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We present an approach to estimate the poses off human heads in natural scenes. The essential features for estimating the head pose are the positions of the prominent facial features relative to the position of the head. We have developed a high-dimensional, randomly sparse representation of a human face using a simplified facial feature model. The representation transforms a raw face image into a vector, representing how well the image matches a large number of randomly-posed and shaped head models. This transformation is designed to collect salient features of the face image that are useful to estimate the pose, while suppressing any irrelevant variations of face appearance. The relation between the sparse representation and the pose is learned using SVR (support vector regression). The sparse representation combined with SVR is shown to estimate the pose more quickly and accurately than SVR applied to raw images.