The analysis of microscopic images of hair has a wide range of applications in the domains of cosmetics, healthcare and forensics. The segmentation of the hair represents the initial step of automatic large-scale quantitative analysis of microscopic images of hair. It ensures that subsequent quantitative measurements are performed in an appropriate area corresponding to the hair, avoiding artifacts near the boundaries. This process can be time-consuming, tedious and susceptible to subjective errors when conducted by a human operator. Deep learning methods represent a promising solution; however, obtaining pixel-level accurate masks is a costly process. This paper presents a novel weakly supervised pipeline for the segmentation of hair SEM (Scanning Electron Microscope) microscopic images, which requires only simple image-level annotations for training. The proposed method incorporates the Radon transform, the Sobel operator and a novel Boundary Discrimination Module (BD-module) for the estimation of the presence of boundaries. The proposed pipeline was evaluated on a recently collected hair SEM dataset (429 images). Furthermore, it is benchmarked with methods including Unet and Segment Anything Model (SAM). The results demonstrated a mean Hausdorff Distance improvement of over 30% and a standard deviation improvement of over 50% in comparison with the Unet and SAM. Moreover, we proposed additional refinement modules to address boundary nonlinear cases and conducted Grad-CAM analysis to enhance the interpretability of the BD-module. Additionally, we proposed a novel quality estimation metric based on gradient map for self-quality assessment. The SEM hair dataset is accessible to the research community in an open-source format.