Abstract—The direction-adaptive partitioned block transform (DA-PBT) is proposed to exploit the directional features in color images to improve coding performance. Depending on the directionality in an image block, the transform either selects one of the eight directional modes or falls back to the nondirectional mode equivalent to the conventional 2-D DCT. The selection of a directional mode determines the transform direction that provides directional basis functions, the block partitioning that spatially confines the high-frequency energy, the scanning order that arranges the transform coefficients into a 1-D sequence for efficient entropy coding, and the quantization matrix optimized for visual quality. The DA-PBT can be incorporated into image coding using a rate-distortion optimized framework for direction selection, and can therefore be viewed as a generalization of variable blocksize transforms with the inclusion of directional transforms and nonrectangular partitions. As a block transform, it can naturally be combined with block-based intra or inter prediction to exploit the directionality remaining in the residual. Experimental results show that the proposed DA-PBT outperforms the 2-D DCT by more than 2 dB for test images with directional features. It also greatly reduces the ringing and checkerboard artifacts typically observed around directional features in images. The DA-PBT also consistently outperforms a previously proposed directional DCT. When combined with directional prediction, gains are less than additive, as similar signal properties are exploited by the prediction and the transform. For hybrid video coding, significant gains are shown for intra coding, but not for encoding the residual after accurate motion-compensated prediction. Index Terms—Direction-adaptive entropy coding, direction-adaptive transform, discrete cosine transform, image coding, transform coding. I.

Abstract—In this paper, we present the design of directional lapped transforms for image coding. A lapped transform, which can be implemented by a prefilter followed by a discrete cosine transform (DCT), can be factorized into elementary operators. The corresponding directional lapped transform is generated by applying each elementary operator along a given direction. The proposed directional lapped transforms are not only nonredundant and perfectly reconstructed, but they can also provide a basis along an arbitrary direction. These properties, along with the advantages of lapped transforms, make the proposed transforms appealing for image coding. A block-based directional transform scheme is also presented and integrated into HD Phtoto, one of the state-of-the-art image coding systems, to verify the effectiveness of the proposed transforms. Index Terms—Directional transform, image coding, lapped transform.

Abstract—Transform-based image coding has been the mainstream for many years, as witnessed in from the early effort in JPEG to the recent advances in HD Photo. Traditionally, a 2-D transform used in image coding is always implemented separately along the vertical and horizontal directions, respectively. However, it is usually true that many image blocks contain oriented structures (e.g., edges) and/or textures that do not follow either the vertical or horizontal direction. The traditional 2-D transform thus may not be the most appropriate one to these image blocks. This well-known fact has recently triggered several attempts towards the development of directional transforms so as to better preserve the directional information in an image block. Some of these directional transforms have been applied in image coding, demonstrating a significant coding gain. This paper presents an overview of these directional transforms as well as a discussion of some existing problems and their potential solutions. I.

Abstract—While directional adaption is introduced into traditional transforms, different orders of two 1-D transforms will result in different results of one 2-D transform. Based upon an anisotropic image model, this paper analyzes the effect of transform orders in terms of theoretical coding gain. Our results reveal that the transform orders have little effect on the coding gain with full decomposition, good directional modes and good interpolation. However, in practical compression schemes, since high-pass bands are not decomposed fully because of the consideration on complexity, different transform orders have different coding performances, which can be solved by an adaptive transform order. Motivated by our analyzed results, a directional filtering transform (dFT, in order to distinguish from the common usage on DFT) is proposed in this paper to better exploit correlations among samples in H.264 intraframe coding. It provides an evenly distributed set of prediction modes with an adaptive transform order. Both interblock and intrablock correlations are exploited in this scheme. Experimental results in H.264 intraframe coding demonstrate its superiority both objectively and subjectively. Index Terms—Adaptive directional filtering, adaptive lifting order, H.264 intraframe coding, lifting-based wavelet transform. I.

Abstract—Compound images are a combination of text, graphics and natural image. They present strong anisotropic features, especially on the text and graphics parts. These anisotropic features often render conventional compression inefficient. Thus, this paper proposes a novel coding scheme from the H.264 intraframe coding. In the scheme, two new intramodes are developed to better exploit spatial correlation in compound images. The first is the residual scalar quantization (RSQ) mode, where intrapredicted residues are directly quantized and coded without transform. The second is the base colors and index map (BCIM) mode that can be viewed as an adaptive color quantization. In this mode, an image block is represented by several representative colors, referred to as base colors, and an index map to compress. Every block selects its coding mode from two new modes and the previous intramodes in H.264 by rate-distortion optimization (RDO). Experimental results show that the proposed scheme improves the coding efficiency even more than 10 dB at most bit rates for compound images and keeps a comparable efficient performance to H.264 for natural images. Index Terms—Base colors and the index map, compound image compression, dynamic programming, residual scalar quantization. I.

This paper presents a scheme to design directional lapped transforms. Lapped transforms can be factorized into lifting steps. By introducing directional operator into each lifting step, the directional lapped transform is constructed. The directional lapped transform proposed not only preserves the advantages of lapped transforms, it also can represent directional signals more efficiently. An image coding scheme using the directional lapped transform is also described. Compared to the state-of-the-art image coding using lapped transform, HD Photo, the proposed scheme shows more than 20dB’s gain for artificial images with strong directional correlations. And for natural images, up to 1.5dB’s gain can also be observed. 1