Keywords

1 Introduction

More and more popular video applications and the increasing video resolution have brought the huge bandwidth consumption and the high storage cost. The existing video compression standard H.264/AVC has been unable to satisfy the high-definition and ultra-high-definition video. Joint Collaborative Team on Video Coding (JCT-VC) [1], established by ITU-T/VCEG and ISO-IEC/MPEG, released the video coding standard HEVC (High Efficiency Video Coding), and the standard is still evolving.

Compared to H.264/AVC, under the similar video quality, HEVC can save 50% of the video stream [2]. However, different from the fixed macroblock of H.264, HEVC uses the quadtree technique to realize adaptive partitioning of CTU which will traverse all possible combinations to determine the best partitioning, greatly increasing the computational complexity of video coding.

HEVC coding techniques can be divided into intra prediction and inter prediction. The compression rate of inter prediction several times that of intra prediction, the main reason of which lies in that inter prediction requires finding the most matching block of PU (Prediction Unit) in the reference frame. According to the relevant statistics, inter prediction accounts for more than 60% of the overall coding time. Therefore, the acceleration of inter prediction is of great significance.

In this paper, a fast CU decision algorithm for inter prediction based on residual analysis is proposed. The residual is analyzed by mean and dispersion, and its optimal RQT depth is used innovatively to measure the residual dispersion. At first we statistically analyze the relationship between mean and dispersion and CU partition. Then the determination threshold of the current frame is predicted based on the distribution of CU partition of the threshold image. At last unnecessary CU calculations are terminated by threshold comparison. Experiments show that the proposed algorithm can significantly reduce the computational complexity of inter prediction without losing the video quality and compression ratio.

The remainder of this paper is organized as follows. Section 2 gives a brief introduction of background knowledge. Section 3 describes the proposed algorithm in detail. Experimental results are shown in Sect. 4. At last Sect. 5 concludes this paper.

2 Background Knowledge

2.1 Brief Introduction of Inter Coding in HEVC

Inter coding can eliminate the redundancy in time domain to achieve the purpose of video compression. For inter coding, current block would find its best matching block by motion estimation in the reference frame as the prediction block. The difference between the matching block and the current block is called the residual.

By using the quadtree technique, the CU with depth d can be divided into four sub-CUs in depth d + 1. And decision-making for partition is determined by the rate distortion of the CU and the sub-CUs. The definition of RD (Rate Distortion) can be seen in Formula (1), where D represents the distortion in the current prediction mode and R is the number of bits required to encode the prediction mode. Figure 1(a) is an example of CTU partition, in which the white indicates that CU continues to be divided and the black stands for stopping CU partition.

Fig. 1.
figure 1

(a) One example of CTU partition (b) PU partition modes

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In HEVC the CU will be further divided into PUs which are basic units of inter prediction. There are eight types of PU partition, containing four types of symmetric partition and four types of asymmetric partition [3], as shown in Fig. 1(b). HEVC will test all the PU partition modes for CU, and ultimately select the optimal PU partition with the minimum RD cost.

$$ {\text{RDCost}} = {\text{D}} +\uplambda{\text{R}} $$
(1)

TU (Transform Unit) is the basic unit for transform and quantization. Similar to CU partition, TU partition can be flexibly fulfilled by quadtree technique in a recursive manner [4].

2.2 Related Work

HEVC inter coding can be accelerated in three aspects: CU level, PU level and TU level.

In the CU level, accelerating can be realized by skipping unnecessary CU partition tests or terminating CU partition earlier. The paper [5] first got the depth range of CU partition based on visual saliency map detection, and then CU partition was determined by the comparison of coding bits and the specific threshold. A RD cost based accelerative algorithm was proposed by [6], where the decision of CU partition was made by comparing RD cost of the current CU with the specific threshold. Paper [7] proposed a fast algorithm determining the depth range of CU partition, which made a comprehensive utilization of zero CU detection, standard deviation of statistic spatiotemporal depth information and edge gradient of CTU. Paper [8] introduced an accelerating algorithm of inter encoding aiming at surveillance videos. Inter-frame difference was utilized to segment out moving objects encoding in CU of small size from background encoding in CU of large size. Wu et al. presented a fast inter encoding algorithm aiming at H.264 in [9] which determined the size of the coding block according to spatial homogeneity based on edge information and temporal stationary characteristics judged by MB differencing. The paper [10] constructed a feature vector for each CU consisting of RD cost and motion category, according to which, the decision of CU partition was determined.

