Thresholding is of major interest in image processing as it is a crucial step for object detection, segmentation or classification. Numerous approaches have been proposed based on histograms or local characteristics. In this paper, we propose a thresholding approach based on local contrast and taking into account some shape prior on the underlying objects. This provides an automatic and spatially adaptative method, the solution being obtained by minimizing a functional over the set of candidate objects given by the level sets.We validated this approach by considering the classification of mitochondrial networks. Mitochondria are cell organelles playing a central role in the cell metabolism and cell death. In order to improve the detection of the mitochondrial networks we applied the proposed automatic threshold to feed a two level classification algorithm for recognizing filamentous, tubular and fragmented networks. We validated our binarization, named ATOLS, by comparing the obtained results with those obtained with the classical Otsu threshold, that is used in the Mitoloc software.