Prompt : You are teacher who removes all abstractions, assumptions and teach from the  first principles . i have no knowledge in ai or machine learning and programming i want you to explain me from absolute beginning for me to understand this . teach only one part at a time deeply  and wait till i say continue to move on to next part 
'''
\begin{figure}
\centering
\vspace{-1em}
\includegraphics[width=\linewidth]{figs/preprocessing_overview.pdf}
\vspace{-1.5em}
\caption{Our preprocessing pipeline annotates both the source repository and the target video with phonemes and registers a $254$-parameter 3D head model to each frame of each video.
% Overview for the preprocessing pipeline. We preprocess both the
% repository and the target video with phoneme alignment and 3D head
% model registration. This gives us the phoneme label, start and
% end time for every phoneme in the videos, as well as $254$ face
% parameters at each frame.
}
\vspace{-1em}
\label{fig:preprocessing_overview}
\end{figure}

\begin{figure*}
\vspace{-1em}
\centering
\includegraphics[width=\textwidth]{figs/synthesis_overview.pdf}
\vspace{-2em}
\caption{Our synthesis pipeline adapts the pipeline of
Fried\etal\shortcite{Fried_2019} by introducing a fast phoneme
search and stitching step (yellow), and a self-supervised neural retargeting step (yellow).
% \maneesh{Only f'' should be highlighted in word fog''. Might be clearer to use a v'' word rather than an f'' word to stress the fact that we are considering visemes, not just phonemes.}\david{I'm trying to show overlapped subsequences here: fog for F-AH-K and ox for AH-K-S. But maybe there's no need to delve that deep in details here?} \maneesh{Showing the overlap makes the figure way too confusing. We should go back to what we had earlier.}
The input to our pipeline is a target video (green) and an edit (green) -- here
changing the word spider'' to fox''.
Our fast phoneme search
finds phonemes in the repository that visually match the desired edit
-- here the v'' in volume and the ox''
in box. We then stitch together the corresponding facial
expression parameters of the 3D head model for the source
repository actor, and use a novel neural retargeting model to
translate those parameters into those for the target actor.
Next, we expand the retargeted expression parameters to the full
face parameters (e.g. pose, illumination) for the target actor.
Finally we render photorealistic frames from the parameters using
a neural rendering approach that first composites the lower part
of the face rendered from the 3D head model, with background
pixels from the original target video and then uses a generative
adversarial network (GAN) to map the composites to photorealistic
frames. }
\label{fig:synthesis_overview}
\end{figure*}

\section{Method}
\label{sec:method}

Given a short talking-head video of a {\em target actor} (often 2-3
minutes in length), and an edit of the video transcript, our system
synthesizes new video of the target actor matching the edit. An
edit is specified as a replacement of one continuous sequence of words
in the original transcript with a new sequence of words. Since a
short target actor video is unlikely to contain all the lip motions
necessary to convincingly synthesize the sequence of phonemes in the
edit, we leverage a large {\em repository} of video from a different,
{\em source actor}.
%that contains the most common phoneme combinations
%(coarticulations) in English.
%
%Specifically, we pre-capture an hour of
%a source actor speaking the TIMIT corpus,\cite{garofolo1993timit} and
%retarget the lip motions of the source actor to the target actor
%during synthesis.
Specifically, we pre-capture an hour of a source actor speaking the
TIMIT corpus,\cite{garofolo1993timit} which includes the most common
phoneme combinations (coarticulations) in English and we retarget
their lip motions to the target actor during synthesis.


Our approach for quickly synthesizing the edited result is based on
the approach of Fried et al.,\shortcite{Fried_2019} but involves
several critical modifications. As in Fried et al.,
%\ohad{wording a bit confusing, since Fried19's repository is not the
%same as ours (different person)},
our {\em preprocessing pipeline} (\Cref{fig:preprocessing_overview})
annotates both the repository and target videos with phonemes and
registers a parametric 3D head model to the face in each frame of each
video. Our {\em synthesis pipeline} (\Cref{fig:synthesis_overview})
provides a new, fast phoneme search algorithm that finds subsequences
of phonemes in the source video that match the desired edit. It then
stitches together the corresponding parameters of the 3D head model
for the source actor across subsequence boundaries to smooth the lip
motions. We introduce a new self-supervised neural
retargeting step that adapts the parameters representing the lip
motion of the source actor to those of the target actor and blend the
resulting parameters into the target video. Finally we render
photorealistic frames from the parameters using neural rendering,\cite{tewari2020state}.
%\maneesh{cut next sentence for space?}\david{No objections.}
%The speed of our synthesis
%pipeline enables iterative editing and our tool provides additional
%controls for refining lip motions, inserting non-verbal mouth gestures
%and manipulating speaking style.

We briefly summarize how we adapt each step in Fried et al.'s
pipelines to our problem in Sections\ref{sec:preprocessing_overview}
and\ref{sec:synthesis_overview}. We then present the details of our
new algorithms; fast phoneme search and stitching in \Cref{sec:search} and neural retargeting algorithm in
\Cref{sec:retargeting}. In\Cref{sec:interaction}, we
describe the iterative refinement and performance controls enabled by
our approach.

%% \maneesh{This high-level summary of the approach might be useful for
%% the intro or abstract.} We achieve this by representing the face
%% shape at each frame of the video with parameters for a 3D head model,
%% then synthesizing a time series of parameters that animates the face
%% to speak the new words, and finally rendering the parameters into
%% photorealistic frames of a talking head to replace the frames that
%% speak the original words.

\subsection{Preprocessing Pipeline}\label{sec:preprocessing_overview}
Our preprocessing pipeline annotates each frame of the repository and
the target videos in two main steps, (1) phoneme alignment and (2)
registration of a parametric 3D head model. These resulting phoneme
and face parameter annotations are used by our synthesis pipeline to
establish correspondences between the target video and source
repository. Note that the repository is only annotated {\em once} and
the resulting {\em annotated repository} is then bundled as part of the
system. In contrast, the target video must be annotated each time a
new target video is given as input.

