A) Color video representations

The inherent color video representation of today's capture and display devices is mostly based on the R′G′B′ color space. The prime symbol (′) is the widely used notation for gamma corrected representation. Gamma correction is always assumed in this paper, and hence, a specific notation is omitted from now on. As opposed to the RGB representation, the separation between luma and chroma provides the opportunity of chroma subsampling. Chroma subsampling keeps the impact on the subjective quality low, while reducing the overall bit-rate significantly. With the support of 4:4:4 chroma formats, in HEVC Version 2, also the direct coding of RGB content got available. As the luma component in HEVC has a preferential treatment compared with chroma components, it is advisable to code the green component (G) as the luma component. This is motivated by the highest contribution to the intensity perception in the HVS among the RGB components and referred to as GBR coding in the following.

1) YC_bC_r

In video compression, the YC_bC_r color space is widely used for video representation. Here, Y refers to the luma component, while C _b and C _r are the chroma components, respectively. This color representation was originally found by principal component analysis (PCA) performed on a set of video signals represented in YIQ color space (i.e., the color space of the NTSC television standard), while trying to approximate the intensity perception of the HVS by the luma component Y [Reference Malvar, Sullivan and Srinivasan7]. Several definitions for the YC_bC_r transform can be found, one is shown in equation (1) and its inverse in (2) [8].

(1) $$\left(\matrix {Y \cr C_{b} \cr C_{r}}\right)= \left(\matrix{0.7152 & 0.0722 & 0.2126 \cr -0.3854 & 0.5 & - 0.1146 \cr - 0.4542 & - 0.0458 & 0.5 }\right) \left(\matrix{ G \cr B \cr R }\right),$$

(2) $$\left( \matrix{G \cr B \cr R } \right) = \left( \matrix{1 & -0.1873 & - 0.4681 \cr 1 & 1.856 & 0 \cr 1 & 0 & 1.575 } \right) \left( \matrix{Y \cr C_b \cr C_r } \right).$$

It can be observed, that the luma component consists of a weighted amount of each RGB component, where the green component (G) contributes with the highest scaling factor. The chroma components on the other hand, are represented relatively to the luma component. Transforming video signals from RGB color space to YC_bC_r reduces the statistical dependencies among the components significantly. This is particularly the case for natural scene content.

The floating point arithmetic involved in the forward and backward transformations of YC_bC_r, is a weakness of this representation. This gets especially relevant, when it comes to high bit-rate coding or even lossless coding. In such cases, the rounding error introduced by transforming becomes significant, and hence, YC_bC_r is not feasible for these applications.

2) YC_oC_g

Motivated by the question, whether the YC_bC_r color space is the best color space for compression, considering that it was derived decades ago and modern high-resolution cameras producing sharper images nowadays, the color space YC_oC_g was developed and presented in [Reference Malvar, Sullivan and Srinivasan7]. This transform was obtained by approximating a Karhunen–Loève–Transform (KLT) estimated on the Kodak image database. Note, also in this transform the green channel contributes most to the luma channel. The forward transform can be described as:

(3) $$\left( \matrix{ Y \cr C_{o} \cr C_{g} } \right) = \left( \matrix{ {1/2} & {1/4} & {1/4} \cr 0 & - {1/2} & {1/2} \cr {1/2} & - {1/4} & - {1/4} } \right) \left( \matrix{ G \cr B \cr R } \right).$$

One advantage of this transform is its simplicity in terms of implementation considerations. Only additions and shift operations are needed. A lossless version of YC_oC_g can be realized by utilizing the lifting technique. This version (YC_oC_g−R) can be exactly inverted in integer arithmetic as described by the following operations:

(4) $$\eqalign{ C_{o} &= R - B, \cr t &= B + \lpar C_{o} \gg 1 \rpar , \cr C_{g} &= G - t, \cr Y &= t + \lpar C_{g} \gg 1 \rpar .}$$

When representing a video in YC_oC_g−R, the dynamic range of both chroma components (C _o ,C _g ) is increased by one bit, compared to the original transformation in (3).

