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\chapter[Error concealment-aware video encoding]{Error concealment-aware video \\ encoding \VERSION{2}}
\label{Chapter:ConcealmentAwareTechniques}

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\vspace*{\fill}
\section{Introduction}

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.

This chapter is organized as follows. Section~\ref{Section5:Problem} introduces the problem definition and motivation for the method proposed in this chapter.
Section~\ref{Section5:ECCandidates} presents an initial evaluation of different \ac{ec} schemes in order to find the relevant ones to be used in the proposed \ac{ec}-aware coding scheme.
Section~\ref{Section5:Architecture} provides an overview of the proposed method architecture followed by a detailed description in Section~\ref{Section5:ProposedMethod}.
Sections~\ref{Section5:ECSignallingPerformance}~and~\ref{Section5:OverallPerformance} present the performance results and discussion of the proposed \ac{ec} optimisation and signalling.
Finally, Section~\ref{Section5:Summary} concludes the chapter.

\clearpage
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\section{Problem definition}
\label{Section5:Problem}

In Chapter~\ref{Chapter:ErrorResilienceReview} different \ac{ec} algorithms that can effectively reconstruct lost video were described, though not all of them exhibit the same accuracy for every lost frame or slice.
Moreover, it was also shown that combining different \ac{ec} approaches at the block level for improving the reconstruction accuracy is not straightforward.
In the past, hybrid \ac{ec} schemes were proposed to improve the quality of recovered frames by either combining spatial and temporal \ac{ec} algorithms~\cite{HybridConcTB2008} or by optimising the \ac{mve} at the pixel and block levels~\cite{HybridConcealmentTB2008,2DConcHybridMotion2010}.
Regarding the \ac{hevc}, existing algorithms also aim to improve the reconstruction accuracy of motion-based recovery approaches by using the information of correctly received neighbouring frames, e.g., block partitions~\cite{HEVCMCBlockAug2013} and prediction residue~\cite{HEVCMCResidueDec2013}.
Although such methods are able to reduce the reconstruction artefacts and improve the overall video quality, decoder-based decisions are still not fully accurate, as they are based on limited information to be used as reference in the decision process.
Therefore, higher reconstructed quality can be achieved by estimating the best \ac{ec} techniques at the encoding-side, based on the original video signal..
Different approaches were proposed in the past to address the problem of \ac{ec}-aware video coding~\cite{ConcealmentDrivenSliceOrdering2008,ConcealmentAwareME2006,ErrorResilienceModeHEVC2016}.
Extra information was also used to aid the \ac{ec} operation at the decoder-side, either by sending redundant information \cite{ResilienceRECAP_ICASSP2009,SaliencyErrorConcealment_TM2013} or by embedding additional coded data into the bitstream \cite{ConcealmentIntraDataHidng2009}.
Although these methods facilitate the \ac{ec} performance either through slice reordering or based on \acs{mv}, they always rely on the assumption that a fixed \ac{ec} method is used at the decoder.

To advance one step further, this chapter presents  an investigation of \ac{ec}-aware video coding and proposes a new scheme to achieve high decoding flexibility in terms of the \ac{ec} approaches, leading to better video quality.
This is accomplished by selecting, at the encoder, among several \ac{ec} algorithms with different characteristics, the one that yields the lowest reconstruction distortion at the decoder and also minimises the \ac{rd} cost considering the necessary signalling rate. Thus, the proposed approach differs from similar previous methods \cite{ConcealmentAwareME2006,ErrorResilienceModeHEVC2016} by selecting the best \ac{ec} method without affecting the encoder optimisation.
To further improve the  quality of recovered frames, an enhancement layer is encoded with the mismatch residue computed as a difference between the transmitted and recovered frames.
This is a dynamic optimisation process, which is more efficient than conventional approaches based on redundant pictures  \cite{RedudantPicsJan2009,VPxResiliencePCS2016}, which transmit the whole frame as redundancy.
In contrast with the previous work presented in Chapter~\ref{Chapter:ErrorResilienceTechniques}, which addressed the error resilience problem by optimising  the coding dependencies, the approach described in this chapter considers both, \ac{ec} performance and the coded rate required for signalling the best \ac{ec} mode to the decoder.


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\section{Error concealment algorithms}
\label{Section5:ECCandidates}


In order to propose a novel \ac{ec}-aware technique different algorithms were taken into consideration.
This section presents a description and evaluation of the most relevant \ac{ec} algorithms used in the proposed method.
Firstly, a technical description of each method is provided followed by a performance comparison between them.

\subsection{EC algorithms based on motion-compensation}
%\subsection{Motion-compensated reconstruction}

The most common algorithms to recover missing frames take advantage of the correctly received \acs{mv} from the neighbouring frames.
This has been widely used in the past for \ac{h264} standard \cite{H264RefConc2006,BlockBasedMVE2002,BlockBasedMVEOverllaped2011} and also in the \ac{hevc} standard~\cite{HEVCMCBlockAug2013,HEVCMCResidueDec2013,DownhillHEVCCon_ICCE2017}.

Let's consider the example of Figure~\ref{FIG5:MotionVectorExtrapolation}, where a missing frame ($f_0$) at time instant $t_0$ is reconstructed based on the information present in the temporally adjacent frames, $f_{-1}$ and $f_{-2}$.
One of the common approaches is \ac{mc} where the missing frame is reconstructed through motion compensation directly using the co-located vectors in the closest neighbour frame ($f_{-1}$). The \acs{mv} used for the motion compensation ($v_0$) are obtained by copying the \acs{mv} $v_{-1}$ from the same spatial position in $f_{-1}$, as illustrated in the figure by the \ac{mv} $v^{1}_{0}$ which is obtained by copying  $v^{1}_{-1}$.

An alternative approach is based on the reconstruction of the missing frame by using motion compensation through extrapolation of the received \acs{mv}, of  frame $f_{-1}$ at time instant $t_{-1}$, according to the following procedure:
\begin{enumerate}
\item
the \acs{mv} ($v_{-1}$) of the neighbouring frame ($f_{-1}$) are extrapolated to compute the set of \acs{mv} ($v_{0}$) for the missing frame as follows:
\begin{equation}
%       v^\zeta_0 = \frac{ t_0 - t_{C} }{ t_{-1} - t_{R} } \times v^\zeta_{-1},\ \zeta=s,r
v_0 = \frac{ t_0 - t_{-1} }{ t_{-1} - t_{R} } \times v_{-1},
\end{equation}
where $t_{R}$ is the time instant of the reference frame pointed by the original \acs{mv} $v_{-1}$, which in the example of Figure~\ref{FIG5:MotionVectorExtrapolation} corresponds to $t_{-2}$.
\item
the \ac{mv} associated to the block  $b_{-1}(x,y)$ at spatial position $(x,y)$ in $f_{-1}$ may be used to recover the block $b^{'}_{{0}}(x^{'},y^{'})$ in $f_0$, at position $(x^{'},y^{'})$ obtained from $v_0$ components as follows:
\begin{align}
x^{'} &=  x - v_{0x}, \\
y^{'} &= y - v_{0y}.
\end{align}
\end{enumerate}
This method, referred to as \glsfirst{mve}, is illustrated in Figure~\ref{FIG5:MotionVectorExtrapolation}, where the \ac{mv} $v^{2}_{0}$ results from the extrapolation of $v^{2}_{-1}$.
One should note that these methods may not result in a complete motion field for the entire frame, resulting in an incomplete reconstruction.
For the regions without \acs{mv} the average of the three top-left neighbouring \acs{mv} are used to complete the motion field.
%\todo{Grid-aligment! Incomplete!}

\begin{figure}[tb]
    \centering
    \input{./042_ConcealmentAwareEncoding/Figures/MotionVectorExtrapolation.tikz}
    \caption{Representation of the video frame with associated original and extrapolated motion vectors represented using full and dashed arrows, respectively.}
    \label{FIG5:MotionVectorExtrapolation}
\end{figure}

Finally, as a base for comparison, the default \ac{ec} in the reference \ac{hevc} implementation the \ac{fc} algorithm is also evaluated.
This method consists in replacing the lost frame with a copy of the previously decoded one, which can also be described as a motion compensated reconstruction using only zero \acs{mv}.

