Stereoscopic image adaptation to the target display devices while minimizing the distortion of significant features and stereoscopic properties is a challenging problem. Conventional methods either fail to preserve the image context or unable to improve the image aesthetics with improved depth perception in the retargeted images. In this paper, we present an automatic warping-based stereoscopic 3D image recomposition to retargeting method, shortly S3D-R2R that improves the stereo image composition in the retargeting results. Our S3D-R2R method resizes both the left and right stereo image pair using a global optimization algorithm that minimizes a set of aesthetic quality errors. These errors are formulated based on the selected photographic composition rules and modify the depth perception. To improve the depth perception of the stereo image pair, the disparity consistency has been modified within the comfort disparity range. Experimental results show that our automatic method changes the position of the salient object in the target image scale and improves the depth perception within the comfort depth range. Empirical user studies indicate that our retargeting results receive more attention than state-of-the-art methods.