We present an algorithm to segment a set of parallel, intertwined and bifurcating fibers from 3D images, targeted for the identification of neuronal fibers in very large sets of 3D confocal microscopy images. The method consists of preprocessing, local calculation of fiber probabilities, seed detection, tracking by particle filtering, global supervised seed clustering and final voxel segmentation. The preprocessing uses a novel random local probability filtering (RLPF). The fiber probabilities computation is performed by means of SVM using steerable filters and the RLPF outputs as features. The global segmentation is solved by discrete optimization. The combination of global and local approaches makes the segmentation robust, yet the individual data blocks can be processed sequentially, limiting memory consumption. The method is automatic but efficient manual interactions are possible if needed. The method is validated on the Neuromuscular Projection Fibers dataset from the Diadem Challenge. On the 15 first blocks present, our method has a 99.4% detection rate. We also compare our segmentation results to a state-of-the-art method. On average, the performances of our method are either higher or equivalent to that of the state-of-the-art method but less user interactions is needed in our approach.