3) GR_bR_r

An even simpler transformation can be obtained by taking the G component as the luma component itself, and represent the remaining components as difference signals to the G component. This transform is also reversible in integer arithmetic and was described in [Reference Marpe, Kirchhoffer, George, Kauff and Wiegand9], where it is referred GR_bR_r transform. The forward GR_bR_r transform can be expressed as:

(5) $$\left( \matrix{ G \cr R_{b} \cr R_{r} } \right) = \left( \matrix{ 1 & 0 & 0 \cr {-1} & 1 & 0 \cr {-1} & 0 & 1 } \right) \left( \matrix{ G \cr B \cr R } \right).$$

B) Adaptive CCP

Having the extra processing steps of color transformations before encoding, and after decoding, is not feasible for all applications (e.g., coding of SC). In this cases, additional methods for exploiting the cross-component correlation within the compression procedure are indispensable. On the other hand, including the action of decorrelation inside the compression process, can lead to an improved coding-efficiency in general, as it rises the opportunity of adapting to local image statistics.

This adaptivity can be achieved by choosing appropriate color transformations for different color characteristics of the video signal. They can be applied at different levels of the encoding/decoding process. In [Reference Marpe, Kirchhoffer, George, Kauff and Wiegand9], the color representation of the residual signal is independently chosen for each macro block. The specified alternatives to the input color space are YC_oC_g and GR_bR_r. Instead of defining a set of available transforms, one can also make use of a prediction model. The transformation defined in equation (5) can be seen as a linear prediction scheme. Here, the component G acts as the predictor for the B and R components, respectively. Adaptivity can be obtained by introducing prediction weights, which can be adjusted as desired. This can be expressed as:

(6) $$\left( \matrix{ G \cr R_{b} \cr R_{r} } \right) = \left( \matrix{ 1 & 0 & 0 \cr - \alpha_{1} & 1 & 0 \cr - \alpha_{2} & 0 & 1 } \right) \left( \matrix{ G \cr B \cr R } \right).$$

The prediction parameters α₁ and α₂ are needed for reconstruction and may be derived backward-adaptively [Reference Zhang, Gisquet, Francois, Zou and Au10], or signaled within the bitstream.

CCP utilizes a prediction model as described in equation (7), which is forward-driven. A detailed description of CCP is given in Section III.

This model can be extended by also allowing the first chroma component to act as predictor for the second chroma component. One of such models is expressed in equation (7) for the GBR domain. Here, an additional parameter ρ∈{0, 1} allows to switch between both predictors. One of the extensions of CCP discussed in this paper, follows this scheme and is described in Section IV.

(7) $$\left( \matrix{ G \cr R_{b} \cr R_{r} } \right) = \left( \matrix{ 1 & 0 & 0\cr - \alpha_{1} & 1 & 0\cr -(1-\rho)\alpha_2 & -\rho\alpha_{2} & 1 } \right) \left( \matrix{ G \cr B \cr R } \right).$$

A) Coding scheme

The CCP scheme operates in the residual domain. Particularly, it is applied to chroma residual samples, obtained, after inter or intra prediction has been performed. Transform coding of prediction residuals in HEVC comprise a partitioning into TBs according to a quadtree structure, which is signaled within the bit stream and denoted as residual quadtree (RQT) [Reference Nguyen11]. This partitioning allows an adaptation to local statistics of the residual signals. Residual samples belonging to the same TB are jointly transform coded. This efficiently helps exploiting the spatial correlation within the same color component. CCP, on the other hand, addresses the correlation between chroma and luma residual samples at the same spatial location. Following the description of Section II-B, a chroma residual sample is predicted by a weighted amount of the spatially aligned luma sample. CCP operates block adaptive at the TB level, namely, chroma residual samples of the same TB share the prediction weight α. This can be expressed as:

