Image analysis is a key tool for describing the detailed mechanisms of folliculogenesis, such as evaluating the quantity of mouse Primordial ovarian Follicles (PMF) in the ovarian reserve. The development of high-resolution virtual slide scanners offers the possibility of quantifying, robustifying and accelerating the histopathological procedure. A major challenge for machine learning is to control the precision of predictions while enabling a high recall, in order to provide reproducibility. We use a multiple testing procedure that gives an overperforming way to solve the standard Precision-Recall trade-off that gives probabilistic guarantees on the precision. In addition, we significantly improve the overall performance of the models (increase of F1-score) by selecting the decision threshold using contextual biological information or using an auxiliary model. As it is model-agnostic, this contextual selection procedure paves the way to the development of a strategy that can improve the performance of any model without the need of retraining it.