\subsection{Algorithms based on motion estimation}

In this sub-section a different method to estimate a motion-field is described. This can be used to reconstruct the missing motion information of a lost frame.
Then, the recovered motion-field is used in combination with the \ac{mve} method to recover the lost frame.

Typically, optical flow estimation algorithms are used to estimate a 2-D motion field, comprising one \ac{mv} $v=(v_x, v_y)$, for each pixel, which minimises the following energy function:
\begin{equation}
E(x,y) = \sum_{x} \sum_{y} \bigg| f_{0}\big(x,y\big) - f_{-1}\big( x + v_x(x,y), y+v_y(x,y)  \big)   \bigg|.
\end{equation}
Besides a full search algorithm, where a block-based approach is used to search for the best \acs{mv} that minimise the sum of absolute errors, three other approaches were tested to evaluate their effectiveness in \ac{ec} algorithms.
These three methods are as follows:
\begin{enumerate}
    \item a method based on the duality between total pixel difference and regularisation term~\cite{DualFlow2016};
    \item a method which approximates the neighbourhood of each pixel by quadratic polynomials on both frames~\cite{PolyFlow2003};
    \item a method based on a combination of feature matching and total pixel difference~\cite{DeepFlow2013}. %\todo{check here!}
\end{enumerate}

\subsubsection{Motion estimation based on a regularisation term (\textit{DualFlow})}

In this method the motion field is estimated based on the minimization of the total difference of pixel values measured using the L-1 norm \cite{DualFlow2007,DualFlow2016}, taking into account a regularisation term obtained from the Horn and Schunck smoothness condition~\cite{HornSchunckOpticalFlow1981}.
This condition forces the estimated field to be regular across neighbouring pixels by penalising deviations in a quadratic sense.
Using this method, for each pixel $\mathbf{p}$, the motion field $v(\mathbf{p})$ is obtained by minimising the following energy function,
\begin{equation}\label{EQ5:DualFlow}
E(v) =
\sum_{\mathbf{p} \in \Omega} \Big( \big| f_{-1}(\mathbf{p}) - f_{-2}( \mathbf{p} + v(\mathbf{p}))\big| + \big|\nabla v(\mathbf{p})\big| \Big)%d\mathbf{p},\ \mathbf{p} \in \Omega
\end{equation}
where $f_{-1}$ and $f_{-2}$ are the two previous frames at time instants $t_{-1}$ and $t_{-2}$, as represented in Figure~\ref{FIG5:MotionVectorExtrapolation}.
In~(\ref{EQ5:DualFlow}), $\Omega$ defines the sets of pixels of those frames, and $|\nabla v(\mathbf{p})|$ is a regularisation term that penalises high variations of the optical flow which effectively disallow discontinuities.
This is based on the assumption that neighbouring regions belong to the same object, thus such regions should have similar motion.


\subsubsection{Motion estimation based on polynomial expansion (\textit{PolyFlow})}

In this method the motion field is estimated based on a polynomial expansion of each pixel neighbourhood~\cite{PolyFlow2003}.
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. 
\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:
\begin{align}
f_2(\mathbf{p})
&= f_1(\mathbf{p}-\mathbf{d}) \nonumber \\
&= (\mathbf{p}-\mathbf{d})\mathbf{A}_1(\mathbf{p}-\mathbf{d})^T+\mathbf{b}_1(\mathbf{p}-\mathbf{d})^T+C_1  \\
&= \mathbf{p}\mathbf{A}_1\mathbf{p}^T - 2\mathbf{d}\mathbf{A}_1\mathbf{p}^T+ \mathbf{d}\mathbf{A}_1\mathbf{d}^T+ \mathbf{b}_1\mathbf{p}^T-\mathbf{b}_1\mathbf{d}^T + C_1 \nonumber \\
&= \mathbf{p}\mathbf{A}_1\mathbf{p}^T + (\mathbf{b}_1-2\mathbf{d}\mathbf{A}_1)\mathbf{p}^T + \mathbf{d}\mathbf{A}_1\mathbf{d}^T - \mathbf{b}_1\mathbf{d}^T + C_1\\
&= \mathbf{p}A_2\mathbf{p}^T+\mathbf{b}_2\mathbf{p}^T+C_2, \nonumber
\end{align}
then, by equating the coefficients of the quadratic polynomials results in the following relations:
\begin{align}
\mathbf{A}_2 &= \mathbf{A}_1 \nonumber \\
\mathbf{b}_2 &= \mathbf{b}_1 - 2 \mathbf{d} \mathbf{A}_1, \\
C_2          &= \mathbf{d}\mathbf{A}_1\mathbf{d}^T + \mathbf{b}_1\mathbf{d}^T + C_1. \nonumber
\end{align}
This allows to find the displacement $\mathbf{d}$ for any signal dimensions by solving the above equations. Detailed implementations of the polynomial expansion and respecting solving can be found in~\cite{NormalizedDiffConvolution1993,farneback2002polynomial}.

\subsubsection{Large displacement optical flow with deep matching (\textit{DeepFlow})}

In this method the motion field is estimated based on extension of the total pixel difference methods using descriptor (feature) matching.
This allows the optical flow estimation to accurately find large displacements, because it is not fully bound by any constrains, such as the Horn \& Such presented in~(\ref{EQ5:DualFlow})\cite{LargeDisplacementOptFlow_TPAMI2011}. Moreover, the correspondences between descriptions are used to apply a coarse-to-fine wrapping, which avoids local minimum values.
The combination of both approaches increases the matching accuracy.

This approach was also exploited in \cite{DeepFlow2013} with the following extensions: (i) use of description matching in the minimisation problem; (ii) introduction of a normalisation parameter to decrease the impact of regions with high spatial changes; (iii) use of different weights for each layer optimisation.
Figure~\ref{FIG5:DeepFlowDiagram} shows the blocks that are included in the description matching process.
The matching algorithm is built upon a multi-stage architecture using six layers with different patch sizes, interleaving convolutions and max-pooling, which is similar to deep convolutional networks \cite{GradientBasedConvNN_ProcIEEE1998}.
As shown in Figure~\ref{FIG5:DeepFlowDiagram}, multi-size response levels are generated from the reference and target images using convolutions with different patch sizes. This method uses a bottom-up approach, i.e., starting at a fine level and moving towards the coarser levels (larger patches), which are built as an aggregation of responses of smaller patches. This results in a multi-size response pyramid.
Subsequently, a local maximum is extracted from each level to achieve a more accurate motion field (quasi-dense correspondence).
Then, an initial motion field is extracted, referred to as $v'$ .
The final optical flow is obtained by minimising an energy function, which can be described by the following equation:
\begin{equation}
E(v) =
\sum_{\mathbf{p} \in \Omega} \Big( E_D(\mathbf{p}) + \alpha E_S(\mathbf{p}) + \beta E_M(\mathbf{p}) \Big),
\end{equation}
where $E_D$ is the data term, $E_S$ is a smoothing term and $E_M$ is the matching term.
The data term is obtained from the difference between matching pixels in both video frames.
The smoothness term is a robust penalisation of the gradient of the flow, similarly to~(\ref{EQ5:DualFlow}), i.e., $E_S(\mathbf{p})=|\nabla v(\mathbf{p})|$. Finally, the matching term ($E_M$) is used to encourage the flow estimation to be similar to the precomputed motion field~($v'$).

\begin{figure}[t]
    \centering
    \includegraphics[width=.95\columnwidth]{./042_ConcealmentAwareEncoding/Figures/DeepFlowBlockDiagram}
    \caption{Block diagram of the deep matching algorithm \cite{DeepFlow2013}.}
    \label{FIG5:DeepFlowDiagram}
    \FIGSVSPACE
\end{figure}

\subsection{Experimental evaluation}

This section presents a simulation study of the different \ac{ec} schemes previously described.
This evaluation aims at finding the suitable methods to be used for efficient reconstruction of the missing frames in case of data loss.
The two \ac{ec} methods based on the correctly received \acs{mv} are tested, i.e., \ac{mc} and \ac{mve}, while  the \ac{fc} method is used as reference for comparison.
Moreover, the four different approaches to estimating the motion field for the missing frame are compared: (i) full search based on the minimisation of the sum of absolute errors (\FULLSEARCH),  (ii) optical flow based on the duality between total difference and regularisation term (\DUALFLOW), (iii) optical flow based on polynomial approximations (\POLYFLOW) and (iv) optical flow based on deep matching (\DEEPFLOW).

