The recent booming of multiphoton imaging of collagen fibrils by means of second harmonic generation microscopy generates the need for the development and automation of quantitative methods for image analysis. Standard approaches sequentially analyse two-dimensional (2D) slices to gain knowledge on the spatial arrangement and dimension of the fibrils, whereas the reconstructed three-dimensional (3D) image yields better information about these characteristics. In this work, a 3D analysis method is proposed for second harmonic generation images of collagen fibrils, based on a recently developed 3D fibre quantification method. This analysis uses operators from mathematical morphology. The fibril structure is scanned with a directional distance transform. Inertia moments of the directional distances yield the main fibre orientation, corresponding to the main inertia axis. The collaboration of directional distances and fibre orientation delivers a geometrical estimate of the fibre radius. The results include local maps as well as global distribution of orientation and radius of the fibrils over the 3D image. They also bring a segmentation of the image into foreground and background, as well as a classification of the foreground pixels into the preferred orientations. This accurate determination of the spatial arrangement of the fibrils within a 3D data set will be most relevant in biomedical applications. It brings the possibility to monitor remodelling of collagen tissues upon a variety of injuries and to guide tissues engineering because biomimetic 3D organizations and density are requested for better integration of implants.