\paragraph{Phoneme Alignment}
The phoneme alignment step takes as input a video (repository or
target) paired with its text transcript, and computes the identity and
timing of the phonemes in the video. Specifically, we use
P2FA,\cite{yuan2008p2fa,rubin2013p2fa} to convert the transcript into
phonemes and align them to the audio speech track of the video. This
produces an ordered sequence $V=(v_1, \ldots, v_n)$ of phonemes, where
each phoneme $v_i$ contains its name, start time and end time.
% We manually fix gross misalignments if they occur (about 10 instances in
%an hour-long video). \maneesh{Delete point about misalignments for space.}
If the transcript is not available, we can
obtain one using a transcription service such as Google Cloud
Speech-to-Text,\shortcite{googlecloudstt}, or
rev.com,\shortcite{rev}.

\paragraph{3D Head Model Registration}
We fit a parametric head
model,\cite{blanz1999facemodel,ThiesZSTN2016a} to each frame of
video using a monocular head
tracker,\cite{garrido2016reconstruction}. At every frame, the fitted
model includes 80 parameters for 3D facial geometry, 80 for facial
reflectance, 3 for head pose, 27 for scene illumination and 64 for
face and lip expressions. In the fitting procedure we hold the facial
geometry and reflectance parameters constant across all the frames of
the same actor, but we allow the pose, illumination and expression to
vary across time.

\subsection{Synthesis Pipeline}
\label{sec:synthesis_overview}

Our synthesis technique is based on matching phonemes in the edit
to phonemes in the repository. Therefore, we first convert the input
text of the edit from words into a sequence of phonemes $W=(w_1,
\ldots, w_m)$, where each phoneme contains its name, start time and
end time.
% \maneesh{I shorted prev. 2 sentences. Orig. longer version is in comments.}
%Our synthesis pipeline takes a target video and an edit as input, and
%generates a video of the target actor that matches the edit. Since
%our synthesis technique is based on matching phonemes in the edit to
%phonemes in the repository, we start by converting the text of the
%edit into a sequence of phonemes $W=(w_1, \ldots, w_m)$, where each
%phoneme contains its name, start time and end time.
%
Specifically, we convert the edit into audio using either
%\maneesh{either a library of voice recordings of the target actor},
text-to-speech voice
synthesis,\cite{wavenet2016,googlecloudtts} or voice cloning techniques,\cite{kumar2019lyrebird,lyrebird},
and then apply P2FA,\cite{yuan2008p2fa,rubin2013p2fa} to
time-align the resulting speech to the phonemes of the edit.
%
Note that our synthesis algorithm only uses the timing of the phonemes
and does not use any other aspect of the synthesized speech audio
signal.
%\maneesh{Do we need prev sentence?}
%
%% Specifically, we use either
%% text-to-speech,\cite{wavenet2016,googlecloudtts} or voice
%% cloning,\cite{jia2018sv2tts,jin2017voco,kumar2019lyrebird} to convert
%% the edit into audio and then apply
%% P2FA,\cite{yuan2008p2fa,rubin2013p2fa} to time-align the resulting
%% speech to the phonemes of the edit.
%
% If the user later captures a recording of the target actor saying the
% new content, they can re-run our fast synthesis pipeline with the new
% timings obtained from the real recording. \maneesh{May want to update
% last line depending on how we talk about real-voice results.}
% \david{If the user is the target actor, they can record speaking the
% new content in real time and use our fast synthesis pipeline with
% timings from the real recording.} \maneesh{Previous sentence is the
% more likely scenario and should be combined with the sentence about
% recording the actor later.}
% \maneesh{Can next sentence (not highlighted) replace sentence starting at ... If the user later captures ...}
If the user has access to the audio of the target actor saying the new
content (either from a prerecorded library of the actor's speech or
recorded by the actor in real-time during editing) they can run
our fast synthesis pipeline with the timings obtained from the
real-voice recordings.



\paragraph{Fast Phoneme Search and Stitching}
The fast phoneme search and stitching step is designed to quickly find the best
subsequences of phonemes in the repository and then stitch together the corresponding
expression parameters of the source actor 3D head model, in order to produce the
the edit $W$ we wish to synthesize.
% \maneesh{We need to say more about the stitching as we did in the previous version of the paper -- from what is written here it is unclear what stitching does. Need to say it ... stitches together the corresponding expression parameters of the source actor 3D head model to produce the edit $W$ we wish to synthesize....
% while conforming to the phoneme timing specified in the edit $W$ we wish to synthesize.}
Our new algorithm
operates three orders of magnitude faster than
Fried\etal\shortcite{Fried_2019} and finds the best repository
subsequences in seconds rather than hours. We present this fast
algorithm in detail in\Cref{sec:search}.
%\maneesh{May want to elevate into intro that we are 1000x faster than Fried19.}
%The result
%of this step is a set of phoneme subsequences from the repository that
%match the edit. \maneesh{Perhaps kill final sentence for space.}
%This step turns the edit into phoneme subsequences found in the repository.

