Feasibility of Spatial Model Checking for Nevus Segmentation

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

doi:10.1109/formalise52586.2021.00007

Cited by 18 publications

(3 citation statements)

References 36 publications

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“…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%

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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Section: Introduction and Related Workmentioning

confidence: 99%

Geometric Model Checking of Continuous Space

Bezhanishvili¹,

Ciancia²,

Gabelaia³

et al. 2021

Preprint

Self Cite

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show abstract

“…The logic and its model checkers have been applied to several case studies [12,10,9] including a declarative approach to medical image analysis [4,3,8,2]. An encoding of the discrete Region Connection Calculus RCC8D of [22] into the collective variant of SLCS has been proposed in [13].…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, they turn out to be rather too strong when one has in mind intuitive relations on space like, e.g. scaling, that may be useful when dealing with models representing images (see [8,2,4,3] for details). For this purpose, we introduce our second, weaker notion of bisimilarity, namely Path-bisimulation that is essentially based on reachability of bisimilar points by means of paths over the underlying space.…”

Section: Introductionmentioning

confidence: 99%

On Bisimilarities for Closure Spaces - Preliminary Version

Ciancia,

Latella,

de Vink

2021

Preprint

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Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure models-we call the resulting equivalence CM-bisimilarity-and refine it for quasi-discrete closure models. We also define two additional notions of bisimilarity that are based on paths on space, namely Path-bisimilarity and Compatible Pathbisimilarity, CoPa-bisimilarity for short. The former expresses (unconditional) reachability, the latter refines it in a way that is reminishent of Stuttering Equivalence on transition systems. For each bisimilarity we provide a logical characterisation, using variants of SLCS. We also address the issue of (space) minimisation via the three equivalences.

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