fix error in equation variables

041_ImprovedErrorResilience/ImprovedErrorResilience.tex

@@ -54,7 +54,7 @@ Therefore, high compression efficiency is achieved, but resilience to transmissi
 \end{figure}
 
 Highly efficient video encoders support the use of multiple reference frames for inter-frame prediction, which are selected based on minimisation of \ac{rd} cost that may lead to an unbalanced use of various reference frames.
-In order to analyse the distribution of the reference frames selected by the \ac{rd} decision method used in the reference \ac{hevc} encoder, different test sequences were encoded using two reference frames, referred to as $r_1$ and $r_2$, and their selection ratios were analysed. 
+In order to analyse the distribution of the reference frames selected by the \ac{rd} decision method used in the reference \ac{hevc} encoder, different test sequences were encoded using two reference frames, referred to as $r_1$ and $r_2$, and their selection ratios were analysed.
 In this study, reference $r_1$ corresponds to the closest neighbouring frame and reference $r_2$ the second closest.
 Figure~\ref{FIG4:ReferenceUsageRatio} illustrates the average usage percentage of reference $r_1$ for different sequences.
 The remaining corresponds to those cases where reference $r_2$ is selected.
@@ -223,7 +223,7 @@ Figure~\ref{fig:mvdependencies} illustrates how \acs{mv} have different importan
 In this figure, each block corresponds to a \ac{pu}, which has an associated \ac{mv}. The arrows point to the \ac{pu} containing the \ac{mv} used as predictor. In the current frame ($f_0$), two \acs{pu} have temporally dependent \acs{mv}.
 While the \ac{mv} of \ac{pu} \MVDEPA is used to predict a total of four other \acs{mv}, the \ac{mv} of \ac{pu} \MVDEPB is only used to predict one single \ac{mv}.
 Thus, in case of data loss (e.g., frame $f_{-1}$), the \ac{mv} of \ac{pu} \MVDEPA has more impact on error propagation to the frame $f_{0}$ and consequently quality degradation than the \ac{mv} of \ac{pu} \MVDEPB, because of its higher number of dependent \acs{mv}.
-For this reason, in the \ac{mv} selection process, the proposed method assigns higher importance to the \ac{mv} of \ac{pu} \MVDEPA than \ac{pu} \MVDEPB. 
+For this reason, in the \ac{mv} selection process, the proposed method assigns higher importance to the \ac{mv} of \ac{pu} \MVDEPA than \ac{pu} \MVDEPB.
 Moreover, in Figure~\ref{fig:mvdependencies} it can be observed that, although the number of \acs{mv}  predicted from the \acs{mv} of \ac{pu} \MVDEPC is higher than \ac{pu} \MVDEPA (6 and 4 \acs{mv}, respectively),
 the image area that depends on the former is smaller that the latter. This is due to the variable size of \acs{pu}.
 Therefore, the image area covered by all dependent \acs{pu} is separately  considered in the \ac{mv} selection process.
@@ -257,7 +257,7 @@ A_{D}(i) = \sum_{j=1}^{DV_i} ( w_j\times h_j ),\hspace{2mm} i = 1, 2 \cdots s,
 \end{equation}
 where $DV_i$ is the number of \acs{mv} dependent from $MV_i$, and $w_j$ and $h_j$ are the width and height of the corresponding \ac{pu}.
 A weighting factor is used to control the amount of bitrate overhead ($R_U$), by increasing the cost of the number of encoded bits based on the duration of the error propagation.
-This duration is given by the ratio between the distance from the current frame ($t_c$) to the next refresh frame ($t_I$) and the \ac{idr} period ($T_{I}$), combined with the control parameter $\alpha$.
+This duration is given by the ratio between the distance from the current frame ($t_C$) to the \HIGHLIGHT{previous refresh frame} ($t_I$) and the \ac{idr} period ($T_{I}$), combined with the control parameter $\alpha$.
 This weight varies in the range $\left[0;1 \right]$, achieving the lowest value for  intra-coded frames and the maximum  for the frame located immediately before an intra-coded one.
 In the proposed approach, for higher values of $\alpha$, less redundant \acs{mv} are selected.
 As pointed out before, this streaming stage operates on coded data and may be implemented at any point of the network, to increase robustness without fully decoding the stream. Note that the parsing operation represented in Figure~\ref{fig:proposedMethod} does not include decoding of the video frames. Furthermore, only one frame delay is introduced because the \ac{mv} selection process is performed on a frame-by-frame basis.
@@ -328,9 +328,9 @@ The error robustness achieved by the encoding-stage was firstly evaluated in reg
 Figure~\ref{fig:RecoveredExample} shows the visual impact of error propagation on a region of the decoded Frame \#10  when Frame \#9 is affected by errors, for Basketball Drill and Race Horses  sequences (the \ac{psnr} corresponds to the entire frame).
 The proposed method is compared with the method~in~\cite{ROPERefGenJan2010}, as both aim at reducing the error propagation.
 The method~in~\cite{ROPERefGenJan2010} uses filtered frames as reference for predictions, therefore, in case of errors, the effects of mismatched predictions are significantly reduced by the filtering operation (see Sub-Section~\ref{SECTION2:LeakyPred}).
-As shown in Figure~\ref{fig:RecoveredExample}, the proposed method is able to reduce the impact of mismatch decoding in comparison with the method~in~\cite{ROPERefGenJan2010}. 
-Although both methods still reveal some predictions mismatch leading to inaccurate reconstructed of the objects contours, the proposed method is able to achieve a smoother reconstruction, which leads to higher quality in terms of \ac{psnr}. 
-This is because, in frame \#10, these predictions that depend on the missing frame \#9 are not used throughout the entire frame, thus, approximately half of the predictions are not affected by errors. 
+As shown in Figure~\ref{fig:RecoveredExample}, the proposed method is able to reduce the impact of mismatch decoding in comparison with the method~in~\cite{ROPERefGenJan2010}.
+Although both methods still reveal some predictions mismatch leading to inaccurate reconstructed of the objects contours, the proposed method is able to achieve a smoother reconstruction, which leads to higher quality in terms of \ac{psnr}.
+This is because, in frame \#10, these predictions that depend on the missing frame \#9 are not used throughout the entire frame, thus, approximately half of the predictions are not affected by errors.
 In contrast, the method~in~\cite{ROPERefGenJan2010} requires several filtering operations to be applied (i.e, different reference frames need to be filtered) in order to reduce the effect of mismatched predictions.
 Summarising, the reconstructed frames illustrated in Figure~\ref{fig:RecoveredExample} reveal the higher efficiency achieved by distributing the use of the references frames.
 