% \paragraph{Subsequence Stitching} \david{Needs to be rewritten. Probably should not be its own subsection.
% It should briefly talk about the forced MBP closure, blending
% overlapping intervals and Gaussian smoothing across each boundary.}
% \maneesh{I wonder if we should just combine this step with fast phoneme search in our pipeline and talk about what we do new at the end of section 3.3. Will require changing Fig 3 a bit to remove Subsequence stitching as a step. Could change name of Fast Phoneme Search to Fast Phoneme Search and Stitching}
% The stitching step takes the subsequences of phonemes found in the
% repository, looks up the corresponding expression parameters of the 3D
% head model and combines them together into a continuous sequence that
% conforms to the phoneme timing specified in the edit. More
% specifically, we linearly retime the expression parameters
% corresponding to each phoneme in each repository subsequence to match
% the phoneme duration specified in the edit. We then connect adjacent
% subsequences by smoothing over a window of 4 frames around the
% subsequence boundaries, to obtain a single temporally coherent
% sequence of source actor expression parameters corresponding to the
% edit.
%\maneesh{We are switching between calling them head parameters'' and face parameters''. Need to make consistent.}

\paragraph{Neural Retargeting}
The retargeting step converts a sequence of expression parameters for the source actor into those for
the target actor.
We introduce a
learned retargeting model, trained in a self-supervised manner from
corresponding pairs of
repository and target video sequences and transforms the expression
parameters as detailed in\Cref{sec:retargeting}.
%
%% Our retargeting method needs only a few minutes of video from target
%% actor and significantly lowers the data requirement on the target
%% video to about 2--3 minutes for high-quality results. \ohad{we can
%% add: "compared to, e.g., the method of Friedetal. which requires
%% ~1.5 hours"}.
%
The result is a sequence of target actor
face expression parameters corresponding to the edit.


\paragraph{Expansion to Full Parameters}
Next, we combine the synthesized target actor expression parameters
with geometry, reflectance, pose and illumination parameters from the
input target video to
produce a sequence of full face parameters for the target
actor corresponding to the edit.
%Next, we augment the newly synthesized target actor expression
%parameters with head pose and illumination parameters from the target
%video, to produce a sequence of full face parameters for the target
%actor.
Specifically, we take an interval of frames around the edit location
in the target video, retime it to account for the duration of the
edit, and use the geometry, reflectance, pose and illumination
parameters from the retimed interval.
%
%% \maneesh{I edited the
%% next sentence, but I'm not sure I really understand what we are
%% doing. I'm also not sure we need to include it as it is a detail.}
%% To ensure that the synthesized expression parameters fit seamlessly
%% back in the target video, we smooth the expression parameters at both
%% ends of the edit boundary with respect to the original expression
%% parameters in the target video.

\paragraph{Neural Rendering}
The neural rendering step takes the sequence of full face
parameters for the target actor and first generates a composite image
in which the lower face region is a rendering of the 3D head
model, while the upper part of the head and the surrounding background
are from the original target video, but retimed to match the length of
the edit. It then uses a GAN trained on the target video to
complete the image-to-image translation from composite image to
photorealistic frame.

%% The neural rendering step produces the final frames corresponding
%% to the edit by synthesizing each frame from the full face
%% parameters for the target actor. We produce an intermediate
%% composite image by masking out the lower face region in the
%% original frame, replacing it with the synthetic render of the lower
%% face of the 3D head from the new face parameters, and finally use a
%% GAN (based on Fried\etal\shortcite{Fried_2019}) trained on the
%% target video to complete the image-to-image translation from
%% composite image to photorealistic frame.

\input{method-search}

\input{method-retargeting}

\input{method-interaction}

\input{method-runtime.tex}

%% LocalWords: photorealistic retargeting retimed coarticulations
%% LocalWords: viseme coarticulation retargeted datasets TIMIT PCA
%% LocalWords: dataset renderer Preprocessing misalignments Garrido
%% LocalWords: crowdsourcing reflectance blendshapes et retarget al
%% LocalWords: preprocessing visemes subsequence Ohad RNN relu pre
%% LocalWords: regularizer Hyperparameters minibatch Tensorflow len
%% LocalWords: memoization bigram unigram bigrams runtime retime
%% LocalWords: retiming subsequences lbl GAN iteratively
%% LocalWords: levenshtein googlecloudstt


\subsection{User Controls} \label{sec:interaction}
%As we will show in Section\ref{sec:runtime} our synthesis pipeline
%can generate video corresponding to a typical edit in about
%40 seconds.
This speed of our synthesis pipeline opens
the door to interactive user controls for iteratively refining the
edit and further manipulating the the facial performance.

%% \begin{figure}
%% \centering
%% \includegraphics[width=\linewidth]{figs/ui.pdf}
%% \caption{The user interface of our tool.}
%% \label{fig:ui}
%% \end{figure}

\paragraph{Refinement Control: Smoothing jumpy transitions}
Our synthesis pipeline stitches together different subsequences of
expression parameters from the source repository by smoothing over a
window of 4 frames around the transition boundary
(Section\ref{sec:search} Fast Phoneme Search and Stitching). At
times however, some transitions may still appears jumpy even after
this smoothing.
%\maneesh{the smoothing introduced by} retargeting model inference.
%\maneesh{Unclear why we are mentioning retargeting inference when we
% first talked about stitching. I added something about smoothing
% introduced, but I don't really understand why retargeting would
% introduce smoothing.}
We allow the user to inspect the result and
further refine it by manually specifying the interpolation radius (in
number of frames) at user-specified transition boundaries to better smooth out visibly
jumpy transitions.

\paragraph{Refinement Control: Adjusting mouth closure}
%\david{Need to rewrite this paragraph. Instead of mentioning forced
% MBP closure in previous sections, an alternative is to introduce it
% here. Since we force-blend MBP shapes automatically already, this
% control is really for adjusting the strength of the blend.}
%\maneesh{I don't think we need to be so detailed about this and can keep it mostly as is. We should discuss.}
%\david{Most content here are now in \Cref{sec:search} when introducing forced MBP mouth closures.}
% \maneesh{Updated section... May want to call it ``Adjusting mouth closure'' I'm not sure. Old version of paragraph is in comments.}
As noted in Section\ref{sec:search} mouth closure on \textbackslash
m, \textbackslash b and \textbackslash p phonemes is crucial for the
mouth motions to appear realistic. Thus our stitching procedure
automatically inserts 2 closed mouth frames at the beginnings of these
three phonemes to ensure the mouth closes correctly for them. We
further allow users refine any synthesized result by
extending (or reducing) the length of the inserted closed mouth
frames.
%
%% Our automated pipeline sometimes fails to fully close the mouth of the
%% target actor properly, such as at the beginning of \textbackslash m,
%% \textbackslash b, \textbackslash p phonemes, due to either inaccurate
%% phoneme alignment in the repository or smoothing from subsequence
%% stitching. We allow the user to inspect the result and further refine
%% it by blending in a manually-annotated closed-mouth expression from
%% the repository at the specified location with different effect radius
%% before the retargeting. Note that we manually annotate the closed
%% mouth expressions in the repository once during repository
%% preprocessing, and later automatically use the one closest to the
%% current parameter values at the specified location when the user
%% inserts it.


