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In this paper we describe mereotopological methods to programmatically correct image segmentation errors, in particular those that fail to fulfil expected spatial relations in digitised histological scenes. The proposed approach exploits a spatial logic called discrete mereotopology to integrate a number of qualitative spatial reasoning and constraint satisfaction methods into imaging procedures. Eight mereotopological relations defined on binary region pairs are represented as nodes in a set of 20 directed graphs, where the node-to-node graph edges encode the possible transitions between the spatial relations after set-theoretic and discrete topological operations on the regions are applied. The graphs allow one to identify sequences of operations that applied to regions of a given relation, and enables one to resegment an image that fails to conform to a valid histological model into one that does. Examples of the methods are presented using images of H&E-stained human carcinoma cell line cultures

Mereotopological Correction of Segmentation Errors in Histological Imaging