Final revised version

042_ConcealmentAwareEncoding/ConcealmentAwareEncoding.tex

@@ -10,7 +10,7 @@
 \vspace*{\fill}
 \section{Introduction}
 
-In this chapter an error concealment-aware encoding scheme is proposed to improve the quality of decoded video in networks prone to errors and data loss.
+In this chapter an error concealment-aware encoding scheme is proposed to improve the quality of video  delivered over networks prone to errors and data loss.
 The method aims to enhance the reconstruction of recovered lost frames by optimising the efficiency of the \ac{ec}.
 The proposed scheme is based on a scalable coding approach where the best \ac{ec} methods to be used at the decoder are optimally determined at the encoder and signalled through \ac{sei} messages. Such optimal \ac{ec} modes are found by simulating transmission losses followed by a Lagrangian optimisation of the \textit{signalling rate - \ac{ec} distortion} cost. A generalised saliency-weighted distortion is used and the residue between coded frames and their EC substitutes is encoded using a rate-controlled enhancement layer. When data loss occurs the decoder uses the signalling information to  improve the reconstruction quality.
 
@@ -133,7 +133,8 @@ In this method only quadratic polynomials are considered, expressed as:
 \begin{equation}\label{EQ5:PolyFlow}
 f(\mathbf{p}) \sim \mathbf{p}\mathbf{A}_1\mathbf{p}^T+\mathbf{b}_1\mathbf{p}^T+C_1
 \end{equation}
-where $\mathbf{p} = [x\ y]$, $\mathbf{A_1}$ is a symmetric matrix, $\mathbf{b_1}$ is a row vector and $C_1$ is a scalar. The coefficients are estimated using weighted least squares fit to the signal values in the neighbourhood. The use of quadratic polynomials was chosen primarily due to simplicity and to keep the computational complexity as low as possible, accepting a small penalty in the estimation accuracy. However, as stated in \cite{farneback2002polynomial} the extension to higher degree is straightforward.
+where $\mathbf{p} = [x\ y]$, $\mathbf{A_1}$ is a symmetric matrix, $\mathbf{b_1}$ is a row vector and $C_1$ is a scalar. The coefficients are estimated using weighted least squares fit to the signal values in the neighbourhood. 
+\HIGHLIGHT{ The use of quadratic polynomials was chosen primarily due to their low computational complexity and acceptable estimation accuracy. Nevertheless, as stated in \cite{farneback2002polynomial} the extension to higher degrees is straightforward.}
 
 Since the result of a polynomial expansion is such that each neighbourhood is approximated by a polynomial, it is necessary to analyse what happens if a polynomial undergoes an ideal translation.
 Let's consider the signal $f_1(\mathbf{p})$ represented by~(\ref{EQ5:PolyFlow}) and a signal $f_2$ which corresponds to a displacement of $f_1$, given by $\mathbf{d}=[v_x \ v_y]$. This can be expressed by the following:
@@ -424,8 +425,8 @@ In this section the performance of the proposed method is evaluated only for int
 Since intra \acs{cu} result in higher amount of bits, they also require a higher number of packets, making them more prone to errors and data loss.
 Results indicate that for an intra-period of 16 frames, approximately 42\% of the packets correspond to intra coded slices, which is a non-negligible probability of one of them being hit by transmission errors which would lead to packet loss.
 Moreover, by limiting the proposed method to intra frames, the amount of required overhead is reduced.
-In this case  a constant $\lambda_0=10$  was used, without taking into consideration saliency estimation. 
-This value results from an exhaustive search targetting acceptable quality gains with a low overhead (i.e., average overhead under 5\%).
+In this case  a constant $\lambda_0=10$  was used for all test cases, without taking into consideration saliency estimation. 
+This value results from an experimental study using several sequences and different packet loss ratios with the objective of obtaining the maximum quality gain with low overhead (i.e., average overhead under 1\%). This is not a critical value for the performance of the proposed method. It was found that small variations do not lead to significant quality changes.
 
 Since a relevant performance indicator is the error propagation over temporally predicted frames, this was evaluated using a single intra-frame loss.
 Figures~\ref{FIG5:singlelosslowdelay} and~\ref{FIG5:singlelossramdon} show the \ac{psnr} results when frame Intra-frame $\#16$ is missing, for \ac{ld} and \ac{ra} encoding configurations, respectively.
@@ -632,7 +633,9 @@ These results reveal that the proposed method is able to improve the reconstruct
 These results also indicate that the proposed method outperforms both reference methods right after the time instant when the loss occurs. The lost frame itself is recovered with much higher quality than using the reference \ac{ec} methods.
 This is due to the use of the optimal \ac{ec} mode to recover each \ac{ecu}, benefiting from the \ac{sei} information received from the encoder.
 In this case, the proposed method is able to achieve quality gains up to 5~dB, decreasing the error propagation and increasing the \ac{psnr} of affected frames by up to 6~dB.
-Comparing the results of Figures~\ref{FIG5:singlelossInter}~and~~\ref{FIG5:singlelossIntra} one may conclude that the loss of intra-frame leads to higher error propagation. For those cases where an intra-coded frame is missing, not only the reconstructions quality is lower for all methods, but also a longer (in terms of number of frames) error propagation occurs.
+Comparing the results of Figures~\ref{FIG5:singlelossInter}~and~~\ref{FIG5:singlelossIntra} one may conclude that the loss of intra-frame leads to higher error propagation. 
+%For those cases where an intra-coded frame is missing, not only the reconstructions quality is lower for all methods, but also a longer (in terms of number of frames) error propagation occurs. 
+Furthermore, as the \ac{idr} period increases, the error propagation also lasts longer with greater impact on video quality.
 
 The visual impact of using the proposed \ac{ec}-aware encoding can be evaluated by observing the recovered frame (i.e., frame \#6) of Basketball Drill, as an example. Figure~\ref{FIG5:RecoveredExample} shows that higher visual quality and less reconstruction artefacts are obtained in comparison with the \MC method. It is worthwhile to note that the proposed method is able to reconstruct the object edges with higher accuracy than the reference \MC.
 
@@ -697,9 +700,9 @@ Since the proposed \ac{ec}-aware scheme is able to achieve higher quality withou
 An advantage of using a feedback channel is the low extra complexity required to implement robust coding because the encoder receives specific information about transmission errors. This allows straightforward spatio-temporal localization of the lost data without computational effort.
 
 
-Table~\ref{tab:overall_gain_ratio} shows the average quality differences (\textbf{$\mathbf{\Delta}$ PSNR})between the reference method (\REF) and the proposed one plus three other previous works. Two different test conditions are shown in the table: \ac{plf} and PLR=10\%. Moreover, an efficiency measure  $R$ is defined, as the  ratio between the quality gains obtained under packet loss and the quality decrease in the \ac{plf} case, i.e.,
+Table~\ref{tab:overall_gain_ratio} shows the average quality differences (\textbf{$\Delta$ PSNR}) between the reference method (\REF) and the proposed one plus three other previous works. Two different test conditions are shown in the table: no packet loss (\NOLOSS) and PLR=10\%. Moreover, an efficiency measure  $R$ is defined, as the  ratio between the quality differences with and without packet loss, i.e.,
 \begin{equation}
-R = \frac{\Delta PSNR(\ac{plr}=10\%)}{-\Delta PSNR(Error\text{-}free)}.
+R = \abs{\frac{\Delta PSNR(\ac{plr}=10\%)}{\Delta PSNR(No\text{-}Loss)}}.
 \end{equation}