Statistically Motivated 3 D Faces Reconstruction

Facial surgeons require a vast amount of knowledge about the human face, in order to decide how to reconstruct an injured or traumatized part. Does this knowledge consist only of explicit notions about face anatomy, or is there also an implicit knowledge of the normal appearance of a face? And if the answer to the latter question is affirmative, is there a way for a computer to automatically learn this implicit knowledge and exploit it to predict the optimal reconstruction of part of a face? A set of examples of human faces, acquired as 3D surfaces, can be used to build a statistical model, which can generate synthetic faces or analyze novel ones. Such a model is also able to reconstruct the missing part of a face in a statistically meaningful way: any face which can be generated by such a model has a certain probability, and the optimal reconstruction can be defined as the one which maximizes it, given the available data. However, since the model is built from a finite set of examples, it cannot generate any possible face, and therefore the purely statistical reconstruction will not perfectly fit the available data, leading to discontinuities at the boundary between the missing and the available data. In order to avoid this, we look for the surface that explicitly satisfies the continuity constraints at the boundary, and at the same time approximates the first derivatives of the statistical prediction. This leads to a partial differential equation, which can be solved numerically as a linear system. As an example, we show how this method performs reconstructing the noses of a set of test faces.