Image representation and compression with steered Hermite transforms

Abstract

In this paper we propose that the Hermite transform can bridge the gap between conventional transform coding techniques and second-generation coding techniques that make use of explicit descriptions of perceptually important image structures (e.g., edge contours and lines). This claim is motivated by two important characteristics of the Hermite transform. First, it shows good image analysis properties in detecting and extracting (local) image primitives such as orientation and position. Second, extracted image features can be used to steer the Hermite transform into a form with high-energy compaction properties. To demonstrate the efficiency of the Hermite transform in image compression, we present an image compression scheme based on a Hermite transform that adapts to local image orientations. Comparisons with other compression techniques such as JPEG show that the proposed scheme performs extremely well at high compression ratios, not only in terms of peak-signal-to-noise ratio but also in terms of perceptual image quality.