Craniofacial superimposition involves the process of overlaying a skull with a number of ante-mortem images of an individual and the analysis of their morphological correspondence. Within the craniofacial superimposition process, the skull-face overlay stage focuses on achieving the best possible overlay of the skull and a single ante-mortem image of a missing person. This technique has been commonly applied following a nonautomatic trial-and-error approach. Automatic skull-face overlay methods have been developed obtaining promising results. In this paper, we present two new variants that are an extension of existing 3-D-2-D methods to automatically superimpose a skull 3-D model on a facial photograph. We have modeled the imprecision related to the facial soft tissue depth between corresponding pairs of cranial and facial landmarks which typically guide the automatic approaches. As an illustration of the model's performance, the soft tissue distances associated to studies for Mediterranean population have been considered for dealing with this landmark matching uncertainty. Hence, we directly incorporate the corresponding landmark spatial relationships within the automatic skull-face overlay procedure. We have tested the performance of our proposal on 18 skull-face overlay instances from a ground truth data set obtaining valuable results. The current proposal is thus the first automatic skull-face overlay method evaluated in a reliable and unbiased way.

Polygonal surface models are typically used in three-dimensional (3D) visualizations and simulations. They are obtained by laser scanners, computer vision systems or medical imaging devices to model highly detailed object surfaces. Surface mesh simplification aims to reduce the number of faces used in a 3D model while keeping the overall shape, boundaries, and volume. In this work, we propose to deal with the mesh simplification problem from an evolutionary multi-objective viewpoint. The quality of a solution is defined by two conflicting objectives: the accuracy and the simplicity of the model. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is adapted to tackle the problem. We compare the NSGA-II performance with a classical approach and a single-objective implementation. The comparison has been carried out using different datasets.