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Innovating Medical Image Analysis via Spatial Logics

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From Software Engineering to Formal Methods and Tools, and Back

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11865))

Abstract

Current computer-assisted medical imaging for the planning of radiotherapy requires high-level mathematical and computational skills. These are often paired with the case-by-case integration of highly specialised technologies. The lack of modularity at the right level of abstraction in this field hinders research, collaboration and transfer of expertise among medical physicists, engineers and technicians. The longer term aim of the introduction of spatial logics and spatial model checking in medical imaging is to provide an open platform introducing declarative medical image analysis. This will provide domain experts with a convenient and very concise way to specify contouring and segmentation operations, grounded on the solid mathematical foundations of Topological Spatial Logics. We show preliminary results, obtained using the spatial model checker VoxLogicA, for the automatic identification of specific brain tissues in a healthy brain and we discuss a selection of challenges for spatial model checking for medical imaging.

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Notes

  1. 1.

    Topochecker: a topological model checker, see http://topochecker.isti.cnr.it, https://github.com/vincenzoml/topochecker.

  2. 2.

    Part of the central nervous system in the brain.

  3. 3.

    Place where neurons are located in the outer part of the brain.

  4. 4.

    VoxLogicA: https://github.com/vincenzoml/VoxLogicA.

  5. 5.

    Sometimes called von Neumann adjacency. The relation is reflexive and symmetric.

  6. 6.

    The reader interested in the formal definition of closure spaces and on their properties is referred to the literature (see e.g. [12, 13, 21,22,23] and references therein). Here it suffices to say that \(\mathcal {C}(Y)\) is essentially the set of points close to any point in Y; note that, since closure spaces generalize topological spaces, in the latter, the closure operator \(\mathcal {C}\) coincides with topological closure, so that, for instance, in the monodimensional Euclidean space \(\mathbb {R}\), \(\mathcal {C}([0,1))= \mathcal {C}((0,1))=\mathcal {C}((0,1])=\mathcal {C}([0,1])=[1,0]\).

  7. 7.

    We refer to [13] for a discussion on paths on the more general class of closure spaces, including e.g. Euclidean spaces, including e.g. Euclidean spaces.

  8. 8.

    Note that this colour does not correspond to any atomic predicate and so it is not part of the model; we use it only for illustration purposes.

  9. 9.

    See https://brainweb.bic.mni.mcgill.ca/brainweb/anatomic_normal_20.html (Publicly available).

  10. 10.

    The NIfTI file format is a special data format by the Neuro-imaging Informatics Technology Initiative, https://nifti.nimh.nih.gov/.

  11. 11.

    Again, note that we are processing a 3D image.

  12. 12.

    See http://brainweb.bic.mni.mcgill.ca/brainweb/anatomic_normal_20.html.

  13. 13.

    \(Dice = 2*\text {TP} / (2*\text {TP} + \text {FN} +\text {FP})\), where \(\text {TP}\) denotes True Positive and \(\text {FN}\) denotes False Negative.

  14. 14.

    The Insight Segmentation and Registration Toolkit, see https://itk.org and http://www.simpleitk.org.

  15. 15.

    Some operators may be derived from others; for this reason in the definition of the language we use a minimal set of connectives. As usual in logics, there are several different choices for such a set.

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Acknowledgments

This paper was written for the Festschrift in honour of Director of Research Dr. Stefania Gnesi. We would like to thank Stefania for the many years she has been coordinating our Formal Methods and Tools Laboratory at ISTI-CNR, and we hope she will continue to contribute to our Lab for many years to come. She guided the group safely through the many periods of instability of very different nature, and she did so with confidence and optimism. If now we have so many young (and less young) motivated formal methods researchers in our group, that explore and develop new and creative directions of formal methods research, both in theory and for applications, this is made possible, in a large part, thanks to her tireless efforts in all these years.

Part of this work has been developed in the context of the Italian MIUR-PRIN 2017 project “IT MaTTerS: Methods and Tools for Trustworthy Smart Systems”.

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Authors and Affiliations

  1. Azienda Ospedaliera Universitaria Senese, Siena, Italy

    Gina Belmonte

  2. Consiglio Nazionale delle Ricerche - Istituto di Scienza e Tecnologie dell’Informazione ‘A. Faedo’, CNR, Pisa, Italy

    Vincenzo Ciancia, Diego Latella & Mieke Massink

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  1. Gina Belmonte
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  2. Vincenzo Ciancia
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  3. Diego Latella
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  4. Mieke Massink
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Correspondence to Mieke Massink .

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Editors and Affiliations

  1. Consiglio Nazionale delle Ricerche, Pisa, Italy

    Maurice H. ter Beek

  2. Università degli Studi di Firenze, Florence, Italy

    Alessandro Fantechi

  3. Università di Pisa, Pisa, Italy

    Laura Semini

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Belmonte, G., Ciancia, V., Latella, D., Massink, M. (2019). Innovating Medical Image Analysis via Spatial Logics. In: ter Beek, M., Fantechi, A., Semini, L. (eds) From Software Engineering to Formal Methods and Tools, and Back. Lecture Notes in Computer Science(), vol 11865. Springer, Cham. https://doi.org/10.1007/978-3-030-30985-5_7

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