The prototyping of nano-objects based devices requires well-mastered processes for the manipulation of nano-objects. However, the various manufactoring processes are validated thanks to microscopy images that are most often interpreted qualitatively. A systematic and automatic characterization of these observations would be highly valuable to devise reliable processes. In the present paper, we specifically focus on carbon nanotubes membranes used in ultrasonic sensors. To characterize the membranes reproducibly, we developped a complete procedure for the processing of scanning electron microscopy images. The main steps are anisotropic denoising, contrast enhancement, segmentation based on mathematical morphology and estimation of the local orientation of filaments by using structure tensors. We also deal with the extraction of individual filaments. This approach does not require any user interaction and can be used in a fully automated way on hundreds of images. We obtained for the first time detailed histograms of the nanotubes orientations within the assembly. The histograms provide objective indicators of the quality of the alignment of nanotubes. It is essential to develop devices with well controlled physical properties.