@@ -364,7 +364,7 @@ In \cite{ROPERefGenJan2010}, the use of interpolated references in the encoding
 The proposed method is also able to outperform the \ac{hevc} reference software when an hierarchical coding structure is used (see results for \ac{ra} configuration in Table~\ref{tab:AverageQualityCHKBEXPRandomAccess}), which implicitly limits the error propagation.
 In comparison to the reference \ac{hevc}, quality improvements  up to $1.42$~dB  at PLR=$10\%$ are obtained for Kendo sequence.%, while the average gain across all test sequences is 1~dB.
 
-When comparing results for both test cases, it is noticeable that the proposed method is able to outperform the reference methods for both cases, regardless whether \ac{idr} frame loss is allowed or not (\LOSTALL and \KEEPINTRA, respectively). 
+When comparing results for both test cases, it is noticeable that the proposed method is able to outperform the reference methods for both cases, regardless whether \ac{idr} frame loss is allowed or not (\LOSTALL and \KEEPINTRA, respectively).
 As the \ac{plr} increases, the gains of the proposed method decrease in comparison with the case where the \ac{idr} frames are delivered error-free (i.e., case \KEEPINTRA), due to the higher error propagation of the missing \ac{idr} frame. Moreover, the quality gains are lower in the \LOSTALL case when comparing with \KEEPINTRA for the same \ac{plr}, for both the \ac{ld} and \ac{ra}.
 Taking into account the above results and the spatio-temporal information shown in Table~\ref{TableTestSequences}, one can observe that the performance of the proposed method is lower for sequences with high spatial details and low temporal activity (e.g., BQSquare and Park Scene), which indicates higher effectiveness for video content with higher motion activity.
 