Table~\ref{TAB5:ECPerformaceComparison} shows the average quality (\ac{psnr}) obtained for the different methods under investigation.
The absolute value of \ac{psnr} is shown for the \FC method, while the differential values are shown for the remaining methods.
The results shown in the table reveal that methods \MC and \MVE are both able to overcome \FC, achieving average quality gains of up to 1.41 dB and 1.46 dB, respectively. Moreover, by extrapolating the \acs{mv} from the correctly receiving frame to the lost one (\MVE), it is also possible to outperform  motion-copy (\MC).
This can be explained by the objects' trajectories of objects which are preserved in the \MVE method (assuming constant translational motion), in contrast with the \MC method, which assumes that neighbouring objects have parallel motion which may result in inaccurate estimations.


\begin{table}[tb]
    \centering
    \caption{Average decoded video quality (\ac{psnr} in dB) for seven error concealment algorithms under 10\% of random packet loss.}
    \label{TAB5:ECPerformaceComparison}
    \TABLESVSPACE
    \input{./042_ConcealmentAwareEncoding/Results/PerformanceConcealmentMethods.tex}
\end{table}


According to the results of Table~\ref{TAB5:ECPerformaceComparison} (columns 5 to 8) the \ac{ec} methods based on motion estimation achieve an overall superior performance when compared with methods which rely on correctly received \acs{mv} (i.e., \MC and \MVE).
Results for \FULLSEARCH method reveal that only minimising the sum of absolute errors between two consecutive frames might not always be directly related with objects' motions, which results in inaccurate motion field to be used in the reconstruction of lost frames.
Finally, results from Table~\ref{TAB5:ECPerformaceComparison} reveal that the \DEEPFLOW algorithm leads to the most accurate motion field, in comparison with the other methods.
It is able to achieve an average quality gain of 1.79 dB, and up to 3.39 dB for Book Arrival sequence, where \POLYFLOW only achieves 3.05 dB.
Since  \POLYFLOW combines different techniques also used by other algorithms in study, e.g., total difference of pixel values also used by \DUALFLOW, it is expected to achieve accurate estimations and consequently higher \ac{ec} reconstruction quality.
Moreover, using feature matching in combination with smoothing conditions, the \DEEPFLOW algorithm is able to correctly estimate large displacements, which results in improved performance for video signals with higher motion, e.g., Tennis sequence.

\subsection*{Remarks}

Summarising, the analysis of the previous results indicates that all \ac{ec} methods are able to cope with lost frames and manage to recover the missing data with reasonable quality.
Nevertheless, it is noticeable that lost frames recovered with an estimated motion field result in higher average quality, especially when using the \DEEPFLOW method.
However, since the other methods are also able to achieve acceptable video quality, they shall not be neglected, as they provide alternative approaches for lost frame recovery with a lower computational complexity (i.e., they not require motion estimation).
Thus, in order to achieve higher reconstruction quality, different approaches shall be considered, aiming at balancing the overall complexity with the quality of the reconstructed frames.

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\section{Architecture for the EC-aware video encoding}
\label{Section5:Architecture}

This section presents the general architecture proposed for \ac{ec}-aware video encoding, describing its main functional blocks, and providing an introduction for the subsequent detailed descriptions.
Figure~\ref{FIG5:BlockDiagram} illustrates the architecture of the proposed \ac{ec}-aware encoding scheme.
After the video encoder, it includes data loss simulation at the \ac{nal} for every slice. Subsequently, \ac{ec} is applied to the simulated losses in order to find the best methods that should be used to reconstruct the lost slices in case of  errors and packet loss.
Saliency-weighted \ac{ec} mode decision is used to select the optimal \ac{ec} mode from the best trade-off between \ac{ec} distortion, using the original input video~($f$) as reference, and the number of bits required for signalling.
Then, the optimal \ac{ec} mode is sent to the decoder along with the mismatch residue computed as a difference between the transmitted and recovered frames.
Finally, the scalable extension of the \ac{hevc} standard is used to encode this residue information.

For the \ac{ec} mode decision optimization the missing slices are reconstructed, as they would be in the decoder, i.e., they are recovered at the encoder by simulating the decoder \ac{ec}, but using several \ac{ec} methods, based on motion estimation and extrapolation techniques, to select the best one at the encoder-side.
In this process, each \ac{ctu} is partitioned to form a quadtree structure of \ac{ecu} that are used to test the different \ac{ec} candidate modes.
Then, the best trade-off between \ac{ecu} partition and signalling is found through \ac{rd} optimisation.
In order to achieve an efficient use of the signalling overhead, a saliency-weighted procedure is embedded in the \ac{rd} optimisation based on a spatio-temporal saliency, where more signalling bits are allocated to regions with higher saliency values.
Finally, the signalling information is transmitted to the decoder by using the \ac{sei} \ac{nal} units~\cite{HEVCHighLevelReferenceDez2012}.
Since, in general, the optimal \ac{ec} mode is still not able to perfectly reconstruct all the missing regions, extra residual information is multiplexed in the stream encoded as a scalable \ac{el}.
This residual information contains the difference between the compressed ($\hat f_t$) and the \ac{ec} frames ($\tilde f$).

\begin{figure}[tb]
	\centering
	%\includegraphics[width=.9\columnwidth]{./042_ConcealmentAwareEncoding/Figures/BlockDiagram}
	\input{042_ConcealmentAwareEncoding/Figures/BlockDiagram.tikz}
	\caption{Architecture of the error concealment-aware encoding scheme.}
	\label{FIG5:BlockDiagram}
	\FIGSVSPACE
\end{figure}

The transmitted information is used to assist the \ac{ec} operation at the decoder to recover erroneous frames with high accuracy, by using the best \ac{ec} mode and also residual information to reduce error propagation.
The remaining of this section describes in detail the building blocks of the proposed encoding architecture, i.e., the \ac{ec} candidate modes, the saliency-weighted optimal \ac{ec} mode decision, signalling and enhancement layer coding.



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\section{Saliency-weighted \ac{ec} mode decision}
%\section{Error concealment mode decision}
\label{Section5:ProposedMethod}

In this section the proposed saliency-weighted \ac{ec} mode decision algorithm is described.
Firstly, the list of \ac{ec} candidates is provided based on the previously described methods.
Then, the \ac{rd} optimisation is performed using a saliency region in each frame, in order to decrease the overall bitrate without compromising the reconstruction quality.
The signalling coding strategy is also described.
Finally, coding the \ac{ec} residue, introduced as auxiliary information to improve the reconstruction quality, is described.


\subsection{\ac{ec} candidates}

A set of four \ac{ec} candidate modes  (M1...M4) is used in the optimisation process that selects one of them as the best match for each particular \ac{ecu}. Each \ac{ec} mode corresponds to a different \ac{ec} method, as shown in Figure~\ref{FIG5:concealmentcandidates}, namely:
\begin{itemize}
    \item M1, M2: These two methods are based on extrapolation of an estimated motion field;
    \item M3: This method is based on \ac{mv} extrapolation of previously received \acs{mv};
    \item M4: This method uses the co-located motion information from the closest neighbour;
\end{itemize}

\begin{figure}[tb]
\centering
%\includegraphics[width=0.7\columnwidth]{./042_ConcealmentAwareEncoding/Figures/ConcealmentCandidates}
 \input{./042_ConcealmentAwareEncoding/Figures/ConcealmentCandidates.tikz}
\caption{\ac{ec} candidates used for optimization.}
\label{FIG5:concealmentcandidates}
\FIGSVSPACE
\end{figure}

The first two methods, M1 and M2 rely on an estimated motion field, using the method \DEEPFLOW \cite{DeepFlow2013}, to recover the lost frame.
Such motion field is extrapolated at the pixel level, i.e., one \ac{mv} is assigned to each pixel, and \ac{pu} level, i.e., one \ac{mv} is assigned to the entire unit.
This results in two different reconstructions of the missing frame, where the former may increase the accuracy of the pixel extrapolation, but the latter has the advantage of keeping the block structure and generate a smoother reconstruction.