(8) $${\hat{\bf{r}}}^{(Ci)} = \alpha_{i} \cdot {\tilde{\bf{r}}}^{(L)},$$

where ${\tilde{\bf{r}}}^{(L)}$ denotes the reconstructed residual samples of one luma TB and ${\hat{\bf{r}}}^{(Ci)} $ denotes the obtained prediction for one of the chroma TBs, aligned with ${\tilde{\bf{r}}}^{(L)}$ . The index i∈{1, 2} emphasizes that each of the two chroma components are predicted individually, and ${\tilde{\bf{r}}}$ indicates that the samples might be degraded due to quantization. It should be noted, that ${\tilde{\bf{r}}}^{(L)}$ can be equal to $\bf{0}$ . This occurs when the luma samples could be perfectly predicted by intra/inter prediction or when signaling of ${\tilde{\bf{r}}}^{(L)}$ is not reasonable in rate-distortion (RD) sense. In such cases, CCP is not meaningful. If the predictor signal is available, on the other hand, the weighting parameters for both corresponding chroma TBs are signaled within the bitstream. CCP can be omitted for each chroma TB by setting its parameter α to 0.

When CCP is applied to a chroma TB, the difference between its residual samples $\bf{r}^{(C)}$ and their predicted samples ${\hat{\bf{r}}}^{(C)}$ is transform coded instead of $\bf{r}^{(C)}$ :

(9) $$\Delta \bf{r}^{(C)} = \bf{r}^{(C)} - \alpha \cdot {\tilde{\bf{r}}}^{(L)}.$$

The following reconstruction rule follows for the decoder:

(10) $${\tilde{\bf{r}} }^{(C)} = \Delta {\tilde{\bf{r}}}^{(C)} + \alpha \cdot {\tilde{\bf{r}}}^{(L)}.$$

In order to keep the overhead for signaling α low, the prediction weights are limited to a fixed set:

(11) $$\alpha \in \bigg\{ 0, \pm{1\over 8}, \pm{1\over 4}, \pm{1\over 2}, \pm 1 \bigg\}.$$

This set of weights allows a simple implementation, which can be expressed for each sample of a TB as follows:

(12) $$\tilde{r}_{c} = \Delta \tilde{r}_{c} + \left\lfloor{\alpha' \cdot \tilde{r}_{l}\over{8}}\right\rfloor$$

(13) $$= \Delta \tilde{r}_{c} + \lpar \alpha' \cdot \tilde{r}_{l} \rpar \gg 3.$$

Hence, only one addition and one shift operation are needed per sample and the value of $\alpha' \in \{ 0, \pm1, \pm2, \pm4, \pm8 \}$ is binarized and entropy coded. Particularly, the sign and absolute value of α′ are coded separately, where the truncated unary binarization scheme of CABAC [Reference Marpe, Schwarz and Wiegand12] is used for the index to the absolute value. The sign of α′ needs to be coded only, if $|\alpha'| \neq 0$ . As the statistics of both chroma components may differ significantly, a separate set of context models is introduced for each chroma component. Furthermore, having separate context models for signaling the sign and for each of the four unary bins, a total amount of ten context models is defined for the CCP scheme.

B) Encoder considerations

During the encoding process, the prediction weight has to be chosen for each chroma TB. A straight forward and optimal method (in sense of RD costs), is to test each allowed weight in (11) and to take that α, that leads to the lowest RD cost. However, this approach is often not practical in terms of encoder run times. When the residual samples are assumed to be realizations of a stationary random process, with known second-order statistics, an analytical solution can be found by the least-mean-square approach for linear models. The α _M with minimum mean-square prediction error is then given by:

(14) $$\alpha_{M} = {\hbox{cov}(\tilde{r}_{l}, {r}_{c}) \over{ \hbox{var}(\tilde{r}_{l})}}.$$

The HEVC reference software encoder (HM 16.2 [13]), for example, utilizes equation (14) by taking sample statistics from aligned chroma and luma TBs, respectively. The obtained $\alpha_{\hbox{s}}$ is then quantized to $\alpha_{\hbox{s}}'$ following equation (15) and look-up-table (LUT) (16):

(15) $$\alpha_{\hbox{s}}' = \hbox{sign}(\alpha_{s}) \cdot \hbox{LUT}_\alpha(|\alpha_{s}|),$$

(16) $$\hbox{LUT}_\alpha(x) =\left\{\matrix{0 & x < {1/ 16}\hfill \cr 1 & {x \in [{1/ 16}, {3/ 16})} \hfill \cr 2 & {x \in [{3/ 16}, {3/ 8})} \hfill \cr 4 & {x \in [{3/ 8}, {3/ 4})}\hfill \cr 8 & {x \geq {3/ 4}}.\hfill}\right.$$

The RD performance of CCP with $\alpha'=\alpha_{\hbox{s}}'$ is then compared with the performance when omitting CCP for the TB (i.e., α′=0), and α′ is set accordingly.

