This paper proposes a novel approach to jointly optimize spatial prediction and the choice of the subsequent transform in video and image compression. Under the assumption of a separable first-order Gauss-Markov model for the image signal, it is shown that the optimal Karhunen-Loeve Transform, given available partial boundary information, is well approximated by a close relative of the discrete sine transform (DST), with basis vectors that tend to vanish at the known boundary and maximize energy at the unknown boundary. The overall intraframe coding scheme thus switches between this variant of the DST named asymmetric DST (ADST), and traditional discrete cosine transform (DCT), depending on prediction direction and boundary information. The ADST is first compared with DCT in terms of coding gain under ideal model conditions and is demonstrated to provide significantly improved compression efficiency. The proposed adaptive prediction and transform scheme is then implemented within the H.264/AVC intra-mode framework and is experimentally shown to significantly outperform the standard intra coding mode. As an added benefit, it achieves substantial reduction in blocking artifacts due to the fact that the transform now adapts to the statistics of block edges. An integer version of this ADST is also proposed.