The method M3 is based on a conventional \ac{mve}, and finally M4 reconstructs the missing frames using the \ac{mc} algorithm.


\subsection{Optimal \ac{ec} mode selection}

As previously described in sub-section~\ref{Section5:ECCandidates}, the proposed method allows to choose between four \ac{ec} candidates, which result in different recovered frames for each lost frame (simulated).
The lost frame is partitioned into quadtree structures, each one forming a set of variable size \acs{ecu}.
Then, the process of finding the optimal \ac{ec} method for each \ac{ecu} is formulated as a rate-distortion cost minimisation. To solve such problem, a Lagrangian optimisation is used to achieve the best trade-off between reconstruction quality and signalling overhead.
Furthermore, image saliency driven by visual attention modelling is used in the optimisation process to weight the cost of the overhead information of each \ac{ecu}, according to the visual relevance of its content.

The optimal \ac{ec} mode $m_{l,i}^*$, for the $i_{th}$ \ac{ecu} of size defined by the quadtree partitioning level $l$, is obtained by minimising the following Lagrangian cost:
\begin{equation}\label{EQ6:OptimalDepth}
\small
\newcommand{\argmin}{\operatornamewithlimits{arg\ min}}
% (m^*,l^*) = \argmin_{m,l} \left\{ D(m,l) + \left(1+\frac{t_0-t_I}{T_{I}}\right) \lambda R(m,l) \right\},
% l^* = \argmin_{l=1..3} \left\{ D(l) + \lambda \left(1-\frac{t_I-t_c}{T_{\ac{ird}}}\right) R(l) \right\},
m_{l,i}^* = \argmin\limits_{\footnotesize \substack{l\in\left\{0...3\right\} \\ i\in\left\{1...4^l\right\}}}\left\{ D(m_{l,i}) + \left(1+\frac{t_C-t_I}{T_{I}}\right) \lambda R(m_{l,i}) \right\},
\end{equation}
where $R(m_{l,i})$ represents the number of overhead bits required to encode the \ac{ec} mode, and $D(m_{l,i})$ is the sum of absolute error of the \ac{ecu}.


In~(\ref{EQ6:OptimalDepth}), besides the parameter $\lambda$, which is used to  trade-off distortion and overhead rate in the minimisation process, there is also a weighting factor to control the cost of $R(m_{l,i})$, according to the duration of the error propagation.
As in the method proposed in the Chapter~\ref{Chapter:ErrorResilienceTechniques}, this method uses the ratio between the temporal distance from the current frame ($t_C$) to the previous refresh frame ($t_I$) and the period of refreshing frames ($T_{I}$).
%This weight varies between $\left[0;1 \right]$, achieving the lowest value for  intra-coded frames and the maximum  for the frame located immediately before an intra-coded one.
This behaviour follows the fact that when a lost frame is closer to the next intra-coded frame, the error propagation is lower.
Thus, it is not worthwhile to spend too many overhead bits to reduce it. This is accomplished by increasing the cost of such bits according to the temporal distance between the missing frame and the next I frame.
Moreover, a dynamic value for $\lambda$ is also used to adjust the amount of  overhead within the frame, according to the visual relevance of each image region, defined by a saliency map (see Section~\ref{Section6:SaliencyDetection}).

The algorithm previously described results in \acs{ecu} with variable size, which is defined by the depth of the quad-tree structure, i.e., level $l$. The partition size is jointly optimised along with the best \ac{ec} candidate method using~(\ref{EQ6:OptimalDepth}). Alternatively, a fixed \ac{ecu} size can also be used by defining a fixed depth for all quad-tree structures, i.e., constant $l$ for the entire frame. This can be achieved by using~(\ref{EQ6:OptimalDepth}) to solely optimise the \ac{ec} methods for each \ac{ecu}.
Although this reduces the overall complexity of the proposed method, it leads to a non-optimal solution which may require additional overhead. In Section~\ref{Section5:ECSignallingPerformance} a comparison between a dynamic and fixed approach is provided.


\subsection{Saliency detection}
\label{Section6:SaliencyDetection}

The saliency maps are computed based on the well-known Itti's attention model \cite{SaliencyItti1998} that applies a hierarchical decomposition, based on a set of spatial features, which are combined with a center-surround weighting to obtain the saliency map.
Since the Itti's model only produces saliency maps for still images, in this work it is further combined with a temporal feature. This is obtained by estimating the optical flow between two consecutive frames, based on the algorithm presented in \cite{HornSchunckOpticalFlow1981}. The final saliency map is achieved by combining the spatial and temporal components, $S_{s}$ and $S_{t}$ respectively, as follows,
\begin{equation}\label{eq:saliency}
S = \rho S_{t} + (1-\rho) S_{s}
\end{equation}
The parameter $\rho$ is used to give higher relevance to the temporal component, since motion is correlated with error propagation, producing longer artefacts and consequently higher impact on visual attention. In this work the temporal component was given a weight slightly higher than 50\%, i.e. $\rho=0.6$.

On the one hand, higher values of saliency (i.e. regions with higher visual relevance) should result in lower values of $\lambda$, which tend to increase the overhead rate value on those regions, thus reducing the \ac{ec} distortion at the decoder, in case of loss. On the other hand, higher values of $\lambda$ should  reduce the overhead, allowing higher \ac{ec} distortion at the decoder. In order to achieve the aforementioned goal, the following definition for $\lambda$ is used:
\begin{equation}\label{eq:lambdasaliency}
% \lambda = \lambda_{0} - \frac{S_{\ac{ctu}} - \mean S}{\Delta S}, \Delta S > 0,
% \lambda = \lambda_{0} + \frac{\Delta S}{S_{\ac{ctu}} - \mean S},
% \lambda = \lambda_{0} e^{\frac{\mean S - S_{\ac{ctu}}}{\Delta S}}, \Delta S > 0,
\lambda=\begin{cases}
\lambda_{0} e^{\frac{\mean S - s}{\Delta S}}, & \text{if $\Delta S > 0$},\\
\lambda_{0}, & if \Delta S=0 \text{ (no saliency used)},
\end{cases}
\end{equation}
where $s$ is the saliency value of the current \ac{ctu}, $\mean S$ is the average saliency value and $\Delta S$ is the difference between the maximum and minimum.
One should note that this method does not depend on the existence of a saliency map. If the saliency map is constant or non-existent, a fixed value of $\lambda$ is used (i.e., $\lambda_0$) defined at the encoder, which means that no distinction is made across image regions.


