Soft biometrics have been emerging to complement other traits and are particularly useful for poor quality data. In this paper, we propose an efficient algorithm to estimate human head poses and to infer soft biometric labels based on the 3D morphology of the human head. Starting by considering a set of pose hypotheses, we use a learning set of head shapes synthesized from anthropometric surveys to derive a set of 3D head centroids that constitutes a metric space. Next, representing queries by sets of 2D head landmarks, we use projective geometry techniques to rank efficiently the joint 3D head centroids/pose hypotheses according to their likelihood of matching each query. The rationale is that the most likely hypotheses are sufficiently close to the query, so a good solution can be found by convex energy minimization techniques. Once a solution has been found, the 3D head centroid and the query are assumed to have similar morphology, yielding the soft label. Our experiments point toward the usefulness of the proposed solution, which can improve the effectiveness of face recognizers and can also be used as a privacy-preserving solution for biometric recognition in public environments.