VoxLogicA: A Spatial Model Checker for Declarative Image Analysis

Abstract

Spatial and spatio-temporal model checking techniques have a wide range of application domains, among which large scale distributed systems and signal and image analysis. We explore a new domain, namely (semi-)automatic contouring in Medical Imaging, introducing the tool VoxLogicA which merges the state-of-the-art library of computational imaging algorithms ITK with the unique combination of declarative specification and optimised execution provided by spatial logic model checking. The result is a rapid, logic based analysis development methodology. The analysis of an existing benchmark of medical images for segmentation of brain tumours shows that simple VoxLogicA analysis can reach state-of-the-art accuracy, competing with best-in-class algorithms, with the advantage of explainability and replicability. Furthermore, due to a two-orders-of-magnitude speedup compared to the existing generalpurpose spatio-temporal model checker topochecker, VoxLogicA enables interactive development of analysis of 3D medical images, which can greatly facilitate the work of professionals in this domain.

Towards Spatial Bisimilarity for Closure Models: Logical and Coalgebraic Characterisations

“…The algorithm then applies one refinement step, by applying the functor F to q and composing the result with η; this yields a new function q = (Fq) • η. Note that such function is "almost always" surjective 8 . Intuitively, at each iteration, function q is obtained from q by splitting the partitions induced by q according to the "observations" that are obtained "in one more step" from η.…”

“…Although the study of such operators has not been developed in full detail in the classical spatial logics literature, they have proved useful in case studies. For instance, the ability to identify two areas, characterised by given logical formulas, that additionally are in contact with each other, while retaining the point-based approach of topo-logics, has been the key to derive a segmentation algorithm that labels brain tumours in three-dimensional medical images, with accuracy in par with manual segmentation, and best-in-class machine learning methods [8].…”

“…This is directly aimed at supporting the future developments of the spatial model checking methodology that is currently in use, e.g. in [8]. In Section 3 we present a set-theoretical definition, and provide some examples.…”

Geometric Model Checking of Continuous Space

“…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].…”

“…In this paper we take the polyhedral semantics one step further by extending the language with a spatial reachability modality, namely a variant the ρ operator originally proposed in [10]. The reachability modality γ we use in the present paper is a binary logical operator that can be seen as a variant of the spatial interpretation of the Existential Until temporal operator.…”