\subsection{Signalling the optimal EC modes}

% \begin{figure}[tb]
% \begin{algorithmic}
% \Procedure{encodectuecm}{$level$}
%   \If{$level<level^*$}
%     \State\Return{$1$}
%   \Else
%     \State\Return{\Call{recurse}{$x-1$}}
%   \EndIf
% \EndProcedure
% \end{algorithmic}
% \caption{Algorithm used to generate \ac{ec} mode signalling.}
% \end{figure}

% \HIGHLIGHT{Figure~\ref{FIG5:signalling} illustrates the structure of the signalling information for each \ac{ctu} comprising a quadtree of ECUs. One symbol is used for the depth $level$, followed by a variable number of $ecm$ symbols.
% The $ecm$ symbols indicate the \ac{ec} mode that should be used for each \ac{ecu}. Adaptive arithmetic coding~\cite{ArithmeticCodingJun1994} was used to compress both the $level$ and $\ac{ec}$ symbols and further reduce the overhead.
% Since the \ac{sei} information uses significantly less bitrate than the video signal, it is less likely to be hit during transmission.}


Figure~\ref{FIG5:signalling} illustrates the structure of the signalling information for each \ac{ctu} comprising a quadtree of \acs{ecu}.
In this structure, one bit is used for the $split$ flag and two bits for the \ac{ec} mode associated to each \ac{ecu} ($ecm \in \{M1, M2, M3, M4\}$).
The $split$ flag indicates whether the \ac{ecu} is further split into the next~level~($split=1$) or \ac{ecu} partitioning stops at the current level ($split=0$) and the corresponding $ecm$ modes are inserted.
Since no split is necessary at the deepest level, then $split=1$ followed by the four $ecm$ modes for each \ac{ecu}.
This structure allows dynamic selection of different values for the level of the quad-tree partitioning ($l$) within each frame.
Adaptive arithmetic coding~\cite{ArithmeticCodingJun1994} is used to efficiently encode both the $split$ and $ecm$ symbols, further reducing the overhead. Note that the \ac{sei} information uses much less bitrate than the video signal, thus it is  very unlikely to be hit during transmission.

\begin{figure}[tb]
    \centering
    \includegraphics[width=0.8\columnwidth]{./042_ConcealmentAwareEncoding/Figures/ConcealmentSignalling}
    % \input{./042_ConcealmentAwareEncoding/Figures/ConcealmentSignalling.tikz}
    \caption{Payload structure of the \ac{sei} \acs{nal}} % to signal the optimal error concealment method.}
    % Symbols transmitted through \ac{sei} messages to signal the optimal error concealment method.}
    \label{FIG5:signalling}
\end{figure}


\subsection{Enhancement-layer: EC residue coding}

As described earlier in this section, in order to allow further improvement of recovered slices, besides the best \ac{ec} mode, the proposed encoding scheme also allows encoding a controlled amount of \ac{ec} residue using the scalable extension of \ac{hevc} (see  Figure~\ref{FIG5:BlockDiagram}).
The enhancement layer module encodes the difference between the coded frame ($\hat f$) and its counterpart recovered by using the optimal \ac{ec} mode ($\tilde f$).
Note that, the higher the accuracy of the best \ac{ec} mode, the lower the
amount of bits carried by the enhancement layer.
At the decoder-side, the reconstruction of a missing frame ($\tilde f$) follows three steps:
\begin{enumerate}
    \item the missing frame is reconstructed using the optimal \ac{ec} methods for each \ac{ecu} $\tilde f'$ received from the encoder;
    \item the enhancement layer residue is decoded ($e^c$);
    \item the recovered frame is obtained as follows:
    \begin{equation}
    \tilde f = \tilde f' + e^{c}.
    \end{equation}
\end{enumerate}

The additional residue decoded from the enhancement layer is particularly useful to improve the quality of those \acs{ctu} where the \ac{ec} strategies are  not able to produce very accurate reconstruction.
Moreover, since the enhancement layer only carries residual information the overhead is affordable.

Note that the generated bitstream is compliant with the standard, as the \ac{ec} signalling is encapsulated in  \ac{sei} \acs{nal}, while the \ac{ec} residue is carried in \acs{nal} related with the scalable extension. Then, an adapted decoder, capable of decoding both the \ac{sei} and the scalable \ac{nal} units is also able to take full benefit from the proposed method. However, any standard \ac{hevc} decoder is also able to reconstruct the video, because it simply ignores the extra \ac{nal} units.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% SECTION                                           %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Error concealment signalling evaluation}
\label{Section5:ECSignallingPerformance}

This section presents the performance of the proposed \ac{ec}-aware optimisation scheme using the \ac{hevc} reference encoder as the basis of the encoding framework.
Two different types of performance evaluation are presented.
In the first one, only robust \ac{ec} of intra-frames is evaluated, while in the second one the proposed \ac{ec}-aware optimisation is applied to all frames, corresponding to a generic robust video transmission using optimal \ac{ec}.
For comparison, it is used the \ac{psnr} obtained from the reference \ac{hevc} decoder using motion-copy (\MC) and frame-copy (\REF) for \ac{ec} of the lost frame.
Realistic conditions were used for transmission, by allowing independent losses for any type of \ac{nal} units, hence there is no guarantee that the decoder conditions are always equal to those at the encoder, which means that sub-optimal \ac{ec} may be used at the decoder.


\subsection{Intra-frame EC optimisation}
\label{SEC4:IntraPerformance}

In this section the performance of the proposed method is evaluated only for intra frames, in order to demonstrate its efficiency in reducing error propagation.
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 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.
These figures show the results for the proposed method (\PROP), the motion-copy method (\MC) and also an alternative proposed method using fixed \ac{ecu} size of $16\times16$ pixels.
These results indicate that the proposed method (\PROP) outperforms the reference one and it is able to achieve quality gains up to {2 dB} for \ac{ld} configuration (see Figure~\ref{FIG5:singlelosslowdelay}), decrease the error propagation and increase the quality of the frames affected from the loss of the intra frame, by up to {3 dB}.
The use of \ac{ra} configuration leads to higher quality degradation than LD, due to the higher temporal distance of the reference frame used for \ac{ec} (Frame $\#8$ is used to recover the lost Frame~$\#16$). Note that when Intra-frame \#16 is lost, all frames within the range \#9 to \#31 (i.e., next I-frame) are affected by error propagation.
Nevertheless, the proposed method still achieves similar quality gains (approximately 2 dB).

\begin{figure}[tb]
    \centering
    \input{./042_ConcealmentAwareEncoding/Results/IntraEC_QualityVsFrameLowDelay.tex}
    \caption{Error propagation using \ac{ld} for the Basketball Drill sequence.}
    \label{FIG5:singlelosslowdelay}
    \vspace{2mm}
    \input{./042_ConcealmentAwareEncoding/Results/IntraEC_QualityVsFrameRandomAccess.tex}
    \caption{Error propagation using \ac{ra} for the Park Scene sequence.}
    \label{FIG5:singlelossramdon}
    \FIGSVSPACE
\end{figure}

Further tests were performed to evaluate the effectiveness of the proposed method under different loss rates. In these experiments the packets corresponding to intra frames were randomly discarded to simulate loss events, at different \acs{plr} rates with an average burst length of 5 packets.
Table~\ref{tab:randomloss} presents the average  quality of the frames affected by errors (the lost frame and dependent ones).
This table also shows the \ac{psnr} variance value in parentheses and the difference to the \ac{psnr} obtained with a reference \ac{hevc} decoder.
% The absolute \ac{psnr} value is shown for the reference case (\MC), while the \ac{psnr} difference is presented for the proposed method.
The results confirm the superiority of the proposed method, outperforming the reference \ac{hevc} for both low and high \ac{plr}. Using the \ac{ld} coding configuration, the proposed method is able to achieve quality gains of 0.88 dB for 3\% of \ac{plr} and 1.50 dB for 10\% of \ac{plr}.
In case of RA, higher quality gains are achieved, leading to an average improvement of 2.14 dB for 3\% of \ac{plr} and 3.44 dB for 10\% of \ac{plr}.
It is also worthwhile to notice that  the  \ac{psnr} variance obtained with the \PROP method is lower, which indicates lower quality variations in the video segments affected by errors.
%The quality gains achieved by the proposed method are similar to those achieved by previous works~\cite{ConcealmentIntraDataHidng2009,ConcealmentSignalling2008} for the same \acs{plr}. However, these require a higher amount of overhead (approximately $3\%$), thus the proposed method achieves a better trade-off between quality and overhead.

