Intra Prediction Based on Markov Process Modeling of Images

Abstract

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.

Intra-frame coding with recursive intra prediction and adapted block transforms

“…The development of both the ODST-3/DCT transform in [2] and the recursive intra prediction approach in [5] assume that image pixels in a local neighborhood follow a 2-D Markov process model, which can be represented with the following recursive relationship u(i, j) = ρ 1 u(i−1, j)+ρ 2 u(i−1, j−1)+ρ 3 u(i, j−1)+e(i, j). Here, u(i, j) represent image pixels (see Figure 1 a) which are assumed to be zero-mean and unit variance, and e(i, j) represent zero-mean white-noise process samples independent of previous image pixels u(i−p, j −q), p, q ≥ 1.…”

“…The recursive intra prediction approach in [5] also models image pixels in a local neighborhood of a block (See Figure 1 a) with the 2-D Markov process in Equation (1). The minimum-mean-square-error (MMSE) estimateû(i, j) of any block pixel can be obtained by determining its conditional expectation E[u(i, j)|n] (n represents all neighbor pixels of the block, see Figure 1 a.)…”

“…While Equation (1) uses only three neighbors, an additional neighbor pixel can be included to model strong angular structures, such as for prediction mode 3 (See [5] for details). The values of the parameters ρ 1 , ρ 2 and ρ 3 (and ρ 4 if four neighbor pixels are used) reflect the directional properties of the 2-D Markov process and the prediction algorithm.…”

“…More recently, a recursive prediction approach has been proposed for intra prediction [5]. In the conventional copyingbased intra prediction method, each block pixel is predicted using only one (or few) directionally aligned neighbor pixel of the block.…”

“…However, other neighbor pixels of the block may also contain useful correlation for prediction. To capture such correlation, block pixels are modeled with 2-D Markov processes in [5] (similar to [2]) and a recursive intra prediction algorithm is obtained. The residual blocks are transformed with the 2-D DCT in [5].…”