A two-stage algorithm is proposed for locating smooth and detailed disparity vector fields in a stereo image pair. The algorithm consists of hierarchical disparity estimation using a region-dividing technique and edge-preserving regularization. The hierarchical region-dividing disparity estimation increases the efficiency and reliability of the estimation process. At the second stage, the vector fields are regularized with an energy model that produces smooth fields while preserving discontinuities resulting from object boundaries. The minimization problem is addressed by solving a corresponding partial differential equation using a finite-difference method. Experiments show that the proposed algorithm provides accurate and spatially correlated disparity vector fields in various types of stereo images, even in the case of images with large displacements.