\paragraph{Performance Control: Inserting mouth gestures}
%\david{recent rewrite}
Users can also insert non-verbal mouth gestures (e.g. a smile)
into an edit. To enable such performance control we manually annotate
mouth gestures including {\em rest, closed-mouth smile, regular teeth-showing
smile, big open-mouth smile, sad, scream, mouth gesturing left} and
{\em mouth gesturing right,} in the repository video. These segments can
then be retrieved by our fast phoneme search just like any other
phoneme annotation.
%\maneesh{I think showing some more of these in our results would help
% -- the mouth left and right gestures are a bit uncommon -- it would
% be great to think of examples that make sure of scream, and sad.}
%\maneesh{Make sure all expressions are shown in some example in the supplemental materials and show generalization -- that is input target video did not contain a gesture but we can still synthesize it.}

Since the annotations are on the repository, this manual annotation only
needs to be done once during repository preprocessing. Note however, that
users do not label the target video with these mouth gestures and our
retargeting network is never explicitly trained with corresponding
pairs of mouth gesture frames between the repository and target
videos. Nevertheless, we have found that our retargeting network is
able to generalize to unseen expressions and produce good quality
expression parameters for the target actor.
%\maneesh{Would be good to show more results of just the gestures generalizing to new target actors.}

With these annotations, the user can add special {\em mouth gesture
directives} like [smile] anywhere in their edit of the
transcript, and our tool constructs a generalized phoneme'' edit<br/>sequence $W$ that contains phonemes and such directives. Any mouth<br/>gesture that appears in $W$ is given a default duration of $0.5$<br/>seconds that the user can override with an explicit duration<br/>e.g. [smile:1.5s]. We employ a special substitution cost in<br/>$\cmatch$ described in \Cref{sec:search} for gesture phonemes'' that
is set to infinity for a non-match to ensure that we retrieve the
correct phoneme'' match for the gesture. When there are multiple<br/>candidates, $\cmatch$ takes duration into account and picks the<br/>gesture with duration closest to the query. The rest of the editing<br/>pipeline (\Cref{sec:synthesis_overview}) is otherwise unmodified.<br/>% \ohad{there are way too many quotation marks'' in this paragraph}

\paragraph{Performance Control: Adjusting speaking style}
%\david{recent rewrite}
Our tool allows the user to select a different speaking style for the
synthesized result by using a version of the repository with the
desired style. In addition to the default repository which captures a
neutral'' speaking style, we have recorded an energetic''
repository of our source actor with more pronounced mouth movements,
and a mumble'' repository with significantly less mouth movements. Figure~\ref{fig:sessions} (third row) shows<br/>frames from these alternative repositories.<br/><br/><br/>Importantly, we do not have to retrain our neural retargeting model<br/>(\Cref{sec:retargeting}) for each additional style repository. We<br/>train this retargeting model once using only the default neutral<br/>repository.<br/>%<br/>We have found that our default retargeting model can extrapolate to<br/>retarget subsequences of source actor face parameters retrieved from<br/>other speaking style repositories of the same actor. Moreover, the<br/>other repository videos can be captured at different times, with<br/>different background and the source actor can even be wearing<br/>different clothes or have a different hairstyle. <br/>%\maneesh{probably should say this point earlier or reinforce in limitations section..}<br/>Thus, our tool generates videos with different speaking styles by<br/>using one of the alternative style repositories in the fast phoneme<br/>search step, but leaves the remainder of the synthesis pipeline<br/>unchanged.<br/>%\maneesh{Make sure supplemental materials contains examples of each style we say we can do. Since a reviewer asked about this one I wonder if we can find an even more exaggerated example -- perhaps on David or Ayush.}<br/>%\maneesh{Again, would be good to show this in some more detail in our results. In fact I think a reviewer asked bout this one specifically, so adding more results on this would be very helpful.}<br/><br/>%% retarget subsequence retrieved from<br/>%% different versions of the repository with the same source actor but<br/>%% speaking with different styles.<br/><br/><br/>%% Recall that our neural retargeting model maps the source actor expression<br/>%% parameters to target actor parameters (\Cref{sec:retargeting}).<br/><br/><br/>%% When the user chooses a different speaking style, we<br/>%% still apply the neutral retargeting model as we have found that it can extrapolate<br/>%% to subsequences retrieved from<br/>%% different versions of the repository with the same source actor<br/><br/>%% We have found that the same retargeting model trained on the<br/>%% natural style repository can extrapolate to subsequence retrieved from<br/>%% different versions of the repository with the same source actor but<br/>%% speaking with different styles.<br/><br/>%% Moreover, the other repository videos<br/>%% can be captured at different times, with different background and the<br/>%% source actor can even be wearing different clothes or have a different<br/>%% hairstyle.<br/><br/>%% In particular, we have recorded an<br/>%% energetic'' repository of our source actor with more pronounced
%% mouth movements, and a ``mumble'' repository with significantly less
%% mouth movements.


%% Our system can then generate videos with a different
%% speaking style by using one of the alternative repositories. Note that our
%% neural retageting pipeline
%% The rest of the synthesis pipeline
%% described in \Cref{sec:synthesis_overview} works unchanged.

