Conventional stereo image coders employ disparity compensated prediction followed by the transform coding of the residual to encode the second image of a stereo pair. However, transform coders, such as DCT, are generally not efficient in coding the residuals. In order to improve the coding gain, subspace projection techniques have been proposed in literature . The idea is to apply a transform to each block, Rb, in the right image in such a way that it exploits stereo and spatial redundancy, simultaneously. The transformation is chosen to be a reduced order operator that projects block Rb onto a subspace that is spanned by a block dependant vector and a set of fixed vectors. Further to their work, we propose a novel local texture adaptive technique that selects between two sets of fixed polynomial vectors to improve the prediction. The choice of this adaptive technique was motivated by the distinctively different orientations of pixel value variation trends that are often present in natural scenes. Extensive experimental results indicate that the proposed technique outperforms the existing techniques both in terms of compression efficiency and reconstructed image quality. Particularly, the proposed algorithm performs well in natural scenes, where most stereo image compression techniques perform sub-optimally.