 216 - 230

https://doi.org/10.1007/978-3-642-31374-5_15

Published: 08 July 2012 Publication History

Abstract

In this paper, we present a formalization of an algorithm to construct admissible discrete vector fields in the Coq theorem prover taking advantage of the SSReflect library. Discrete vector fields are a tool which has been welcomed in the homological analysis of digital images since it provides a procedure to reduce the amount of information but preserving the homological properties. In particular, thanks to discrete vector fields, we are able to compute, inside Coq, homological properties of biomedical images which otherwise are out of the reach of this system.

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Heras, J., Dénès, M., Mata, G., Mörtberg, A., Poza, M., Siles, V.: Towards a certified computation of homology groups for digital images. In: Proceedings 4th International Workshop on Computational Topology in Image Context (CTIC 2012). LNCS (to appear, 2012).

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Heras, J., Mata, G., Poza, M., Rubio, J.: Homological processing of biomedical digital images: automation and certification. In: 17th International Conferences on Applications of Computer Algebra. Computer Algebra in Algebraic Topology and its Applications Session (2011).

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Heras, J., Pascual, V., Rubio, J.: Proving with ACL2 the Correctness of Simplicial Sets in the Kenzo System. In: Alpuente, M. (ed.) LOPSTR 2010. LNCS, vol. 6564, pp. 37-51. Springer, Heidelberg (2011).

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Lambán, L., Martín-Mateos, F.J., Rubio, J., Ruiz-Reina, J.L.: Applying ACL2 to the Formalization of Algebraic Topology: Simplicial Polynomials. In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, pp. 200-215. Springer, Heidelberg (2011).

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Cited By

Poza MDomínguez CHeras JRubio J(2014)A Certified Reduction Strategy for Homological Image ProcessingACM Transactions on Computational Logic10.1145/263078915:3(1-23)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2630789
Heras JCoquand TMörtberg ASiles V(2013)Computing persistent homology within Coq/SSReflectACM Transactions on Computational Logic10.1145/252892914:4(1-16)Online publication date: 28-Nov-2013
https://dl.acm.org/doi/10.1145/2528929
Heras JMata GRomero ARubio JSáenz R(2013)Verifying a plaftorm for digital imagingProceedings of the 2013 international conference on Intelligent Computer Mathematics10.1007/978-3-642-39320-4_5(66-81)Online publication date: 8-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39320-4_5

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Published In

cover image Guide Proceedings

CICM'12: Proceedings of the 11th international conference on Intelligent Computer Mathematics

July 2012

472 pages

ISBN:9783642313738

Editors:
Johan Jeuring
Department of Information and Computing Sciences, Utrecht University and Open Universiteit Nederland, Princetonplein 5, Utrecht, The Netherlands
,
John A. Campbell
Department of Computer Science, University College London, Gower Street, London, UK
,
Jacques Carette
Department of Computing and Software, McMaster University, 1280 Main Street West, Hamilton, ON, Canada
,
Gabriel Reis
Department of Computer Science and Engineering, Texas A&M University, 1280 Main Street West, College Station, TX, Canada
,
Petr Sojka
Department of Computer Graphics and Design, Masaryk University, Botanická 68a, Brno, TX, Czech Republic

Sponsors

DFKI: DFKI GmbH
Jacobs University Bremen: Jacobs University Bremen

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 08 July 2012

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Cited By

Poza MDomínguez CHeras JRubio J(2014)A Certified Reduction Strategy for Homological Image ProcessingACM Transactions on Computational Logic10.1145/263078915:3(1-23)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2630789
Heras JCoquand TMörtberg ASiles V(2013)Computing persistent homology within Coq/SSReflectACM Transactions on Computational Logic10.1145/252892914:4(1-16)Online publication date: 28-Nov-2013
https://dl.acm.org/doi/10.1145/2528929
Heras JMata GRomero ARubio JSáenz R(2013)Verifying a plaftorm for digital imagingProceedings of the 2013 international conference on Intelligent Computer Mathematics10.1007/978-3-642-39320-4_5(66-81)Online publication date: 8-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39320-4_5

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