From equation (9) it can be seen that $\Delta\bf{r}^{(C)}$ has an increased dynamic range of 1 bit compared with $\bf{r}^{(C)}$ . Hence, the internal bit-depth of the chroma component representation should be increased by 1 bit, in order to prevent an excessive quantization of the prediction differences $\Delta\bf{r}^{(C)}$ .

A) Additional predictor

As described in Section II it might be valuable to also exploit the correlation among the first and second chroma components. Because the first chroma component is reconstructed first, it can serve as a predictor for the second chroma component. In this section, an extension to CCP is described in which the predictor for the second chroma component can be chosen adaptively on the TB level. An additional flag ρ∈{0, 1} is introduced for each TB of the second chroma component. Here, a value of ρ=1 indicates that the reconstructed samples of the first component, weighted by α₂, are used for prediction. The reconstructed luma residual samples are used otherwise:

(17) $$\hat{\bf{r}}^{(C2)} = \alpha_{2} \cdot {\tilde{\bf{r}}}^{(L)},\;\quad \hbox{if}\, \rho = 0, $$

(18) $$\hat{\bf{r}}^{(C2)} = \alpha_{2} \cdot {\tilde{\bf{r}}}^{(C1)},\quad \hbox{if}\, \rho = 1.$$

These predictions are only meaningful, when the reconstructed TB of the predictor component contains significant residuals. Hence, only when both conditions, ${\tilde{\bf{r}}}^{(L)} \neq \bf{0}$ and ${\tilde{\bf{r}}}^{(C1)} \neq \bf{0}$ hold, the value of ρ has to be signaled. Its value can be derived otherwise. It should be noted, that the first chroma component can also act as a predictor, when it got predicted by the luma component itself, but no prediction difference was signaled (i.e., CBF^(C1)=0 and $\alpha_{1} \neq 0$ ).

Table 1 summarizes the different predictors ${\hat{\bf{r}}}^{(C2)}$ for the second chroma component residual.

Table 1. Condition for ρ and choice of the predictor.

The additional syntax element ρ is signaled using CABAC entropy coding. The prediction weight α₂ is binarized following the same scheme as in CCP. However, a distinct set of context models is used when the first chroma component is used as the predictor (i.e., ρ=1).

B) Predicting the model parameter α

As seen in Section III-B, the optimal prediction weight α _M (in sense of mean square error), is described by equation (14) and can be estimated on the encoder side by the residual sample-statistics of the current TB. If a local stationarity can be assumed, an estimator $\hat{\alpha}$ obtained from sample-statistics of already decoded neighboring blocks can also be reasonable and serve as a predictor for the CCP model parameter α of succeeding TBs.

Following this approach, the second extension to CCP presented in this paper defines the following prediction scheme: For each decoded TB one separate weight $\hat{\alpha_{i}}$ is estimated from its quantized luma $\tilde{\bf{r}}^{(L)}$ and chroma $\tilde{\bf{r}}^{(C)}$ residual samples, which then serves as a predictor for neighboring TBs. In the case were no residual was signaled, the corresponding $\hat{\alpha}_{i}$ is set to zero. Now, let $\hat{\alpha}_{L}$ denote the estimated prediction weight of the left neighboring TB, and $\hat{\alpha}_{T}$ the corresponding weight of the TB above. The CCP model parameter used for the current TB is then given by the arithmetic mean of both predictors, plus some correction term $\Delta\alpha$ :

(19) $$\alpha = \hbox{mean}( \hat{\alpha}_{L} , \hat{\alpha}_{T} ) + \Delta\alpha.$$

Here, $\Delta\alpha$ allows a correction of the predicted parameter and is signaled for each TB where CCP is applicable. More precisely, a flag is signaled whether a correction term is present, the correction value itself is coded utilizing a unary binarization. It should be noted, that in this extension the resulting CCP prediction weight α is no longer restricted to the set defined in (11). Both, the prediction and the correction factor, are uniformly quantized with a step size of 1/8. This not only allows a finer CCP compared with the base variant of CCP, but also results in an increased signaling cost when the prediction $\hat{\alpha}$ from neighboring blocks is poor.