%% \maneesh{May need to make a bigger deal of this. Mention this in
%% limitations -- recording source actor takes time, but can likley do
%% it in more than one setting and sitting.}

% LocalWords: iteratively subsequences Subsequence subsequence
% LocalWords: retargeting preprocessing retarget


\subsection{Neural Retargeting}\label{sec:retargeting}
Given a stitched-together sequence of face expression parameters for
the source actor in the repository, the goal of retargeting is to
generate a matching sequence of expression parameters for the target actor.
%\ohad{should we add a sentence explaining why these two sets of
% parameters are different in the first place?}
We have developed a self-supervised neural network model for retargeting
and in Section\ref{sec:eval_algo_data} we show that
using a neural network for retargeting produces
%%with self-supervision based on
%%corresponding pairs repository and target video
%%visemes
%%produces
higher-quality results than baseline
methods such as directly copying source actor expression parameters to
the target actor, or applying a linear retargeting model.

%as we will show in \Cref{sec:eval_retarget}. \maneesh{May want to
% move the comparison to end of this section.}

\begin{figure}
\centering
\includegraphics[width=\linewidth]{figs/correspondence.pdf}
\caption{To automatically build training data for our neural
retargeting model, we consider a sequence of phonemes $S$ (red) in
the repository and find up to two best matches $T^A$ and $T^B$ (red)
in the target video.
%
%
% Phonemes in the video are represented as cells. For a
% sequence $S$ (red) in the repository, we find up to two best matches
% $T^A$ and $T^B$ (red) in the target video.
We then find
matches for the next repository sequence (green) starting at
the last phoneme of the previous sequence. The overlap allows
us to capture the phoneme transition out of the final phoneme in the red subsequence.}
\label{fig:build_correspondence}
\end{figure}

\paragraph{Self-supervised training data}
%\david{recent rewrite}
To train our retargeting network we require sequences of expression
parameters for the source and target actor that correspond to one
another with respect to their mouth motions. Assuming that uttering
the same sequence of visemes will produce similar mouth motions, we
automatically construct corresponding pairs of training data by
finding the longest matching sequences of phonemes between the source
repository video and the target video, as follows.

Since we apply our retargeting model to a stitched-together
subsequences of phonemes that can come from anywhere in the source
repository, we would like the training sequences to cover as much of
the repository as possible.
Therefore, we start from the first phoneme $s_1$ in the
repository, and find the longest sequence $S=(s_1,\ldots,s_k)$ for
which there is at least one corresponding sequence
$T=(t_1,\ldots,t_k)$ in the target video where $t_i$ and $s_i$ belongs
to the same viseme group (i.e. phonemes that require the same lip expressions
are in the same viseme group).
We take up to two best matches in the
target video with respect to $\cmatch$ score defined in
\Cref{sec:search}, and call them $T^A=(t^A_1,\ldots,t^A_k)$ and
$T^B=(t^B_1,\ldots,t^B_k)$. We add the pairs $(S,T^A)$ and $(S,T^B)$
to the set of phoneme sequences in correspondence, and continue the
scan through the source repository at $v_k$, until we finish scanning
through the entire repository for subsequence matches
(\Cref{fig:build_correspondence}). To quickly find the best $T^A$ and
$T^B$ sequences in the target video, we apply fast search techniques discussed
in \Cref{sec:search}.
%
Finally, to convert each resulting phoneme sequence pair into a parameter
sequence pair, we linearly retime the target video phoneme interval to
the corresponding repository interval and similarly interpolate the
% corresponding
expression parameters.
The retargeting model is trained once for each new target video.
%\maneesh{Are we now doing this in a context aware way? Also have we
% tried using more than the top two matches? I wonder if considering
% more matches would help us get the mouth to open when it should.}
%\david{
% Our neural retargeting step is unchanged from January submission.
%}
%\maneesh{ok, but in the paper here we say we use the score defined in section 3.3 and that score is described in a context-aware way so the assumption would be that we would be doing this here in a context aware way. My sense is that we should try the context aware approach if we are not doing it that way now.}

%% Note that because of coarticulation effects, the phonemes at the start
%% and end of a sequence may not produce similar mouth motions in the
%% corresponding repository and target videos. We therefor discard first
%% half of the frames in the first phoneme interval and last half in the
%% last interval, effectively discarding all single-phoneme sequence
%% pairs. \maneesh{This is a detail we might consider removing later.}

\begin{figure}
\centering
\includegraphics[width=\linewidth]{figs/network.pdf}
\caption{The retargeting network with the unrolled recurrent unit $F$, which looks two frames back at each time step and uses the previous two outputs as its state.
The diagram shows how the RNN processes the input of $T$ frames of source actor parameters $(s_1, s_2,\ldots,s_T)$ and produces the prediction for $T$ frames of target actor parameters $(t_1, t_2,\ldots,t_T)$.}
\label{fig:retargeting_network}
\end{figure}

\paragraph{Neural Network Architecture}
%\david{recent rewrite}
We employ a recurrent neural network (RNN) manually unrolled for $T$
time-steps to encode the temporal dynamics of the facial expressions
and regress from source parameters to target parameters
(\Cref{fig:retargeting_network}). The resulting network takes as
input $T$ frames of $64$ expression parameters for the source actor,
and outputs $T$ frames of $64$ parameters for the target actor. At
the core of the network is the recurrent unit that is made up of $3$
fully connected layers of $1024$ nodes with relu activation. The
inputs to the recurrent unit are $64$ expression parameters of the
current time-step, as well as the parameters and outputs of the
recurrent unit for the previous $H$
%\maneesh{I am a little lost. Is H shown in the figure at all? Feels
%like it should be.} \david{The figure only shows the case for $H=2$
%which is what we used.}
time-steps. To facilitate
learning of deviations from the identity transformation, the output
layer of the recurrent unit with $64$ nodes and no activation produces
the residual values that are added to the input source parameters
element-wise to obtain the prediction for the target parameters for
the current time-step. We zero-pad the unavailable inputs at the
first $H$ time-steps. We empirically found that setting $H=2$ and
$T=7$ produced high-quality retargeting results.

