Systems and methods provide directional discrete cosine transformation (DCT) and motion compensated DCT. In one implementation, an exemplary system finds a directional property of an image, such as a visual trend, factorizes a DCT operation into primal operations, and applies the primal operations along a corresponding direction to perform the DCT. Motion compensated DCT applies the primal operations along a motion trajectory of a video sequence. When the directional DCT is applied blockwise, the directional coding modes for adjacent blocks can be optimized in view of each other using a weighted graph to represent the related coding mode decisions.