Laser-induced damage is a major issue in high power laser facilities such as the Laser MégaJoule (LMJ) and National Ignition Facility (NIF) since they lower the efficiency of optical components and may even require their replacement. This problem occurs mainly in the final stages of the laser beamlines and in particular in the glass windows through which laser beams enter the central vacuum chamber. Monitoring such damage sites in high energy laser facilities is, therefore, of major importance. However, the automatic monitoring of damage sites is challenging due to the small size of damage sites and to the low-resolution images provided by the onsite camera used to monitor their occurrence. A systematic approach based on a deep learning computer vision pipeline is introduced to estimate the dimensions of damage sites of the glass windows of the LMJ facility. The ability of the pipeline to specialize in the estimation of damage sites of a size less than the repair threshold is demonstrated by showing its higher efficiency than classical machine learning approaches in the specific case of damage site images. In addition, its performances on three datasets are evaluated to show both robustness and accuracy.