Various directional transforms have been developed recently to improve image compression. In video compression, however, prediction residuals of image intensities, such as the motion compensation residual or the resolution enhancement residual, are transformed. The applicability of the directional transforms on prediction residuals have not been carefully investigated. In this paper, we brie y discuss differing characteristics of prediction residuals and images, and propose directional transforms speci cally designed for prediction residuals. We compare these transforms with the directional transforms proposed for images using prediction residuals. The results of the comparison indicate that our proposed directional transforms can provide better compression of prediction residuals than the directional transforms proposed for images.

The Discrete-Cosine-Transform (DCT) is the most widely used transform in image and video compression. Its use in image compression is often justi ed by the notion that it is the statistically optimal transform for rst-order Markov signals, which have been used to model images. In standard video codecs, the motion-compensation residual (MC-residual) is also compressed with the DCT. The MC-residual may, however, possess different characteristics from an image. Hence, the question that arises is if other transforms can be developed that can perform better on the MC-residual than the DCT. Inspired by recent research on direction-adaptive image transforms, we provide an adaptive auto-covariance characterization for the MC-residual that shows some statistical differences between the MC-residual and the image. Based on this characterization, we propose a set of block transforms. Experimental results indicate that these transforms can improve the compression ef ciency of the MC-residual.

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In recent video coding standards, intraprediction of a block of pixels is performed by copying neighbor pixels of the block along an angular direction inside the block. Each block pixel is predicted from only one or few directionally aligned neighbor pixels of the block. Although this is a computationally efficient approach, it ignores potentially useful correlation of other neighbor pixels of the block. To use this correlation, a general linear prediction approach is proposed, where each block pixel is predicted using a weighted sum of all neighbor pixels of the block. The disadvantage of this approach is the increased complexity because of the large number of weights. In this paper, we propose an alternative approach to intraprediction, where we model image pixels with a Markov process. The Markov process model accounts for the ignored correlation in standard intraprediction methods, but uses few neighbor pixels and enables a computationally efficient recursive prediction algorithm. Compared with the general linear prediction approach that has a large number of independent weights, the Markov process modeling approach uses a much smaller number of independent parameters and thus offers significantly reduced memory or computation requirements, while achieving similar coding gains with offline computed parameters.

Typically the same transforms, such as the 2-D Discrete Cosine Transform (DCT), are used to compress both images in image compression and prediction residuals in video compression. However, these two signals have different spatial characteristics. In [1], we analyzed the difference between these two signals and proposed 1-D directional transforms for prediction residuals. In this paper, we provide further experimental results using these transforms in the H.264/AVC codec and present other related information which can provide insights in understanding the use of these transforms in video coding applications.