The popularity of stereo images and various display devices poses the need of stereo image retargeting techniques. Existing warping-based retargeting methods can well preserve the shape of salient objects in a retargeted stereo image pair. Nevertheless, these methods often incur depth distortion, since they attempt to preserve depth by maintaining the disparity of a set of sparse correspondences, rather than directly controlling the warping. In this paper, by considering how to directly control the warping functions, we propose a warping-based stereo image retargeting approach that can simultaneously preserve the shape of salient objects and the depth of 3D scenes. We first characterize the depth distortion in terms of warping functions to investigate the impact of a warping function on depth distortion. Based on the depth distortion model, we then exploit binocular visual characteristics of stereo images to derive region-based depth-preserving constraints which directly control the warping functions so as to faithfully preserve the depth of 3D scenes. Third, with the region-based depth-preserving constraints, we present a novel warping-based stereo image retargeting framework. Since the depth-preserving constraints are derived regardless of shape preservation, we relax the depth-preserving constraints to fulfill a tradeoff between shape preservation and depth preservation. Finally, we propose a quad-based implementation of the proposed framework. The results demonstrate the efficacy of our method in both depth and shape preservation for stereo image retargeting.