In this paper we present a new approach to categorize the wear of cutting tools used in edge profile milling processes. It is based on machine learning and computer vision techniques, specifically using B-ORCHIZ, a novel shape based descriptor computed from the wear region image. A new Insert dataset with 212 images of tool wear has been created to evaluate our approach. It contains two subsets: one with images of the main cutting edge, and the other one with the edges that converge to it (called Insert-C and Insert-I, respectively). The experiments were conducted trying to discriminate between two (Low-High) and three (Low-Medium-High) different wear levels and the classification stage was carried out using a Support Vector Machine (SVM). Results show that B-ORCHIZ outperforms other shape descriptors (aZIBO and ZMEG) achieving accuracy values between 80.24% and 88.46% in the different scenarios evaluated. Moreover, a hierarchical cluster analysis was performed, offering prototype images for wear levels, which may help researchers and technicians to understand how the wear process evolves. These results show a very promising opportunity for wear monitoring automation in edge profile milling processes.