Learning to count biological structures with raters' uncertainty.

Exploiting well-labeled training sets has led deep learning models to astonishing results for counting biological structures in microscopy images. However, dealing with weak multi-rater annotations, i.e., when multiple human raters disagree due to non-trivial patterns, remains a relatively unexplored problem. More reliable labels can be obtained by aggregating and averaging the decisions given by several raters to the same data. Still, the scale of the counting task and the limited budget for labeling prohibit this. As a result, making the most with small quantities of multi-rater data is crucial. To this end, we propose a two-stage counting strategy in a weakly labeled data scenario. First, we detect and count the biological structures; then, in the second step, we refine the predictions, increasing the correlation between the scores assigned to the samples and the raters' agreement on the annotations. We assess our methodology on a novel dataset comprising fluorescence microscopy images of mice brains containing extracellular matrix aggregates named perineuronal nets. We demonstrate that we significantly enhance counting performance, improving confidence calibration by taking advantage of the redundant information characterizing the small sets of available multi-rater data.