We present a method for 3D face acquisition using a set or sequence of 2D binary silhouettes. Since silhouette images depend only on the shape and pose of an object, they are immune to lighting and/or texture variations (unlike feature or texture-based shape-from-correspondence). Our prior 3D face model is a linear combination of "eigenheads" obtained by applying PCA to a training set of laser-scanned 3D faces. These shape coefficients are the parameters for a near-automatic system for capturing the 3D shape as well as the 2D texture-map of a novel input face. Specifically, we use back-projection and a boundary-weighted XOR-based cost function for binary silhouette matching, coupled with a probabilistic "downhill-simplex" optimization for shape estimation and refinement. Experiments with a multi-camera rig as well as monocular video sequences demonstrate the advantages of our 3D modeling framework and ultimately, its utility for robust face recognition with built-in invariance to pose and illumination.