A) Experimental setup

All schemes are implemented on top of HEVC RExt reference software HM-10.1 RExt 3 [14]. Whenever CCP or one of its extensions is enabled, the internal chroma bitdepth is increased by 1. In the CCP variants where the model parameters are signaled directly, the encoder is configured to select α by testing all allowed values. In the case of predicting α from its neighborhood, the correction term $\Delta\alpha$ is estimated as described in Section III-B. The performed simulations are based on the common test conditions (CTC) [Reference Flynn, Sharman and Rosewarne15], defined during the standardization of HEVC RExt. The set of test sequences include camera captured (CC) sequences and computer rendered sequences, referred to as SC material. The evaluation is focused on random access (RA) configuration. However, in the application of SC coding a low latency is of great interest. Hence, SC results are also presented for low-delay (LD) configuration. Only sequences with 4:4:4 chroma format, and those included in both, RGB and YC_bC_r test sets, are considered. For simplicity reasons, when coded in YC_bC_r domain, the reconstructed video is not converted back to RGB domain. Instead, the distortion is measured in the coding domain and its contribution to the components of RGB is estimated mathematically. In particular, the distortion of different components is assumed to be uncorrelated, then taking the square of each weight of the inverse transform, equation (2), leads to the following estimation:

$$\left(\matrix{ \hbox{MSE}_G \cr \hbox{MSE}_B \cr \hbox{MSE}_R } \right) = \left( \matrix{ 1 & 0.351 & 0.2191 \cr 1 & 3.443 & 0 \cr 1 & 0 & 2.48 } \right) \left( \matrix{ \hbox{MSE}_{Y}\cr \hbox{MSE}_{Cb} \cr \hbox{MSE}_{Cr} } \right).$$

It should be noted, that the rounding error due to transformation before compression cannot be measured in this setup. Hence, only main tier configurations (i.e., quantization parameter QP ∈{22, 27, 32, 37}) are considered. At those RD operation points the rounding errors are assumed to be negligible.

B) BD-rate performance

The bit-rate saving for each test condition is given in terms of Bjøntegaard delta (BD) rate [Reference Bjøntegaard16]. The obtained results, averaged over sequences of each class, are listed in Tables 2–4. The first three rows show the obtained bit-rate saving when coding in GBR representation, while the results in the bottom rows are obtained by coding the sequences in YC_bC_r representation. Here, the additional predictor extension is denoted as CCP-AP, and the extension for predicting the model parameter α, as CCP-PP. The + sign indicates that the coding tool is applied in addition to the color transformation to YC_bC_r domain. According to the observations of bit-rate distributions among the color components made in [Reference Nguyen, Khairat and Marpe17], the $\overline{\hbox{G}\hbox{B}\hbox{R}}$ -BD rate is calculated based on an weighted average over the PSNRs of each component:

Table 2. BD-rate of CC sequences (RA).

Table 3. BD-rate of SC sequences (RA).

Table 4. BD-rate of SC sequences (LD).

(20) $$\overline{\hbox{GBR}}_{\hbox{PSNR}}={4\cdot\hbox{G}_{\hbox{PSNR}}+\hbox{B}_{\hbox{PSNR}}+\hbox{R}_{\hbox{PSNR}}\over 6}.$$

The following can be observed for the set of CC sequences: The average bit-rate saving due to coding after a transformation to YC_bC_r representation amounts to 50% in terms of the $\overline{\hbox{G}\hbox{B}\hbox{R}}$ -BD rate. A similar, yet smaller, coding efficiency can be achieved with the CCP scheme when coding in GBR representation directly. Moreover, when coding in YC_bC_r domain the remaining cross-component redundancy can still be reduced by CCP, and hence, an additional coding gain is achieved. Both of the described extensions generate a further minor bit-rate reduction when applied in the YC_bC_r domain, however, no extra coding gain can be achieved in the GBR representation, when compared with the unmodified version of CCP.