The acceleration algorithm in TU level can predict TU partition by some means. The paper [11] could adaptively determine the optimal RQT depth according to spatial neighboring blocks and the co-located block at the previously coded frame. The experimental results showed that the improved algorithm could save 60% to 80% of encoding time. A fast decision algorithm in TU level based on Bayesian model was introduced in [12] which took the depths of current TU, upper TU, left TU and co-located TU as reference features. TU partition could be terminated earlier in [13] by taking advantage of the feature of all coefficients of TU being zero. The paper [14] created three decision trees for CU, PU and TU respectively obtained through data mining techniques. Decision trees for CU and TU decided whether to terminate the partition of CU and TU and the decision tree of PU determined whether to test the rest of PU partition modes.

In paper [15], an improved algorithm in PU level for HEVC inter prediction was proposed whose core idea was to reduce motion estimation calls. The CU was divided into four blocks of the same size, and then the PU partition was determined by comparing the motion vectors of the four PU blocks. Gao et al. in [16] calculated a quadtree probability model based on a quantization parameter and a group of pictures and then a new quadtree was constructed by skipping low probability tree nodes.

Algorithms above have achieved a good acceleration effect with minimal impact on video quality and the increment of bitrate on average is also in a reasonable range. However, the increment of bitrate between different videos has a big difference in this paper, we propose a fast CU decision algorithm based on residual analysis in which no extra calculation is required and intermediate results are fully utilized. CU splitting decision is fulfilled by thresholds comparing and the thresholds can adaptively be adjusted as the video content changes. Experimental results prove that the improved method can significantly reduce encoding time.

3 Fast CU Decision Algorithm Based on Residual Analysis

3.1 Residual Analysis

Generally speaking, for the same image region, compared to encoding in large-size CU, small-size CU can achieve better matching effect with smaller prediction error but larger coding bits. If the matching performance of current CU in 2N × 2N PU mode is in good condition, coding bits become larger and prediction error reduces slightly after CU is divided, leading to larger RD cost. So current CU is not appropriate to be divided into smaller CUs. On the contrary, if the matching performance is too bad, current CU has significant reduction of prediction error after being divided, bringing smaller RD cost. Further CU partition should be performed.

The residual is the result after motion compensation which directly reflects the matching performance of the current block. Therefore the decision of CU partition can be made by analyzing the residual.

In this paper, dispersion and mean of residuals are utilized to analyze residuals. Dispersion refers to the degree of difference between values in residuals. And mean is the average of all data items in residuals.

3.2 How to Measure the Dispersion

There are two commonly used methods for measuring the dispersion:

  • Standard deviation: Calculate standard deviation of data items in the residual.

  • Edge detection: Edge detection such as Sobel operator or Canny operator is operated on the residual block to extract edges. And then calculate the number of nonzero values in the edge map.

Both of the two methods require additional computation, and they also need to set thresholds between uniform and non-uniform artificially. Here we make use of the optimal RQT depth of current CU to measure dispersion of residuals creatively.

After inter prediction, the residual block is imputed into the transform module for further compression. In the transform module, DCT (Discrete Cosine Transform) is performed on the residual block, which can remove the correlation between data items in the residual block.

If the residual block is in uniform distribution, DCT coefficients that have been quantized remain a small amount of larger value with most of them being zero, resulting in lower coding bits and smaller RD cost. Then current TU will not be divided into smaller TUs, as shown in Fig. 2(a). On the other hand, if the residual has rich texture, there are many larger values and a small amount of smaller values, leading to more coding bits and larger RD cost. Therefore current TU can get more zero DCT coefficients by further TU partition, as shown in Fig. 2(b). According to the local variation characteristics of the predicted residuals, TU can adaptively select the optimal TU partition.

Fig. 2.
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(a) TU partition of residual block in uniform distribution (b) TU partition of residual block in rich texture

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Based on the above analysis, we can see that the optimal RQT depth has a close relationship with dispersion. The deeper the optimal RQT depth is, the greater dispersion is. Thus the optimal RQT depth can be used to measure dispersion directly. The maximum depth of TU can be set in the configuration file, default as three. In this paper, the maximum partition depth of TU adopts the default value.

3.3 The Relationship Between CU Partition and Dispersion and Mean

As described in Sect. 3.2, dispersion is measured using optimal RQT depth denoted as opRdepth which has three cases: 0, 1 and 2. The optimal RQT depth doesn’t require additional computation which is the intermediate result. In order to simplify the calculation, mean is replaced by average value of ssd (short for avgdis) produced by HEVC, which is the sum of the squared error of original pixels and reconstructed pixels.

$$ D_{split} = f\left( {{\text{opRdepth}},{\text{avgdis}},{\text{CUsize}}} \right) $$
(2)

We can get opRdepth and avgdis of current CU after inter encoding in 2N × 2N PU mode is fulfilled. Then the splitting decision \( D_{split} \) can be represented as a function of opRdepth, avgdis and CU size.

