We present an appearance-based 3D hand posture estimation method that determines a ranked set of possible hand posture candidates from an unmarked hand image, based on an analysis by synthesis method and an image retrieval algorithm. We formulate the posture estimation problem as a nonlinear, many-to-many mapping problem in a high dimension space. A general algorithm called ISOSOM is proposed for nonlinear dimension reduction, applied to 3D hand pose reconstruction to establish the mapping relationships between the hand poses and the image features. In order to interpolate the intermediate posture values given the sparse sampling of ground-truth training data, the geometric map structure of the samples\' manifold is generated. The experimental results show that the ISOSOM algorithm performs better than traditional image retrieval algorithms for hand pose estimation.