\begin{table}[!t]
    \newcommand{\somespaces}{}
    \centering
    \caption{Average \ac{psnr} (dB) of the frames affected by errors and its variance for two different methods under random loss of packets carrying intra-coded frames.}
    %\caption{Average  \ac{psnr} and variance of affected frames}
    \label{tab:randomloss}
    \TABLESVSPACE
    \small
    \footnotesize
    \newcommand{\colwidth}{1.6cm}
    \begin{tabular}{p{2.8cm}|x{\colwidth}|x{\colwidth}|x{\colwidth}|x{\colwidth}|x{\colwidth}|x{\colwidth}}
        \toprule
        \multirow{2}{*}{\vbox{\centering \textbf{Sequence}}} & \multicolumn{3}{c|}{\textbf{PLR=3\%}} & \multicolumn{2}{c}{\textbf{PLR=10\%}}\\
        & \MC & \PROP & $\Delta$PSNR& \MC & \PROP & $\Delta$PSNR \\
        \midrule
        \multicolumn{7}{c}{Low-delay configuration (LD)} \\ [2pt]
        \hline
        Basketball Drill  & 33.15 (0.42) & 34.26 (0.24) & \optbold{+1.11} & 32.97 (0.47) & 35.90 (0.27) & \optbold{+2.93}\\ \hline
        Race Horses       & 30.78 (1.32) & 31.55 (0.94) & \optbold{+0.77} & 30.26 (1.55) & 31.12 (1.20) & \optbold{+0.86}\\ \hline
        Kendo             & 34.33 (1.28) & 36.57 (1.11) & \optbold{+2.24} & 33.84 (1.26) & 37.49 (1.05) & \optbold{+3.65}\\ \hline
        Park Scene        & 35.22 (0.12) & 35.33 (0.08) & \optbold{+0.11} & 34.75 (0.11) & 34.96 (0.09) & \optbold{+0.21}\\ \hline
        People On Street  & 34.36 (0.32) & 34.98 (0.22) & \optbold{+0.62} & 32.17 (0.65) & 33.45 (0.50) & \optbold{+1.28}\\ \hline
        Traffic           & 36.77 (0.48) & 36.88 (0.57) & \optbold{+0.11} & 36.04 (0.30) & 36.31 (0.27) & \optbold{+0.27}\\ \hline
        Jockey            & 36.00 (1.14) & 37.20 (1.05) & \optbold{+1.20} & 35.44 (1.21) & 36.74 (1.18) & \optbold{+1.30}\\ \hline
        \textbf{Average}  & \textbf{34.37 (0.73)} & \textbf{35.25 (0.60)} & \textbf{+0.88} & \textbf{33.64 (0.79)} & \textbf{35.14 (0.65)} & \textbf{+1.50} \\
        \midrule
        \multicolumn{7}{c}{Random-access configuration (RA)} \\ [2pt]
        \hline
        Basketball Drill  & 30.22 (8.46) & 30.81 (7.66) & \optbold{+0.59} & 29.19 (7.60) & 29.84 (6.88) & \optbold{+0.65} \\ \hline
        Race Horses       & 27.35 (8.02) & 29.92 (5.89) & \optbold{+2.57} & 25.75 (7.76) & 28.61 (6.14) & \optbold{+2.86} \\ \hline
        Kendo             & 27.45 (23.9) & 32.38 (18.6) & \optbold{+4.93} & 25.22 (28.3) & 36.98 (22.4) & \optbold{+11.8} \\ \hline
        Park Scene        & 33.91 (1.40) & 34.46 (1.07) & \optbold{+0.55} & 31.38 (1.85) & 32.50 (1.48) & \optbold{+1.12} \\ \hline
        People On Street  & 29.30 (5.12) & 31.44 (3.17) & \optbold{+2.14} & 24.89 (5.37) & 27.69 (4.09) & \optbold{+2.80} \\ \hline
        Traffic           & 35.64 (1.34) & 38.12 (1.24) & \optbold{+2.48} & 32.85 (1.88) & 35.60 (1.40) & \optbold{+2.75} \\ \hline
        Jockey            & 32.35 (12.7) & 34.06 (8.60) & \optbold{+1.71} & 29.96 (12.5) & 32.11 (8.90) & \optbold{+2.15} \\ \hline
        \textbf{Average}  & \textbf{30.89 (5.64)} & \textbf{33.03 (2.14)} & \textbf{+2.14} & \textbf{28.46 (5.68)} & \textbf{31.90 (4.44)} & \textbf{+3.44}\\
        \bottomrule
    \end{tabular}
    % }
\end{table}

%\subsubsection{Overhead analysis}

Subsequently, the percentage of overhead bitrate introduced by the proposed method is compared against fixed \ac{ecu} sizes of $32\times32$ and $16\times16$, i.e., $Level=1$ and $Level=2$.
These results are presented in Table~\ref{TAB6:RedundancyIntra} and were obtained for the total bitrate shown in Table~\ref{TableTestSequences}.
It is noticeable from the results that reducing the \ac{ecu} size (see results for $32\times32$ and $16\times16$) increases the overhead ratios as more symbols are transmitted (one for each \ac{ecu}).
While the maximum overhead of these fixed partitions is  $1.81\%$ (Traffic), the proposed dynamic partitioning method is able to reduce the overhead to a maximum of $0.19\%$ (Kendo).
Moreover, comparing the results of Table~\ref{TAB6:RedundancyIntra} with the video quality obtained under packet loss reveals that the proposed method only incurs in a small reduction of the reconstruction quality, with a significantly lower overhead.
This indicates that using dynamic partitioning allows to achieve a better trade-off between the amount of overhead and the \ac{ec} performance.
In summary, the proposed technique is able to enhance the performance of the standard decoding of intra coded frames by finding the best \ac{ec} method to be used, for each \ac{ecu}, at the encoder using with a small amount of signalling overhead.

\begin{table}[tbp]
    \newcommand{\somespaces}{}
    \centering
    \caption{Percentage of overhead (\%) when using the proposed method solely for intra-coded frames.}
    \label{TAB6:RedundancyIntra}
    \TABLESVSPACE
    \footnotesize
    % \resizebox{\columnwidth}{!}{
    \begin{tabular}{p{3.2cm}|x{2cm}|x{2cm}|x{3.5cm}}
        \toprule
        \multirow{2}{*}{\vbox{\centering \textbf{Sequence}}}
        & $32\times32$ & $16\times16$ & \PROP \\
        & \textbf{Level: 1} & \textbf{Level: 2} & \textbf{Level: dynamic} \\
        \hline
        Basketball Drill & 0.08 & 0.27 & 0.08 \\  \hline
        Race Horses & 0.16 & 0.65 & 0.08 \\   \hline
        Kendo & 0.27 & 1.05 & 0.19 \\   \hline
        Park Scene & 0.42 & 1.72 & 0.05 \\ \hline
        People On Street & 0.06 & 0.25 & 0.11\\ \hline
        Traffic & 0.50 & 1.81 & 0.06  \\ %\hline
        %Jockey & 0.38 & 1.53 & 0.24 \\
        \bottomrule
    \end{tabular}
    % }
\end{table}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SECTION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Robust video transmission with optimal EC}
% \subsection{Overall performance evaluation}
\label{SEC4:OverallPerformance}

In this section the proposed \ac{ec}-aware optimisation scheme is evaluated for a generalised robust video transmission of both intra and inter coded frames.
The experimental results presented in this section were obtained by applying the proposed technique to all video frames.
As in the previous subsection, a  $\lambda_0=10$ was used.
This section is organised in the following subsections:
\begin{itemize}
 \item evaluation of the usage distribution of each \ac{ec} mode;
 \item performance evaluation of the \ac{ec} optimal mode decision (without using the enhancement layer);
 \item evaluation of the error propagation under single loss events;
%  \item overall performance evaluation of the proposed method using the \ac{ec} enhancement layer and benchmarking with existing techniques.
\end{itemize}

% Moreover it is used for comparing the use of redundant pictures based on the method proposed in \cite{VPxResiliencePCS2016}, compressed at 30\% of the total bitrate and \HIGHLIGHT{using the error concealment signalling as proposed in~\cite{ConcealmentSignalling2008}}.


\subsubsection{\ac{ec} mode usage distribution}

The \ac{ec} mode usage distribution is an indicator of the usefulness of each \ac{ec} mode.
Table~\ref{tab:useratio} shows the average $Level$ selected for the \ac{ecu} quadtree and the usage percentage of each \ac{ec} mode.
It is noticeable from these results that the proposed method leads to low average $Level$ values (lower than 1), resulting in larger \acs{ecu}, which requires a lower amount of \ac{ecu} to be transmitted than if higher values of $Level$ were chosen. This implicitly results in low signalling information.
This also justifies the low overhead shown in Table~\ref{tab:redundancy_signalling}.