\paragraph{Loss function}
%\david{recent rewrite}
Our loss function is a linear combination of a data term and a
temporal regularizer with regularization weight $\lambda$:
$$\mathcal{L} = \frac{1}{T}\sum_{i=1}^T \|F(s_i)-t_i\|_1 +
\lambda\|F^{(2)}(s_i)\|_2$$
where $s_i,t_i$ are $64$-dimensional vectors representing the $i$th time-step of the source and target parameters
respectively,
$F(s_i)$ is a $64$-dimensional vector of the predicted target actor parameters and
$F^{(2)}(s_i)$ is a $64$-dimensional vector that is the second temporal difference
vector, or acceleration, of the predicted values.
Empirically
we found that using an $L_1$ norm for the data term significantly outperforms
$L_2$ by generating more expressive motions and better preserving mouth closures.
The temporal regularization term is needed to make the network
predict temporally stable parameters.

\paragraph{Hyperparameters and training}
Since the network takes a fixed-size input of $T$ frames, we run a
sliding window on each matching parameter sequences to obtain the
training examples. Experimentally we set the temporal window $T=7$
frames. For training we set $\lambda=10$, and dropout rate at 25%,
50% and 25% for the three layers in the recurrent unit,
respectively. To train the network we use stochastic gradient descent
with the Adam solver,\cite{Kingma2014Adam} and set an initial learning
rate of $0.0002$ with an exponential decay rate of $0.5$. We employ
gradient clipping,\cite{pascanu2013clipping} to avoid exploding
gradients. We train the network with minibatch size $100$ and
training typically converges within $100$ epochs.

\paragraph{Inference}
At inference time, we convert a sequence of source actor expression
parameters into target actor parameters. Since our retargeting model
accepts fixed-size $T$ frames of input and produces $T$ frames of
output, we run a sliding window of length $T$ over the new sequence of
source actor expression parameters at inference time. Each frame is
covered by exactly $T$ such sliding windows. In order to obtain a
more temporally stable output, at each frame we average the $T$
outputs produced by those $T$ sliding windows as the final output of
the frame. The result is a synthesized sequence of target actor
expression parameters that animate the face to speak the new content
of the edit with the desired timing.
We then proceed to expand these expression parameters into parameters
for the whole head and use neural rendering to generate the video frames
(\Cref{sec:synthesis_overview}).

\vspace{0.5em}
Training our retargeting model typically requires 2--3 minutes of
target actor video speaking arbitrary speech to produce high-quality
synthesis results. Retargeting allows our tool to leverage the large
repository of controlled source actor video (speech consists of TIMIT
sentences) to generate the target actor lip motions and opens our tool
to many practical applications where large amounts of controlled
target actor video are not available.

% LocalWords: retargeting na ve eval retarget uncanniness viseme RNN
% LocalWords: visemes subsequence bigram retime coarticulation Ohad
% LocalWords: relu regularizer th Hyperparameters minibatch TIMIT NN
% LocalWords: Tensorflow cmatch subsequences


\subsection{Implementation Details}
\label{sec:runtime}
%\maneesh{I think this stuff on running time should either go in an implementation section before results -- and also show the source actor video, or somewhere in the results section.}
%\maneesh{I think we should call this implementation and open by describing the machine that we've implemented on -- NVIDIA GTX... Then give running times.}
We implemented the fast phoneme search in Python and both our neural
retargeting model and the GAN renderer in
TensorFlow,\cite{tensorflow2015}. The monocular head tracker and
renderer are written in C++ with shader language extensions.

In preprocessing the repository and target videos, phoneme
alignment takes one third of the video time, and face registration takes
110 ms per frame. It takes 30 minutes to generate training data for
our neural retargeting model and another 30 minutes to train it on one NVIDIA
GTX 1080Ti. Training the GAN for neural rendering takes 17 hours on
one NVIDIA Tesla V100.
%Preprocessing, retargeting model training and
%neural renderer training is done once for each target video.


In our synthesis pipeline,
our fast
phoneme search requires 5 seconds for a
typical edit of
5 words containing 20 phonemes. Retargeting inference speed is 10K
fps. Composite images are rendered at 12 fps and final GAN rendering
takes 7 fps on two NVIDIA GTX 1080Ti. All together, a typical 5 word edit takes
around $30$ seconds for the full video generation (\Cref{tab:runtime}).
%We have also
%profiled our tool on edits of varying length and the runtime summary
%is in \Cref{tab:runtime}.

\begin{table}\small
\centering
\begin{tabular}{cccSSS}
\toprule
{#words} & {#phonemes} & {#frames} & {search (s)} & {render (s)} & {total (s)} \
\midrule
1 & 4 & 24 & 1.51 & 9.96 & 12.39 \
% 2 & 10 & 32 & 2.12 & 10.00 & 15.45 \
3 & 15 & 49 & 2.67 & 12.94 & 20.30 \
% 4 & 18 & 53 & 4.18 & 13.56 & 22.26 \
% 5 & 23 & 66 & 6.21 & 16.74 & 28.25 \
6 & 25 & 72 & 5.32 & 17.74 & 28.95 \
% 7 & 27 & 71 & 6.68 & 17.70 & 29.89 \
8 & 39 & 105 & 7.57 & 24.33 & 37.97 \
% 9 & 45 & 109 & 9.58 & 25.58 & 41.43 \
10& 49 & 134 & 11.60 & 31.19 & 50.60 \
% 19& 71 & 174 & 15.41 & 39.21 & 63.02 \
\bottomrule
\end{tabular}
\caption{Runtime of our tool on a variety of edit lengths.
Search time scales roughly linearly with the number of phonemes, and render time scales linearly with the number of frames.
Even for long edits of 10 words, our system can generate video in approximately a minute.}
\label{tab:runtime}
\vspace{-3em}
\end{table}