In order to determine the mapping relationship f, we make a mass of statistics on opRdepth, avgdis and its corresponding CU splitting decision. Each video has 50 frames to participate in statistics. For example, detailed statistical results of BasketballDrill can be seen in Fig. 3, where the horizontal axis stands for the number of CU and the vertical axis is avgdis. The green dots mean the current CU need to be divided further while the red dots mean not. We can see that there is a boundary between red dots and green dots. According to statistical results of numerous videos, we propose a fast CU decision algorithm denoted as CUDecision which can be seen in Table 1. \( TH\_bootom_{ij} \) and \( TH\_up_{ij} \) is the threshold for CU splitting decision, where i respresents the depth of current CU and j is opRdepth.

Fig. 3.
figure 3

BasketballDrill (a) CUsize = 64 opRdepth = 0 (b) CUsize = 64 opRdepth = 2 (c) CUsize = 32 opRdepth = 0 (d) CUsize = 32 opRdepth = 2 (e) CUsize = 16 opRdepth = 0 (f) CUsize = 16 opRdepth = 2 (Color figure online)

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Table 1. Detailed process of CUDecision
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3.4 Determination of Thresholds

Due to the similarity of image content, CU partition between adjacent images has a strong correlation. Thus TH_up and TH_bottom in current frame can be predicted from previous frames.

A data structure denoted as drawer is defined for describing CU partition. It contains two variables, red and green, which are arrays with a size of 60. \( red_{i} \) is the i-th element of red, representing the number of not divided CUs with avgdis in the range of 5i to 5(i + 1). The meaning of green is similar to that of red.

Given a drawer, TH_up and TH_bottom can be obtained by threshold calculating methods CalTHup and CalTHbottom respectively. The detailed process of CalTHbottom is listed in Table 2 and CalTHup has a flow similar to CalTHbottom.

Table 2. Detailed process of CalTHbottom
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The image that serves to predict TH_up and TH_bottom is called THimage. PredictSet is a set of THimages defined as follows where Pi is the POC (Picture Order Count) of corresponding THimage. The size of PredictSet equals to GOP (Group Of Pictures) size which is set to four in our experiments.

$$ {\text{PredictSet}} = \left\{ {P_{i } | {\text{i}} = 0,1,2,3} \right\} $$
(3)

Updating PredictSet.

RD1 in Eq. (4) is RD cost of current CU which is not divided and RD2 in Eq. (5) is the corresponding RD cost of divided CU. With Eq. (4) and Eqs. (5) and (6) is deduced. What’s more, \( \uplambda \) is positively correlated with the QP (Quantization Parameter), as shown in Eq. (7) where \( \upalpha \) and \( W_{k} \) are weighting factors related to different configurations. Accordingly we can conclude that QPs will make a difference on distribution of CU partition. The HEVC encoder sets a series of QP values for each frame in a GOP, and each GOP has the same QP configuration. Therefore, THimages in PredictSet should contain all QP values in one GOP. In our experiments, QP values are set to be 35, 34, 35 and 33 in one GOP. A PredictSet updating algorithm named UpdatePed is proposed to initialize and update PredictSet, as shown in Table 3.

Table 3. Detailed process of UpdatePed
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$$ {\text{RD}}1 = {\text{D}}1 +\uplambda{\text{R}}1 $$
(4)
$$ {\text{RD}}2 = {\text{D}}2 +\uplambda{\text{R}}2 $$
(5)
$$ \uplambda > = \frac{D2 - D1}{R1 - R2} $$
(6)
$$ \uplambda =\upalpha \cdot W_{k} \cdot 2^{{\frac{{\left( {QP - 12} \right)}}{3}}} $$
(7)

Threshold Calculation.

Each THimage \( P_{i} \left( {i = 0,1,2,3} \right) \) in PredictSet has its corresponding drawer set \( D_{i} \) defined in Eq. (8) where \( d_{ijk} \) is the drawer of CUs in depth j with opRdepth being k. Dsum is the sum of \( D_{i} \), defined in Eq. (9). \( TH\_up_{j0} \) and \( TH\_up_{j2} \) can be obtained by inputting \( dsum_{j0} \,{\text{and}}\, \) \( dsum_{j2} \) into CalTHup respectively.

$$ D_{i} = \{ d_{ijk} |j = 0,1,2;k = 0,2\} $$
(8)
$$ {\text{Dsum}} = \{ (dsum_{jk} = \sum\nolimits_{i = 0}^{3} {d_{ijk} } ) |{\text{j}} = 0,1,2;{\text{k}} = 0,2\} $$
(9)

\( TH\_up_{j0} \,{\text{and}}\, TH\_up_{j2} \) are predicted without considering the influence of QPs. Differing from prediction of TH_up, the calculation of TH_bottom takes QPs into consideration and each QP value has its corresponding prediction threshold. \( TH\_GOPbottom_{ijk} \) and \( TH\_QPbottom_{ijk} \) are defined for i-th QP value where j is the depth of CUs and k is opRdepth. In fact, we just need to calculate \( TH\_GOPbottom_{ij0} \) and \( TH\_OPbottom_{ij0} \).

