Depth from stereo is an important research field in computer vision due to the wide range of its applications. In this work, we present a stereo matching algorithm based on belief propagation (BP). The algorithm is designed to work on sparse images originating from image content adaptive mesh representation techniques. There, an image is approximated with a mesh. The nodes of the mesh are the non-uniform samples which are the ones that form the sparse image. The key issue in the proposed method is to formulate BP such that it matches a sparse left stereo image with a dense right image to obtain a sparse depth map. Moreover, we propose a simple method that recovers the dense disparity map of the scene from the sparse one using the approximating mesh of the image. The results obtained show that the proposed method leads to an average of 40% improvement in the quality of depth maps when compared to existing sparse stereo matching techniques.