It should be possible to further reduce the feedback time by
parallelizing our synthesis pipeline. Phoneme search could be
distributed where each worker job is responsible for searching a
fraction of the repository. Both parts of the neural rendering step
-- forming the composite images from target actor head parameters and
applying the GAN to generate photorealistic frames -- are
parallelizable by distributing the frames. \new{We have performed
initial experiments on parallelizing the GAN rendering which is the main bottleneck in our pipeline. Distributing the GAN rendering
across a cluster of 8 NVIDIA Tesla V100s
achieved a rendering rate of 24fps, a 3.4x speedup from the original 7fps for this step. Note that this speed up rate includes image compression overhead. Overall this experiment cuts the end-to-end synthesis time from $40$
to $20$ seconds for a typical 8-word sentence.} Similarly parallelizing the other parts of the pipeline and using sufficient hardware we believe that the end-to-end video generation feedback time could
be reduced significantly. Streaming the frames as they are ready
could also further reduce the latency from issuing an edit to seeing
the first frames of the result, enabling real-time interactive editing
sessions.
%\maneesh{Perhaps should say this more strongly and emphasize it more. Make the case that we should be able to get to interactive rates.}

% LocalWords: retargeting GAN renderer shader preprocessing GTX
% LocalWords: cccSSS parallelizing photorealistic parallelizable


\subsection{Fast Phoneme Search and Stitching}\label{sec:search}
Our synthesis pipeline takes an edit $W$ specified as a sequence of
phonemes with timings $(w_1, \ldots, w_m)$ and starts by finding
matching subsequences of video in the source repository $V$, that can be
combined to produce $W$.
% \david{Do we talk about vanilla Fried'19 here or
% go straight to context-aware search? I think it's more clear to recap Fried19 as is done here,
% and talk about the improvement later, although that might make the novelty appear more incremental.}
% \maneesh{I think we just want to lightly lace it into what is already here. Isn't it just that we partition the edit into slightly overlapping subsequences?}
More precisely, we partition the edit $W$
into phoneme subsequences $(W_1, W_2, \ldots, W_k)$ and for each
subsequence $W_i$ find its best match $V_i$ in the repository $V$.
%
Fried\etal,\shortcite{Fried_2019} use a brute-force method that
considers all possible partitions $\mbox{split}(W)$ of the edit $W$,
and all possible matches with subsequences of $V$ to find $(V_1, V_2,
\ldots, V_k)$ that minimizes the objective:
$$C(W,V)=\min_{\substack{
(W_1,W_2,\ldots,W_k)\in\mbox{split}(W)\\ (V_1,V_2,\ldots,V_k)
}}\sum_{i=1}^k \cmatch(W_i,V_i) + C_{\mbox{len}}(W_i)$$ where
$\cmatch$ is a custom Levenshtein edit
distance,\shortcite{levenshtein1966} between two phoneme subsequences
that takes into account the phoneme label, the viseme label and the
timing difference, and $C_{\mbox{len}}$ penalizes short subsequences.
In order to find subsequences that transition well at their
endpoints, during the search, we expand each subsequence $W_i$ by a
single phoneme on either end. Thus, adjacent subsequences overlap by
two {\em context} phonemes. We find that this new {\em context expansion}
approach better captures co-articulation effects between the
subsequences, than the algorithm of Fried et al. which does not use
context expansion (see user studies in \Cref{sec:user_study}).
% Note that unlike Fried et al, we
% expand each $W_i$ by one phoneme on either side during this search so that adjacent subsequences overlap by a phoneme.
% In practice we have found that we
% obtain better transitions between the matching phoneme subsequences using
% this {\em context aware approach} as the overlapping phonemes better
% account for coarticulation effects.}
%\david{In order to find subsequences that transition better from one into the next, we
%employ a new \emph{context aware} scheme where each $W_i$ is expanded to include the phoneme before and after.}
%\maneesh{Prev sentence is a little unclear -- I put an alternate version earlier. What do you think?}

We further modify Fried et al.'s search algorithm in three key
ways to obtain a speedup of over 3 orders of magnitude: (1) we propose
a fast alternative to to the Levenshtein distance, (2) we reduce the
size of the search space on $W_i$ and, (3) given $W_i$, we use a
viseme-based indexing scheme to quickly find the optimal $V_i$.
%\maneesh{Move context awareness to here as ... In addition, unlike Fried et al., we expand each subsequence $W_i$ by one phoneme (i.e. a context phoneme) on either side so that the resulting matches from the repository overlap by a phoneme on each end. In practice we have found that we obtain better transitions between the phoneme subsequences using this {\em context aware approach} as the context phonemes better handle coarticulation effects.}
Finally, we stitch together source actor expression parameters corresponding to the $V_i$s
to produce a single coherent sequence of expression parameters.
% \maneesh{Probably need to mention stitching in a short sentence here as we will not how a paragraph or two on that.}

\paragraph{(1) Fast alternative to edit distance}
The full Levenshtein edit distance allows substitution, insertion and
deletion of phonemes when computing $\cmatch$. However, we have observed that when the
matching subsequences between the edit $W$ and the repository
video $V$ contain phoneme insertions or deletions, the final
synthesized video appears out-of-sync with the audio; it either
contains extraneous mouth motions due to phoneme insertion, or it
misses mouth motions due to deletion. In practice we find it is beneficial
to disallow insertions and deletions and only allow phoneme
substitutions. Given a subsequence $W_i$ of the edit $W$, this approach
forces $\cmatch$ to only consider subsequences $V_j$ of the
repository $V$ that contain the same number of phonemes as $W_i$. We
can therefore replace the Levenshtein distance with the sum of
element-wise substitution cost which requires linear time in the
number of phonemes rather than the quadratic time required for
computing the full Levenshtein distance,\cite{wagner1974string}.

