Steerable Discrete Cosine Transform

TL;DR

This paper introduces a steerable discrete cosine transform (SDCT) that adapts to image block discontinuities by rotating basis vectors, improving compression efficiency over traditional DCT and other directional transforms.

Contribution

The paper presents a novel steerable DCT that can be rotated in any direction, with algorithms to optimize rotation angles for better image compression.

Findings

SDCT outperforms traditional DCT in image compression tasks.

SDCT achieves higher coding efficiency compared to existing directional transforms.

The proposed iterative methods effectively optimize rotation angles for SDCT.

Abstract

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.