We propose an Isometric Self-Organizing Map (ISOSOM) method for nonlinear dimensionality reduction, which integrates a Self-Organizing Map model and an ISOMAP dimension reduction algorithm, organizing the high dimension data in a low dimension lattice structure. We apply the proposed method to the problem of appearance-based 3D hand posture estimation. As a learning stage, we use a realistic 3D hand model to generate data encoding the mapping between the hand pose space and the image feature space. The intrinsic dimension of such nonlinear mapping is learned by ISOSOM, which clusters the data into a lattice map. We perform 3D hand posture estimation on this map, showing that the ISOSOM algorithm performs better than traditional image retrieval algorithms for pose estimation. We also show that a 2.5D feature representation based on depth edges is clearly superior to intensity edge features commonly used in previous methods.