Innovating Medical Image Analysis via Spatial Logics

Belmonte, Gina; Ciancia, Vincenzo; Latella, Diego; Massink, Mieke

doi:10.1007/978-3-030-30985-5_7

Cited by 12 publications

(6 citation statements)

References 33 publications

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“…The tool is written in the functional language FSharp 8 . PolyLogicA is Free and Open Source Software, distributed under the Apache 2.0 license 9 .…”

Section: Polylogica: a Model Checker For Polyhedramentioning

confidence: 99%

“…These tools have been used in several application areas, ranging from collective adaptive systems [25,23,22] to signals [41] and medical image analysis [33]. Recently, in this latter domain of application, promising results have been obtained for the segmentation of malignant brain lesions [10] and normal brain tissue such as white and grey matter [9], as well as for segmentation of nevi 4 [8]. Note that in medical image analysis, model checking addresses static properties of space instead of dynamic properties of agents moving through space as in [23].…”

Section: Introduction and Related Workmentioning

confidence: 99%

“…See https://www.fsharp.org9 The tool is currently available in a branch of the main VoxLogicA repository, see https://github.com/vincenzoml/VoxLogicA.…”

mentioning

confidence: 99%

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Geometric Model Checking of Continuous Space

Bezhanishvili¹,

Ciancia²,

Gabelaia³

et al. 2021

Preprint

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Topological Spatial Model Checking is a recent paradigm that combines Model Checking with the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. In particular, the spatial model checker VoxLogicA, that uses an extended version of SLCS, has been used successfully in the domain of medical imaging. However, SLCS is not restricted to discrete space. Following a recently developed geometric semantics of Modal Logic, we show that it is possible to assign an interpretation to SLCS in continuous space, admitting a model checking procedure, by resorting to models based on polyhedra. In medical imaging such representations of space are increasingly relevant, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We demonstrate feasibility of our approach via a new tool, PolyLogicA, aimed at efficient verification of SLCS formulas on polyhedra, while inheriting some well-established optimization techniques already adopted in VoxLogicA. Finally, we cater for a geometric definition of bisimilarity, proving that it characterises logical equivalence.

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“…The tool is written in the functional language FSharp 8 . PolyLogicA is Free and Open Source Software, distributed under the Apache 2.0 license 9 .…”

Section: Polylogica: a Model Checker For Polyhedramentioning

confidence: 99%

Section: Introduction and Related Workmentioning

confidence: 99%

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Geometric Model Checking of Continuous Space

Bezhanishvili¹,

Ciancia²,

Gabelaia³

et al. 2021

Preprint

Self Cite

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“…For more derived operators the reader is referred to [14]. 6 In [14] the following definition has been used: 7 Named "spatial until" and denoted by "U" in [13].…”

Section: Slcs and Logical Equivalencementioning

confidence: 99%

Towards Spatial Bisimilarity for Closure Models: Logical and Coalgebraic Characterisations

Ciancia¹,

Latella²,

Massink³

et al. 2020

Preprint

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The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial structures, such as finite graphs and digital images, with applications in various case studies including medical image analysis. These recent developments required a generalization step, from topological spaces to closure spaces. In this work we initiate the study of bisimilarity and minimization algorithms that are consistent with the closure spaces semantics. For this purpose we employ coalgebraic models. We present a coalgebraic definition of bisimilarity for quasi-discrete models, which is adequate with respect to a spatial logic with reachability operators, complemented by a free and open-source minimization tool for finite models. We also discuss the non-quasi-discrete case, by providing a generalization of the well-known set-theoretical notion of topo-bisimilarity, and a categorical definition, in the same spirit as the coalgebraic rendition of neighbourhood frames, but employing the covariant power set functor, instead of the contravariant one. We prove its adequacy with respect to infinitary modal logic.

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“…There is also a surrounded constructor, to represent a notion of (un)reachability. Actually, SLCS has been proved to be quite effective and expressive, as it has been applied to reachability problems, vehicular movement, digital image analysis (e.g., street maps, radiological images [5]), etc. The model checking problem for this logic over finite quasi-discrete structures is decidable in linear time, making it suitable for the verification of spatial properties [7].…”

Section: Introductionmentioning

confidence: 99%

Closure hyperdoctrines, with paths

Castelnovo¹,

Miculan²

2020

Preprint

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Spatial logics are modal logics whose modalities are interpreted using topological concepts of neighbourhood and connectivity. Recently, these logics have been extended to (pre)closure spaces, a generalization of topological spaces covering also the notion of neighbourhood in discrete structures.In this paper we introduce an abstract theoretical framework for the systematic investigation of the logical aspects of closure spaces. To this end we define the categorical notion of closure (hyper)doctrine, which are doctrines endowed with inflationary operators (and subject to suitable conditions). The generality and effectiveness of this notion is demonstrated by many examples arising naturally from topological spaces, fuzzy sets, algebraic structures, coalgebras, and covering at once also known cases such as Kripke frames and probabilistic frames (i.e., Markov chains). In order to model also surroundedness, closure hyperdoctrines are then endowed with paths; this construction allows us to cover all the logical constructs of the Spatial Logic for Closure Spaces. By leveraging general categorical constructions, we provide a first axiomatisation and sound and complete semantics for propositional/regular/first order logics for closure operators.Therefore, closure hyperdoctrines are useful both for refining and improving the theory of existing spatial logics, but especially for the definition of new spatial logics for various applications.

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Innovating Medical Image Analysis via Spatial Logics

Cited by 12 publications

References 33 publications

Geometric Model Checking of Continuous Space

Geometric Model Checking of Continuous Space

Towards Spatial Bisimilarity for Closure Models: Logical and Coalgebraic Characterisations

Closure hyperdoctrines, with paths

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