Counting Melanocytes with Trainable h-Maxima and Connected Component Layers

Bright objects on a dark background, such as cells in microscopy images, can sometimes be modeled as maxima of sufficient dynamic, called h-maxima. Such a model could be sufficient to count these objects in images, provided we know the dynamic threshold that tells apart actual objects from irrelevant maxima. In this paper we introduce a neural architecture that includes a morphological pipeline counting the number of h-maxima in an image, preceded by a classical CNN which predicts the dynamic h yielding the right number of objects. This is made possible by geodesic reconstruction layers, already introduced in previous work, and a new module counting connected components. This architecture is trained end-to-end to count melanocytes in microscopy images. Its performance is close to the state of the art CNN on this dataset, with much fewer parameters (1/100) and an increased interpretability.