The results in Table~\ref{tab:useratio} also show that all \ac{ec} modes are effectively used, which indicates that all of them are found relevant to recover the missing data.
The \ac{ec} candidate methods based on motion field estimation (i.e., M1, M2) are selected more often because they provide more accurate representation of the scene's motion than the others (i.e., M3, M4).

\begin{table}[tb]
    \newcommand{\somespaces}{}
    \centering\small
    \caption{Average Level and usage ratio of each \ac{ec} mode.} \label{tab:useratio}
    \TABLESVSPACE
    \footnotesize
    \begin{tabular}{p{3.2cm}|x{1.5cm}|x{1.5cm}|x{1.5cm}|x{1.5cm}|x{1.5cm}}
        \toprule
        \multirow{2}{*}{\vbox{\centering \textbf{Sequence}}} &
        \multirow{2}{*}{\vbox{\centering \textbf{Avg. Level}}} &
        \multicolumn{4}{c}{\textbf{Avg. usage ratio (\%)}} \\
        &      & M1    & M2    & M3    & M4 \\ \hline
        Basketball Drill & 0.81 & 59.61 & 16.62 & 14.40 &  9.37 \\ \hline
        Book Arrival     & 0.34 & 66.77 & 18.79 &  7.15 &  7.29 \\ \hline
        BQSquare         & 0.41 & 15.23 & 0.64  & 72.97 & 11.16 \\ \hline
        Four People      & 0.17 & 85.84 & 3.22  &  8.09 &  2.86 \\ \hline
        Kimono           & 0.88 & 33.76 & 23.87 & 26.03 & 16.35 \\ \hline
        Park Scene       & 0.69 & 39.34 & 13.58 & 34.19 & 12.89 \\ \hline
        People on Street & 1.51 & 31.17 & 34.39 & 16.15 & 18.29 \\ \hline
        Race Horses      & 1.62 & 34.05 & 29.89 & 17.06 & 19.01 \\ \hline
        Tennis           & 1.17 & 25.27 & 30.03 & 23.22 & 21.48 \\ %\hline
        \bottomrule
    \end{tabular}
\end{table}

\subsubsection{Evaluation of optimal \ac{ec} mode decision}
\label{sec:ECModeSelectionPerformance}

The evaluation of the proposed saliency-weighted \ac{ec} mode decision (\DYNLAMBDA) was carried out under random loss events and it was compared with the reference methods.
The video  quality was evaluated by using two quality metrics: \ac{psnr} and a \ac{fsim}~\cite{FSIM_TIP2011}, in order to validate the performance of the proposed method in a consolidated manner.
The results obtained without saliency weighting are also shown for comparison (\FIXEDLAMBDA).

Tables~\ref{TAB4:SignallingPSNR}~and~\ref{TAB4:SignallingFSIM} show the average quality under different \acs{plr} for the \ac{ld} configuration.
Table~\ref{TAB4:SignallingPSNR} shows the \ac{psnr} and \ac{wpsnr} between parentheses.
The \ac{mse} weights used in the \ac{wpsnr} are defined by the saliency values~\cite{SaliencyQualityMetric2011}.
Table~\ref{TAB4:SignallingFSIM} shows the results obtained for the \ac{fsim} quality metric.
Note that, the absolute value is shown for the reference case (\REF), while the differential values are shown for the remaining methods.
From the \ac{psnr} results shown in Table~\ref{TAB4:SignallingPSNR}, one may conclude that the proposed method (\DYNLAMBDA) consistently outperforms the reference ones for both low and high \acs{plr}. Average \ac{psnr} gains up to 2.95~dB for PLR=3\%  and 2.58~dB for PLR=10\% are achieved. It is also worthwhile to notice that higher performance is obtained for sequences with high motion, such as Basketball Drill, which results in \ac{psnr} gains up 4.82~dB.
Moreover, the results of Table~\ref{TAB4:SignallingFSIM} confirm the quality improvement achieved by the proposed method, leading to an increase of \ac{fsim} up to 4.32, which indicates that the proposed method is able to recover important image features with higher accuracy than the others.

\input{042_ConcealmentAwareEncoding/Results/TableSignallingPerformance.tex}

Table~\ref{tab:redundancy_signalling} shows the percentage of overhead in the total rate with and without saliency-weighted optimisation, i.e., \FIXEDLAMBDA and \DYNLAMBDA, respectively.
As shown in this table, the saliency-weighted optimisation reduces the amount of overhead by dynamically assigning unequal number of bits to image regions of different visual importance.
These results show that using an adaptive value of $\lambda$, based on the saliency values, leads to an average overhead reduction of 28\%  in comparison with the case where no saliency is used, i.e., constant $\lambda$.
It is worthwhile to note that using the saliency-weighted optimisation to reduce the overhead does not compromise the video quality, as can be seen in the results shown in Tables~\ref{TAB4:SignallingPSNR}~and~\ref{TAB4:SignallingFSIM}.
The \ac{psnr} values for \FIXEDLAMBDA and \DYNLAMBDA are very close, but in terms of overhead savings the results are significant for most sequences.
The achieved \ac{wpsnr} and \ac{fsim} results further demonstrate the effectiveness of the saliency-based optimisation, because the lower overhead does not affect the most relevant image regions, i.e., those with higher saliency values. Thus, the proposed method, using a adaptive  $\lambda$ (i.e., using saliency), is able to not only achieve higher \ac{ec} quality than the reference methods, but also  higher quality gains than using a constant $\lambda$ (i.e., without saliency).
This confirms the two-fold superiority of adaptive $\lambda$, i.e. not only the total overhead is reduced but also higher quality gains are achieved.
%\todo{\HERE}


\subsubsection{Error propagation evaluation}

In this section the error propagation is evaluated using single loss events and compared against the reference methods.
In this simulation a whole frame loss is enforced in order to assess the impact of error propagation on the worst case scenario.
Experimental evaluations were performed for both intra and inter-coded frame loss.
Figure~\ref{FIG5:singlelossInter} shows the \ac{psnr} over a \ac{gop} with an \ac{idr} period of 16 frames, where the whole frame \#6 is missing in sequences Basketball Drill and People On Street.
%The figure shows the results obtained by decoding the stream using the proposed method with adaptive $\lambda$ but without any information sent in the enhancement layer.
Figure~\ref{FIG5:singlelossIntra} shows the \ac{psnr} for the same conditions but with a loss event on the intra-coded Frame \#16, in sequences Kimono and Tennis.

\input{042_ConcealmentAwareEncoding/Results/ECMQualitySingleloss.tex}

These results reveal that the proposed method is able to improve the reconstruction of inter-coded frames and also outperforms the existing techniques, whenever a intra-coded frame is missing.
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. 
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.


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% SECTION
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\section{Overall performance evaluation}
\label{Section5:OverallPerformance}


As in the previous simulations, the packets were randomly discarded to simulate loss events, at different \acs{plr}.
The quality obtained with the proposed method is compared with the default method used by reference \ac{hevc} , i.e., frame-copy (\REF), motion-copy (\MC)~\cite{HEVCMCResidueDec2013}, and the method proposed in \cite{ROPERefGenJan2010}, which implements a robust scheme to minimise error propagation.
In this experiment both layers, i.e., video stream and enhancement layer with the EC residue, may be affected by errors.

\subsection{Quality evaluation}

Tables~\ref{tab:concealmentResidueRandomLoss_PLR3}~and~\ref{tab:concealmentResidueRandomLoss_PLR10} present the average \ac{psnr} of decoded video for different \acs{plr} and different percentages of total overhead (i.e., signalling rate plus enhancement layer rate). The absolute \ac{psnr} value is shown for the reference case, while the \ac{psnr} difference is presented for the remaining methods.
These results show that transmitting the \ac{ec} residue in the enhancement layer further improves the reconstruction quality obtained when only the optimal \ac{ec} method is used (see previous section).
By only using 10\% of the total bit rate, the proposed \ac{ec}-aware coding scheme is able to outperform the reference \ac{hevc}, the \MC and the  method proposed in \cite{ROPERefGenJan2010} for both \ac{ld} and \ac{ra} configurations.
Using 20\% of the total bitrate the quality gains increase up to 6.90~dB for the Basketball Drill sequence when comparing with the reference \ac{hevc}, achieving an average gain of 3.79~dB for the \ac{ld} configuration (1.33~dB for the \ac{ra}).

