Local histograms for classifying H&E stained tissues

We introduce a rigorous mathematical theory for the analysis of local histograms, and consider the appropriateness of their use in the automated classification of textures commonly encountered in images of H&E stained tissues. We first discuss some of the many image features that pathologists indicate they use when classifying tissues, focusing on simple, locally-defined features that essentially involve pixel counting: the number of cells in a region of given size, the size of the nuclei within these cells, and the distribution of color within both. We then introduce a probabilistic, occlusion-based model for textures that exhibit these features, in particular demonstrating how certain tissue-similar textures can be built up from simpler ones. After considering the basic notions and properties of local histogram transforms, we then formally demonstrate that such transforms are natural tools for analyzing the textures produced by our model. In particular, we discuss how local histogram transforms can be used to produce numerical features that, when fed into mainstream classification schemes, mimic the baser aspects of a pathologist's thought process.