Steerable Discrete Cosine Transform
This work addresses image compression inefficiencies for applications requiring precise directional matching, representing an incremental improvement over existing directional transforms.
The paper tackles the inefficiency of classical block-based transforms in handling arbitrarily shaped discontinuities in image compression by introducing a steerable discrete cosine transform (SDCT) that can be rotated to match directionality, achieving improved coding efficiency as proven by analytical and numerical results.
In image compression, classical block-based separable transforms tend to be inefficient when image 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, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.