An experimental study on fuzzy distances for skull-face overlay in craniofacial superimposition

Skull-face overlay is the most time-consuming and error-prone stage in craniofacial superimposition, an important skeleton-based forensic identification technique. This task focuses on achieving the best possible overlay of an unknown skull found and a single ante-mortem image of a candidate missing person. The process is influenced by some sources of uncertainty since two objects of different nature are involved, i.e. a skull and a face. In previous works we have developed a computer-aided craniofacial superimposition system aimed to assist forensic anthropologists in obtaining the best possible skull and face overlay. The system has successfully allowed us to reduce the processing time, simplify the forensic anthropologists work, and make the process more objective and reproducible. Our approach is based on automatically overlaying a skull three dimensional model onto a facial photograph by minimizing the distance between two subsets of corresponding cranial and facial landmarks. The proposed method properly deals with the inherent uncertainty sources to the skull-face overlay process by considering fuzzy sets to model imprecise landmark location, and imprecise cranial and facial landmarks spatial correspondence (resulting from the presence of soft tissues in the face). Accordingly, our methodology requires computing two kinds of distance metrics: between a point and a fuzzy set, and between two fuzzy sets. This contribution is devoted to study the performance and influence of the most significant and suitable fuzzy distances proposed in the specialized literature, as well as other new ones proposed, on our skull-face overlay system. In particular, we have tested the behavior of our automatic method when considering eight different distance measurements. The system performance has been objectively evaluated considering 18 case studies resulting from a ground truth dataset following a rigorous statistical experimental setup. The fact that the choice of a good distance metric is crucial to our method has been demonstrated since it significantly affects the quality of the final solutions. It has been shown that our skull-face overlay approach presents the best performance using the weighted mean distance in most of the cases and that the results are both more accurate and robust than the other studied metrics.