Inputting \( dsum_{j0} \) into CalTHbottom can get \( TH\_bottom_{j0} \) and Inputting \( d_{ij0} \) can output \( TH\_QPbottom_{ij0} \). \( TH\_GOPbottom_{ijk} \) is the optimal threshold selected from them. In most cases, \( TH\_bottom_{j0} \) is an appropriate prediction threshold. However if \( TH\_QPbottom_{ij0} \) is greater more than \( TH\_bottom_{j0} \), maybe \( TH\_QPbottom_{ij0} \) is more accurate (see Fig. 4.), which is caused by QP difference. According to derivation process of CU partition in last section, we can see the larger the QP value is, the greater the threshold is. Similarly the larger the QP value is, the more not divided TUs are. Therefore the QP value is measured by the number of CUs with opRdepth being zero denoted as \( CUnum_{i} \). Thus the optimal threshold can be chosen through \( CUnum_{i} \).

Fig. 4.
figure 4

CU partition of BQTerrace in depth one

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Based on the above analysis, the method of threshold calculation denoted as CalTHpred describes the flow for calculating \( TH\_GOPbottom_{ijk} \), shown in Table 4.

Table 4. Detailed process of CalTHpred
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4 Experiments and Results

The proposed algorithm is implemented on HM13.0 and the coding performance can be evaluated by \( \Delta {\text{PSNR}} \) (Peak Signal to Noise Ratio), \( \Delta {\text{BR}} \) (Bitrate), and \( \Delta {\text{ET}} \) (Encoding Time) defined in (10) to (12) under lowdelay P configuration. PSNR is calculated by Eq. (13). In our experiments, 50 frames are tested for each video.

$$ \Delta {\text{PSNR}} = \frac{{PSNR_{proposed} - PSNR_{HM} }}{{PSNR_{HM} }} $$
(10)
$$ \Delta {\text{BR}} = \frac{{BR_{proposed} - BR_{HM} }}{{BR_{HM} }} $$
(11)
$$ \Delta {\text{ET}} = \frac{{ET_{proposed} - ET_{HM} }}{{ET_{HM} }} $$
(12)
$$ {\text{PSNR}} = \left( {{\text{PSNRY}} \times 4 + {\text{PSNRU}} + {\text{PSNRV}}} \right)/6 $$
(13)

Table 5 shows the acceleration effect of the proposed algorithm. Through careful observation and analysis, we can get the following points.

Table 5. Results of the proposed algorithm compared to HM13.0
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  1. 1.

    The improved algorithm could save about 56% of encoding time on average, with 0.2034% increase of bitrate and 0.0423 reduction in PSNR.

  2. 2.

    If the video content changes slowly such as Flowervase, Mobisode2 and so on, the proposed method can reduce execution time by about 70% with a small change in bitrate and PSNR. In some cases, the bitrate is even reduced.

  3. 3.

    If the video content changes quickly such as BasketballDrill, Tennis and so on, the proposed algorithm can reduce execution time by 36%–50% and the increment of bitrate is a little higher than that of small changing videos.

  4. 4.

    The PSNR of SlideShow decreases by 0.1164% which is greatest in test sequences and the increment of bitrate reaches 1.4575%, a little higher than that of other videos.

  5. 5.

    The increment of bitrate is limited within 1.11%. This proves that the proposed algorithm can guarantee compression ratio when it realizes accelerating.

We can find that the video with small changes can achieve more reduction of computational complexity. That’s because CUs in the small changing video can get good matching performance and then terminates CU partition earlier. For the video with fast content change, prediction of TH_up and TH_bottom is less accurate, leading to more bitrate increasing.

SlideShow has much more sudden changes and sometimes image content is completely different between adjacent frames. Under this circumstance, thresholds are not accurate, contributing to slightly larger image distortion and more bitrate increasing. In fact, due to big difference between adjacent frames, inter coding is not suitable for SlideShow to realize compression.

5 Conclusion

For one CTU, HEVC will traverse all possible divisions with the quadtree technique to make the coding efficiency optimized. However, the exhaustive search process greatly aggravates the computational burden. A fast CU decision algorithm based on residual analysis is proposed to predict whether current CU will be divided and then skip redundant computation process. The residual is analyzed by mean and dispersion, and then the measure of dispersion is fulfilled by the optimal RQT depth. When the optimal RQT depth equals to 0 or 2, the decision of CU partition will be determined by comparing avgdis with the corresponding threshold. What’s more, the proposed algorithm could realize adaptive changes of thresholds for different videos.

Experimental results show that the proposed algorithm can achieve good performance on speeding up calculation without affecting compression ratio and the quality of reconstructed videos.