How to build an average model when samples are variably incomplete? Application to fossil data

Abstract : In paleontology, incomplete samples with small or large missing parts are frequently encountered. For example,dental crowns, which are widely studied in paleontology because of their potential interest in taxonomic and phylogenetic analyses, are nearly systematically affected by a variable degree of wear that alters considerably their shape. It is then difficult to compute a significant reference surface model based on classical methods which are used to build atlases from set of samples. In this paper, we present a general approach to deal with the problem of estimating an average model from a set of incomplete samples. Our method is based on a state-of-the-art non-rigid surface registration algorithm. In a first step, we detect missing parts which allows one to focus only on the common parts to get an accurate registration result. In a second step, we try to build average model of the missing parts by using information which is available in a subset of the samples. We specifically apply our method on teeth, and more precisely on the surface in between dentine and enamel issues (EDJ). We investigate the robustness and accuracy properties of the methods on a set of artificial samples representing a high degree of incompleteness. We compare the reconstructed complete shape to a ground-truth dataset. We then show some results on real data.