  Cell detection and counting in the image-based ELISPOT and Fluorospot
immunoassays is considered a bottleneck. The task has remained hard to
automatize, and biomedical researchers often have to rely on results that are
not accurate. Previously proposed solutions are heuristic, and data-based
solutions are subject to a lack of objective ground truth data. In this paper,
we analyze a partial differential equations model for ELISPOT, Fluorospot, and
assays of similar design. This leads us to a mathematical observation model for
the images generated by these assays. We use this model to motivate a
methodology for cell detection. Finally, we provide a real-data example that
suggests that this cell detection methodology and a human expert perform
comparably.
