Derivation for Adaptive Scan of Intra Prediction in Video Coding

H.264 [1] and AVS [2] are the emerging state-of-art video coding standards, in which the block-based hybrid coding framework is employed. DCT or its approximation such as Integer Cosine Transform (ICT) is the centerpiece for signal decorrelation and energy compaction. After DCT, the transform coefficients are quantized and scanned into one-dimensional (1-D) signals, named run-level pairs. The knowledge of DCT coefficient properties is important and would be useful, for instance, in quantizer design and scan design. The statistical properties of DCT coefficients have been widely studied for more than 30 years. Experimental test [3] and mathematics analysis [4] have proved that distributions of DCT coefficients resemble Laplacian distribution. In [5], a theoretical model for DCT coefficient is proposed for analyzing inter prediction error. Based on that, variances of coefficients at different frequencies are estimated. In this paper, a mathematical derivation for DCT coefficient properties of intra prediction is given based on ESM proposed in [6]. Furthermore, the adaptive scan is designed. The paper is organized as follows: Section 2 gives the mathematical derivation for DCT coefficient properties. In section 3, the adaptive scan is designed and the corresponding experiments are carried on the platform of H.264 and AVS. Section 4 concludes the paper.