\input{042_ConcealmentAwareEncoding/Results/TableOveralPerformance.tex}

When comparing the results of Tables~\ref{tab:concealmentResidueRandomLoss_PLR3}~and~\ref{tab:concealmentResidueRandomLoss_PLR10} with the spatial and temporal information of each sequence (SI/TI in Table~\ref{TableTestSequences}) it is noticeable  that higher quality gains are achieved for sequences with higher motion information, i.e., Basketball~Drill and Tennis sequences.
Moreover, for sequences with higher spatial information (e.g., BQSquare and People on Street) considerable quality gains are also achieved.
This indicates the superior performance of the proposed method when dealing with complex sequences, both in temporal and spatial levels.


\subsection{Visual quality evaluation}

To provide an informal subjective quality comparison between the proposed method (using 20\% of overhead) and the reference \ac{hevc} using \MC as error concealment, Figure~\ref{FIG5:ReconstructedFrames} shows a region of the decoded frames  \#8 and \#12 when Frame \#6 is lost.
The visible artefacts  demonstrate how the decoder is able to recover from whole frame loss in both methods, and also the impact of error propagation. Figure~\ref{FIG5:ReconstructedFrames} shows that the proposed method clearly improves the reconstructed quality in comparison with \MC.


\begin{figure}[t]
    \centering
    \includegraphics[width=\textwidth]{042_ConcealmentAwareEncoding/Figures/ReconstructedFrames}
    \caption{Crop of the decoded video frame for the Race Horses and Kimono sequences (Loss event at Frame \#6)}
    \label{FIG5:ReconstructedFrames}
    \FIGSVSPACE
\end{figure}

A closer look at the Race Horses sequence reveals that the horse rider is not correctly reconstructed by the \MC method (highlighted by the circles and ellipses).  As shown in the figure, the proposed method not only results in a more accurate reconstruction of the lost frame, but also increases the visual quality of the subsequent frames.
In the Kimono sequence, some artefacts are also noticeable in the \MC case, but not visible when the proposed method is used (highlighted with circles).
Moreover, the edges of the women's kimono (highlighted with ellipses) are also improved by the proposed method, resulting in a smooth reconstruction without error propagation.
From the results discussed above, it is clearly observed that the proposed method is able to reconstruct the contours of the moving parts more accurately than traditional \ac{ec} algorithms.


\subsection{Comparison with previous works}

The achieved results were compared with previous works, where fair comparisons could be made.
In \cite{ConcealmentSignalling2008} a method was proposed to improve the recovery quality by signalling the suitable \ac{mv}  to be used for \ac{ec}.
The proposed \ac{ec}-aware scheme of Figure~\ref{FIG5:BlockDiagram} is able to achieve similar quality gains with less amounts of redundancy, allowing a better trade-off between quality and overhead.
In comparison with the work described in \cite{SignallingRobustScalable2015}, the proposed method is able to select among more complex \ac{ec} methods, which allows for higher quality gains.
Both of the above mentioned methods search for the optimal \ac{ec} method at the encoder-side, which results in similar complexity as the proposed method.


The methods in \cite{ErrorResilienceModeHEVC2017,HEVCROIErrorResilience2015} both use a feedback channel and intra-refresh to reduce the error propagation.
The results presented in \cite{HEVCROIErrorResilience2015} revealed an average quality gain of approximately 1.68~dB.
Since the proposed \ac{ec}-aware scheme is able to achieve higher quality without requiring any feedback channel, it presents better performance and functional advantages.
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{$\Delta$ 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 = \abs{\frac{\Delta PSNR(\ac{plr}=10\%)}{\Delta PSNR(No\text{-}Loss)}}.
\end{equation}


The results shown in Table~\ref{tab:overall_gain_ratio},  demonstrate that the effectiveness of the \ac{ec}-aware coding scheme is higher than all other methods under comparison. In fact, not only the absolute \ac{psnr} difference (i.e., \ac{psnr} gain)  is higher for the same \ac{plr}, but also the efficiency of the overhead is also higher.
This means that the overhead bits spent to encode the signalling information and the enhancement residue carry more useful information than the other methods.
For instance, in comparison with the method in \cite{DualFrameME2015} the proposed method leads to higher quality degradation in those cases without errors. However,  for PLR=10\%  it clearly outperforms the method in \cite{DualFrameME2015}, achieving an higher $R$, indicating a superior efficiency.
Results in Table~\ref{tab:overall_gain_ratio} also show that the small loss of coding efficiency in packet loss free transmission is clearly surpassed by the quality gains under error-prone transmission conditions.
The methods in \cite{ROPERefGenJan2010,DualFrameME2015} are based on modified predictions, while the method in \cite{VPxResiliencePCS2016} uses redundant data without any further optimisation.
Both of these approaches require low additional computational complexity.
However, as observed in the results shown in Table~\ref{tab:overall_gain_ratio}, the lower additional complexity also corresponds to lower quality gains in case of packet loss.



The proposed method uses  \ac{ec} techniques  with different levels of computational complexity for each \ac{ecu}. Since an adaptive approach is used, the average complexity tends to be lower in comparison with other methods that rely on a fixed approach. Thus, less complex video decoding is obtained when using the proposed method in comparison with other straightforward methods that always use the same \ac{ec} technique for all \acs{ctu}.


\begin{table}[t]
\newcommand{\somespaces}{}
\centering
\caption{Comparison of the proposed EC-aware robust coding architecture against existing techniques in environments with and without packet loss.}\label{tab:overall_gain_ratio}
\footnotesize
% \resizebox{\columnwidth}{!}{
\begin{tabular}{p{2.4cm}x{2.4cm}x{2.4cm}x{2cm}}
% \begin{tabular}{l|c|c|c}
\toprule
\multirow{2}{*}{\vbox{\textbf{Method}}} & \multicolumn{2}{c}{\textbf{$\mathbf{\Delta}$ PSNR (dB)}} & \multirow{2}{*}{\centering \vbox{$\mathbf{R}$ }} \\
& {\NOLOSS} & {PLR=10\%} & \\
% \hline
\midrule
\AVG                                            & -0.88 & 1.64 & 1.9 \\ \midrule %\hline
\textit{Ref~\cite{VPxResiliencePCS2016}}        & -0.37 & 2.03 & 5.5 \\ \midrule %\hline
\textit{Ref~\cite{DualFrameME2015}}             & -0.24 & 1.42 & 5.9 \\ \midrule %\hline
\PROP                                           & -0.35 & 2.10 & 6.0 \\  %\hline
\bottomrule
\end{tabular}
% }
\end{table}


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% SECTION
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\section{Summary}
\label{Section5:Summary}

In this chapter a novel \ac{ec}-aware encoding scheme was proposed by incorporating loss simulation at the encoder-side to enhance the EC efficiency at the decoder.
% The proposed method relies on loss simulation at the encoder-side to optimise the error concealment proposed. Then, the optimal error concealment is signalled to the decoder.
The novelty of this method is to include optimal \ac{ec} mode decision at the encoder, to be used by the decoder in case of packet loss, and also to allow encoding of the \ac{ec} residue using the enhancement layer of the \ac{hevc} standard. The use of \ac{ec} signalling was firstly proposed for the use on intra-coded frames in (\ref{Conf:ConcAware}), and then improved and proposed for a generic robust video transmission, resulting in a more detailed analysis published in (\ref{Journal:ConcAware}).
The overall results demonstrate that the proposed method is able to efficiently reconstruct lost frames and reduce the error propagation compared with other reference methods.
A consistent quality improvement achieved at the cost of low overhead allows the use of this method in broadcasting video services and network applications where packet loss probability is not negligible.