This paper presents a fingerprinting method based on equivalence classes. An equivalence class is composed of a reference image and all its variations (or replicas). For each reference image, a decision function is built. The latter determines if a given image belongs to its corresponding equivalence class. This function is built in three steps: synthesis, projection, and analysis. In the first step, the reference image is replicated using different image operators (like JPEG compression, average filtering, etc). During the projection step, the replicas are projected onto a distance space. In the final step, the distance space is analyzed, using machine learning algorithms, and the decision function is built. In this study, three machine learning approaches are compared: orthotope, support vectors machine (SVM), and support vectors data description (SVDD). The orthotope is a computationally efficient ad-hoc method. It consists in building a generalized rectangle in the distance space. The SVM and SVDD are two more general learning algorithms.