For the SC sequences the results are given for RA (Table 3) and LD (Table 4) configuration, respectively. In both cases, a smaller bit-rate saving, of about 33%, is obtained due to the coding in YC_bC_r domain. However, the remaining dependencies can be reduced by CCP and a further BD rate saving of 4% is attained. In the RA case, the additional predictor gives a further saving of almost 1%, while in LD configuration the improvement is only about 0.2%. Predicting α spatially in YC_bC_r domain gives the highest coding-gain among the tested conditions. Here, a total $\overline{\hbox{G}\hbox{B}\hbox{R}}$ -BD rate saving of about 39% (RA) and 40% (LD) is reached. When it comes to direct coding in GBR representation, CCP achieves a higher gain compared with coding in YC_bC_r without any further decorrelations processes. Here, only the additional predictor achieves a slightly higher coding gain when coded in RA configuration. Predicting the model parameter α, and signaling a correction term instead, leads to a significant decrease in coding performance of about 2–3% in the case of coding in GBR representation.

In order to get a more detailed impression of the advantages of each decorrelation approach, the results of individual sequences are shown and discussed for the RA configuration in the following. For each class, the BD-rate of sequences with different color characteristics are shown in Table 5. They have been chosen because of their quite different behavior when coded in color representations other than GBR. It is of interest how well CCP and the extensions deal with those characteristics. The results for YC_oC_g and GR_bR_r are taken from [Reference Nguyen, Khairat and Marpe17] and are also shown in Table 5. It should be pointed out, that the simulations performed in [Reference Nguyen, Khairat and Marpe17] are based on different conditions compared to the results presented in this paper. Hence, these results serve only as an indicator for the sequence characteristics and the coding performance cannot be compared directly.

Table 5. $\overline{\hbox{GBR}}$ BD-rate for a subset of sequences (RA).

It can be seen that the impact of color transforming differ immensely between the SC sequences. The sequence TwistTunnel is mainly monochromatic, consequently the correlation among the components in RGB representation is close to 1, and hence, transforming to GR_bR_r domain should be almost optimal in sense of decorrelation. Also all CCP-based coding tools show a high bit-rate saving for this sequence. However, it can be seen that a representation in YC_bC_r already decorrelates the luma and chroma components almost completely, hence applying CCP additionally, only results in signaling overhead. Predicting the model parameter α from the spatial neighborhood, as in CCP-PP, compensates this overhead, and the finer CCP even leads to a small coding gain. When a color transform is not applicable, CCP also gives a comparable gain when applied in GBR domain. Here however, the signaling overhead is even increased by CCP-PP. This can be explained by the fact that α is assumed to be zero in the case when no residual signal is available for neighboring blocks. Knowing that in the GBR case the optimal α is close to one for this sequence, the prediction for α is very poor in this cases. When coding in YC_bC_r domain on the other hand, the remaining correlation between color components should be close to zero. Hence, the correction factor $\Delta\alpha$ is also small and its finer granularity leads to a further improvement in the YC_bC_r domain.

For the Waveform sequence even a loss in terms of bit-rate savings can be observed when coding in YC_oC_g−R. This can be explained by the high in-stationarity of color characteristics in this sequence. Thus, an adaptive approach such as CCP is essential. It can be seen that the option of chroma-to-chroma prediction increases the coding-efficiency. For both sequences, Waveform and Webbrowsing, coding in YC_bC_r with CCP and an additional predictor leads to the best coding gain in our setup.

Even though both selected CC sequences differ in there BD-rate saving when coded in YC_oC_g−R representation, they show quite similar behavior for all test scenarios in our setup. These results are consistent with the averages shown in Table 2.