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Discrete Mereotopology in automated histological image analysis

Discrete Mereotopology (DM) is two-sorted spatial logic that fuses together mereology (as the theory of parthood relations) and topology and applies this to modelling discrete space. We show how DM can be used to augment classical mathematical morphology by introducing a set of eight jointly exhaustive and pairwise disjoint spatial relations that can be directly implemented as digital imaging procedures in ImageJ. The two sorts assumed by DM are mapped to pixels and regions in digital images with the result that segmented and labelled images function as models in this logic-based approach to image interpretation and analysis. Applications and the scope of logic-based approaches to automated histological image segmentation and analysis are discussed. In particular we show how spatial logics such as DM can supply a much needed algorithmic context to blind image processing routines that still dominate conventional image processing. This it does in two key ways. Firstly it reinforces the ontological point that the main carriers of histological content are regions, not pixels. Secondly, its axioms, definitions and theorems when taken together limit or constrain how an image satisfying the logical domain model may be segmented, labelled and hence interpreted. This means search, for example, can be restricted to targeted regions in the segmented image. Another key advantage offered by implemented logics is that it opens up the the opportunity to mechanically reason by symbolic means about the domain model, and thus place inference at the core of image processing and segmentation operations. In particular the use of symbolic models enables one to verify queries about the domain model without necessarily having to verify this in terms of a sequence of image processing operations on actual images. We illustrate the general framework with two examples drawn from the histological domain: segmenting NIH 3T3 fibroblasts in culture and basal cell nuclei in odontogenic keratocyst tissue sections

Mereotopology, Regions, Qualitative Spatial Reasoning, RCC8, Mathematical Morphology, Artificial Intelligence, Lattices, Automated Reasoning

David A. Randell and Gabriel Landini

Oral Pathology Unit, School of Dentistry,The University of Birmingham, Birmingham, UK

David Randell (not available); Gabriel Landini:

Short Biography
Dr David A Randell is a Honorary Senior Research Fellow at the School of Dentistry, University of Birmingham, UK. He is well known in the Qualitative Spatial Reasoning (QSR) research community as a co-author of the popular spatial logic RCC8. His research interests cover both theoretical and applied aspects of QSR, Cognitive Robotics, abductive models of visual perception; and latterly in the application of spatial logics to quantitative histopathology and digital histological image analysis.

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