4. Rate-Distortion Optimized Quantization

Previously, adaptive rounding was proposed to improve quantization, which captures the statistics of the incoming residual signal and adjusts the rounding offsets accordingly. However, the adaptive rounding quantization is still based on the criterion which minimizes the mean-squared quantization error between the original signal and the quantization reconstructed signal. From the sense of rate-distortion optimization, the cost from the rate should also be considered.

The basic idea underlying the rate-distortion optimized quantization is to minimize a cost function D+ λR such that both the rate R and the distortion D are considered in coding decisions. For quantization case, the RD optimal coding is to solve a minimization problem of

                                                   (7)

where S is the original signal, and T-1 denotes the inverse transform operation. Consider that the DCT is a unitary transform, which maintains the Euclidean d[......]

Read More…

Permanent Link: Quantization Techniques in JM/KTA – Part 4

3. Adaptive Rounding Encoding Technique using an Equal Expected-Value Rule

As discussed above, if the input p.d.f. is Laplacian distributed and if we can estimate λ, then the optimal f can be found analytically. But, usually the estimate of input p.d.f. is not available, then, how to select the rounding offset f?

In order to select rounding offset f adaptively, an adaptive quantization encoding technique using an equal expected-value rule is proposed by Gary Sullivan from Microsoft. The adaptive adjustment of the rounding offset f occurs only in the encoding quantization process, which tries to select f without using any priori model knowledge on the input W. The aim is to make that the mean of the absolute value of the input, |W|, is equal to its expected reconstruction value |W’|, i.e.,

                                                                                          (5)

Any values in an interval would be reconstructed to some W’, so the distribution of W’ is a probability ma[......]

Read More…

Permanent Link: Quantization Techniques in JM/KTA – Part 3

2. Principle of H.264/AVC Normal Quantization Scheme

2.1. Scalar dead-zone quantization

In this section the principle of H.264/AVC normal quantization scheme is described in a generalized form.

A scalar quantizer for input signal W can be decomposed into a function Z=C[W] called a classification rule that selects an integer-valued class identifier called the quantization index at the encoder, and a reconstruction rule that produces a real-valued output W’=R[Z] at the decoder. Video encoder applies entropy coding to the quantization indices and communicates to the decoder. Although H.264/AVC JM reference software implements some classification functions, only reconstruction function is standardized.

In the quantization step of the encoder, the transform coefficients of the prediction error are quantized. This quantization is used to reduce the precision of the coefficients. Furthermore, the quantizer is designed to map insignificant coefficient values to zero whilst retaining a reduced [......]

Read More…

Permanent Link: Quantization Techniques in JM/KTA – Part 2

1. Overview

Currently most image and video coding systems and standards, such as MPEG-1/2 and H264/AVC, use transform-based techniques followed by quantization and entropy coding. The key idea is that transforms de-correlate the signal and compact the energy of a block into a few coefficients, which still represent the signal rather accurately after quantization and de-quantization. Nevertheless, this quantization/de-quantization process needs to be carefully designed in order to have the best possible subjective and objective quality.

In the encoder of H.264/AVC reference software, the scalar dead-zone quantization is adopted. In order to improve further the performance, other two adaptive quantization techniques are also introduced, which are both based on how to adjust the size of dead-zone and control the rounding behavior. In this tutorial, we will first introduce the principle of H.264/AVC normal quantization scheme, then discuss the adaptive rounding method which select adaptive[......]

Read More…

Permanent Link: Quantization Techniques in JM/KTA – Part 1