@@ -422,9 +422,9 @@ Table~\ref{tab:bd_error_free} shows the Bjontegaard's Delta PSNR (BD-PSNR)  valu
 \end{table}
 
 The results in  Table~\ref{tab:bd_error_free} indicate a small loss of coding efficiency of the proposed method, as well as, the reference methods tested.
-The fixed checkerboard approach leads to an average quality reduction of $1.22$~dB for the \ac{ld} ($0.32$~dB for \ac{ra}), while the proposed method only loses $0.82$~dB and $0.24$~dB in the \ac{ld} and \ac{ra} configurations, respectively. 
+The fixed checkerboard approach leads to an average quality reduction of $1.22$~dB for the \ac{ld} ($0.32$~dB for \ac{ra}), while the proposed method only loses $0.82$~dB and $0.24$~dB in the \ac{ld} and \ac{ra} configurations, respectively.
 This results clearly show that dynamically selecting the reference frames is more efficient than using a fixed pattern, confirming the previous results for error-prone conditions.
-Moreover, in comparison to \LONG and the method in~\cite{ROPERefGenJan2010}, the proposed method is still more efficient, because it consistently achieves better results. 
+Moreover, in comparison to \LONG and the method in~\cite{ROPERefGenJan2010}, the proposed method is still more efficient, because it consistently achieves better results.
 Comparing, the results for both error-free and error-prone conditions, one may conclude that the proposed method not only achieves higher quality gains, but also reduces the impact on coding efficiency.
 Overall, the loss in the quality compared to the reference \ac{hevc} is considered acceptable, given the increase in robustness obtained in lossy transmission.
 
@@ -526,7 +526,7 @@ Thus, using the proposed two-stage approach to recover temporal predictions cons
 
 In this chapter a two-stage approach was proposed to increase the error robustness of \ac{hevc} streaming and reduce the error propagation in case of packet loss.
 A  constrained coding approach was devised to select reference frames and dynamically distribute temporal dependencies.
-This is jointly used with a controlled amount of side information in coded streams, comprising a small set of the most relevant \acs{mv}, in order to minimise \ac{mv} mismatch at the decoder in the presence of frame loss. The use of \acs{mv} as side information was firstly proposed and evaluated in the publication~(\ref{Conf:MotionVectorRedundancies}) and the reference frame selection was further discussed in the publication~(\ref{Conf:Chkb}). Subsequently, a wider analysis was carried out and published in (\ref{Journal:TwoStage}). 
+This is jointly used with a controlled amount of side information in coded streams, comprising a small set of the most relevant \acs{mv}, in order to minimise \ac{mv} mismatch at the decoder in the presence of frame loss. The use of \acs{mv} as side information was firstly proposed and evaluated in the publication~(\ref{Conf:MotionVectorRedundancies}) and the reference frame selection was further discussed in the publication~(\ref{Conf:Chkb}). Subsequently, a wider analysis was carried out and published in (\ref{Journal:TwoStage}).
 As can be concluded from the results, this method contributes to reduce the temporal dependencies with consistent quality gains for different \ac{plr} and coding configurations, only incurring in a small drop of coding efficiency.
 Overall, the proposed approach is an effective method to cope with video transmission over error-prone networks.
 

042_ConcealmentAwareEncoding/ConcealmentAwareEncoding.tex

@@ -354,7 +354,7 @@ where $R(m_{l,i})$ represents the number of overhead bits required to encode the
 
 
 In equation~\ref{EQ6:OptimalDepth}, besides the parameter $\lambda$, 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 next refresh frame ($t_I$) and the period of refreshing frames ($T_{I}$).
+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 \HIGHLIGHT{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.

carreira_phd_thesis.tex

@@ -16,7 +16,7 @@
 \selectoriginallanguage
 
 % \newcommand{\HIGHLIGHT}[1]{\textcolor{red}{#1}}
-%\newcommand{\HIGHLIGHT}[1]{\textcolor{red}{#1}}
+\newcommand{\HIGHLIGHT}[1]{\textcolor{red}{#1}}
 %\newcommand{\HERE}{\textcolor{red}{CHECK HERE!}}
 %\newcommand{\VERSION}[1]{\textcolor{red}{(r#1)}}
 \newcommand{\VERSION}[1]{}