The detection of small objects is a challenging task in computer vision. Conventional object detection methods have difficulty in finding the balance between high detection and low false alarm rates. In the literature, some methods have addressed this issue by enhancing the feature map responses, but without guaranteeing robustness with respect to the number of false alarms induced by background elements. To tackle this problem, we introduce an $\textit{a contrario}$ decision criterion into the learning process to take into account the unexpectedness of small objects. This statistic criterion enhances the feature map responses while controlling the number of false alarms (NFA) and can be integrated into any semantic segmentation neural network. Our add-on NFA module not only allows us to obtain competitive results for small target and crack detection tasks respectively, but also leads to more robust and interpretable results.
