Segmentation of 3D medical images, and brain segmentation in particular, is an important topic in neuroimaging and in radiotherapy. Overcoming the current, time consuming, practise of manual delineation of brain tumours and providing an accurate, explainable, and replicable method of segmentation of the tumour area and related tissues is therefore an open research challenge. In this paper, we first propose a novel symbolic approach to brain segmentation and delineation of brain lesions based on spatial model checking. This method has its foundations in the theory of closure spaces, a generalisation of topological spaces, and spatial logics. At its core is a high-level declarative logic language for image analysis, ImgQL, and an efficient spatial model checker, VoxLogicA, exploiting state-of-the-art image analysis libraries in its model checking algorithm. We then illustrate how this technique can be combined with Machine Learning techniques leading to a hybrid AI approach that provides accurate and explainable segmentation results. We show the results of the application of the symbolic approach on several public datasets with 3D magnetic resonance (MR) images. Three datasets are provided by the 2017, 2019 and 2020 international MICCAI BraTS Challenges with 210, 259 and 293 MR images, respectively, and the fourth is the BrainWeb dataset with 20 (synthetic) 3D patient images of the normal brain. We then apply the hybrid AI method to the BraTS 2020 training set. Our segmentation results are shown to be in line with the state-of-the-art with respect to other recent approaches, both from the accuracy point of view as well as from the view of computational efficiency, but with the advantage of them being explainable.

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 easy replicability . Furthermore, due to a two-orders-of-magnitude speedup compared to the existing general-purpose 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.