The creation of realistic 3D face models is still a fundamental problem in computer graphics. In this paper we present a novel method to obtain the 3D shape of an arbitrary human face using a sequence of silhouette images as input. Our face model is a linear combination of eigenheads, which are obtained by a Principal Component Analysis (PCA) of laser-scanned 3D human faces. The coefficients of this linear decomposition are used as our model parameters. We introduce a near-automatic method for reconstructing a 3D face model whose silhouette images match closest to the set of input silhouettes.