A method is proposed that can generate a ranked list of plausible three-dimensional hand configurations that best match an input image. Hand pose estimation is formulated as an image database indexing problem, where the closest matches for an input hand image are retrieved from a large database of synthetic hand images. In contrast to previous approaches, the system can function in the presence of clutter, thanks to two novel clutter-tolerant indexing methods. First, a computationally efficient approximation of the image-to-model chamfer distance is obtained by embedding binary edge images into a high-dimensional Euclidean space. Second, a general-purpose, probabilistic line matching method identifies those line segment correspondences between model and input images that are the least likely to have occurred by chance. The performance of this clutter-tolerant approach is demonstrated in quantitative experiments with hundreds of real hand images.