• 3D data acquisition and segmentation: CT-Scan images are more and more used in paleo-anthropology. Devices that are routinely used in medical radiology have a resolution of one millimeter whereas special industrial micro-scanners can reach up to a resolution of one ten to one hundred microns. The first problem is to segment the structure to study by image processing techniques. It may be complex if the structure is very small or low contrasted with respect to the image background. Different techniques will be carefully tested on different fossils and will be described.
• paleontological "reconstruction": it consists in associating different structures, which may be parts of different fossils, in order to try to reconstitute a complete fossil. This interpretation work can only be done by a skilled palaeontologist. It would require powerful and user-friendly tools to visualize and interact in real-time the virtual structures. Moreover, it deals the problem of "fusing" 3D models: how to deal with imperfect joints, how to smooth the 3D models?
• automatic extraction of 3D geometric landmarks: comparing the different fossils requires extracting some landmarks which are common to all the structures. In general, these landmarks are points which are manually plotted by a paleo-anthropologist. But representing precisely the complex 3D shape of a fossil requires to collect several thousands landmarks located all over the structure and this can be only done by an automatic process. The difficulty is then to determine a class of landmarks that can be defined by an unambiguous mathematical formula to be automatically computed and, that are also anatomically relevant to characterize the structure.
• compensation for the taphonomic deformations: these are post-mortem deformations due, for example, to the movement of the geological layers or due to the compression of the sediments that piled-up onto the fossils. It is necessary to identify these deformations in order to recover the original shape of the fossil. In some cases, they were so important that the fossil lost completely its proportions, preventing any morphometrical analysis! We propose to study three different and innovative methods to compute the taphonomic deformations. The first one aims to find automatically the symmetry plane of the structure and to rectify it. The second method consists in registering the deformed structure with a reference one. This makes possible to compute a global deformation between the two structures and to extract the taphonomic one. In the third method, we assume that we are able to simulate the evolution of the geological layers since the burying of the fossil. It is then possible to infer the constraints that have applied on the structure.
• computation of a 3D deformation field: once we have extracted landmarks on two different structures, we have to find the correspondences between them in order to study the differences in their localization. Usually, this is done manually by an anatomist who knows the biological homology: two features are put into correspondence if they characterize the same biological functionality. In our case, there is so many points that a manual process is no more relevant and we have to design an algorithm to find automatically the correspondences. This is a very well known problem in 3D image processing called "registration". It is then possible to compute a 3D deformation field, based on the landmark correspondences, that superimposes at best, the two structures.
• 3D morphometrical analysis: the analysis of the 3D deformation field or of the landmark correspondences opens very new and difficult research topics: how to perform a multivariate statistical analysis of vector fields or of deformation parameters? Which probability law do we have to take into account to model the complex process of Evolution whereas only a very limited sample of fossil data are available? How to take into account the inaccuracy in the localization of landmarks? How to separate (or correlate) the morphological differences due to the Evolution, the regular growth or the inter-individual variations?
• 3D facial reconstruction: this innovative application consists in inferring the unknown 3D shape of the face from skull data, by assuming that the surface of the face follows more or less the shape of the skull. We will test an entirely automatic method that applies the 3D deformation computed between a reference skull and a fossil one, to the corresponding reference face.
We plan to study three types of anatomical structures: the skull which is the richest structure to define the different lineages; the pelvis that gives information on bipedy and the teeth, which are in general well preserved and emphasize in particular the alimentary habits.