Steerable Discrete Cosine Transform

Block-based separable transforms tend to be inefficient when blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, designing a new transform that can be steered in any chosen direction and that is defined in a rigorous mathematical way. This new steerable DCT allows to rotate in a flexible way pairs of basis vectors, enabling precise matching of directionality in each image block, and thereby achieving improved coding efficiency. We tested the proposed transform on several images and the results show that it provides a significant performance gain compared to the DCT. Moreover, the mathematical framework on which the steerable DCT is based allows to generalize the transform to more complex steering patterns than a single pure rotation.