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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. [ABSTRACT FROM PUBLISHER]