Model-based Correction of Segmentation Errors in Digitised Histological Images

This paper describes an application of model-based methods for the algorithmic correction of segmentation errors in digitised histo- logical images. This is a real-world application where qualitative spatial reasoning and constraint-satisfaction programming methods have been integrated with classical image processing methods to develop context- based histological imaging algorithms. The context here arises from: (i) making an ontological stand whereby regions rather than pixels in digi- tised images are deemed to be the main carriers of histological content, and (ii) highlighting the importance of and explicitly modelling topo- logical (and in particular relational) information encoded in digitised histological images. The topological analysis and representational frame- work used is provided by the spatial logic Discrete Meterotopology. We use this to augment classical Mathematical Morphology pixel and region- based operations by explicitly encoding sets of binary relations on pairs of regions such as contact, overlap and the part-whole relation. These mereotopological relations are used both to model the domain and to guide resegmentation algorithms so that our interpreted images conform to the requirements for a valid histological model.