\paragraph{(2) Reduce search space for partitioning}
The brute force search considers all possible partitions of $W$ into
$(W_1,\ldots,W_k)$. But, an extremely long edit subsequence $W_i$ is
unlikely to have a good match with a repository subsequence $V_i$.
Thus, we can reduce the search space of possible partitions by capping
the maximum length of the $W_i$'s to $L$. In our experience,
99% of the matches found by the brute force search
are of length $6$ or less, and we therefore set $L=6$.
This approach reduces the number of partitions to search.
More importantly, it typically reduces the number of distinct $W_i$'s we need to
consider by over an order of magnitude, especially when $W$ the full edit
sequence is itself very long.

\paragraph{(3) Viseme-based index to search repository}
For each edit subsequence $W_i$ we consider in our search space, we
must find the optimal $V_i$ in the repository with respect to
$\cmatch$. Instead of checking all possible subsequences in the
repository, we impose an additional constraint on $V_i$ that restricts
the set of $V_i$ we consider to only the most likely match candidates
and allows us to build an index structure on the set of $V_i$ to
retrieve the likely candidates quickly.

As in Fried et al., our $\cmatch$ cost function considers phonemes to
match when they appear visually similar -- that is, their
corresponding visemes match. By imposing the restriction that $V_i$
start with the same viseme n-gram as $W_i$ we can pre-compute an index
for the repository using viseme n-grams as the key and the location of
the n-gram in the source repository video as the value.
%
At search time, we look up all possible candidate $V_i$'s using this
index and only compute the $\cmatch$ for them. While this indexing
approach speeds up the search significantly it also reduces the space
of subsequence matches the search considers. In general, the longer the n-gram
key, the stronger the reduction and the more likely it is that no good
match will be found. In practice, we find that using a bi-gram index
best balances this trade-off between search speed and result quality.

\paragraph{Stitching}
% \maneesh{updated section.}
After we find the best matching phoneme subsequences $V_1,\ldots,V_k$
from the repository, we look up the expression parameters of the
source actor's 3D head model corresponding to each phoneme, and
linearly re-time them to match the phoneme durations specified in the
edit. We then stitch together adjacent subsequences by first linearly
blending the the expression parameters across the overlapping context
phonemes and then applying a Gaussian filter over a window of 4 frames
around the transition boundaries between the subsequences to further
smooth the transition.

We have found in practice, that errors in tracking expression
parameters, timing misalignments and our linear blending can sometimes
fail to fully close the mouth of the 3D head model at the beginning of
\textbackslash m, \textbackslash b, and \textbackslash p phonemes. However,
proper mouth closures for these phonemes is crucial for producing
perceptually realistic results,\cite{agarwal2020}. We therefore force the desired
mouth closure by linearly blending in a closed-mouth expression from
the repository at the beginning of all \textbackslash m,
\textbackslash b, and \textbackslash p phonemes with a default length of 2
frames. Note that the closed-mouth expressions are manually annotated
once during repository preprocessing and we automatically use the one
closest to the parameter values at the point of insertion.

%% \david{Phoneme misalignments and the blending procedure can sometimes
%% fail to fully close the mouth of the 3D head model, such as at the
%% beginning of \textbackslash m, \textbackslash b, \textbackslash p
%% phonemes. Proper mouth closures at the right time are crucial to
%% the perceived realism of results \cite{agarwal2020}.
%% We therefore
%% force the desired mouth closure by linearly blending in a
%% closed-mouth expression from the repository at the beginning of all
%% \textbackslash m, \textbackslash b, \textbackslash p phonemes with a
%% default effect radius of 2 frames. Note that the closed-mouth
%% expressions are manually annotated once during repository
%% preprocessing and we automatically use the one closest to the
%% parameter values at the point of insertion. }
% \david{Mouth closures at \textbackslash m, \textbackslash b, \textbackslash p phonemes are crucial to the perceived realism of results \cite{agarwal2020},
% but misalignments of phonemes and the blending procedure can sometimes fail to close the mouth of the 3D head model fully.
% We therefore force the desired mouth closure by linearly blending in a manually-annotated closed-mouth expression from the repository at the beginning of all \textbackslash m, \textbackslash b, \textbackslash p phonemes.
% }
% \maneesh{Needs more detail and also a better lead in -- talk about the misalignment problem, then about the realism. How did we obtain the closemouthed frames. How long do we blend them in for? }

\vspace{0.5em}
Overall, the fast search strategy reduce the runtime of
the phoneme search process by three orders of magnitude compared to
the brute-force approach. It takes around $5$ seconds to find
and stitch snippets $V_1,\ldots,V_k$ for an edit $W$ of $20$
phonemes in an hour-long repository.

% \david{Added two paragraphs here to talk about the algorithmic changes}
% Simply concatenating phoneme subsequences $V_i$ and $V_{i+1}$ can introduce transition artifacts because the phoneme after $V_i$ in the repository may be very dissimilar to the phoneme before $V_{i+1}$.
% We therefore employ a \emph{context-aware} searching algorithm, where we slighly expand each segment $W_i$ of the partition to include the phoneme before and after, so that $W_i$ and $W_{i+1}$ have two overlapping phonemes.
% The search procedure then finds overlapping phoneme subsequences $V_1,\ldots,V_k$ from the repository to form the edit.
% \david{A detail that can probably be cut:} In the event that no matches can be found for the expanded $W_i$, we fall back to include only the context phoneme before or the one after, and if still no match can be found, finally fall back to the original segment without context expansion.

% From the subsequences $V_1,\ldots,V_k$, we look up from the repository the corresponding expression parameters of the 3D head model.
% We then linearly retime the expression parameters corresponding to each phoneme in each repository subsequence to match the phoneme duration specified in the edit.
% Finally, we combine them into one continuous sequence of parameters.
% Specifically, we transition from one subsequence to the next by linearly blending over the overlapped region.
% To further smooth the transitions, we run a Gaussian filter on the blended values in the overlapped region.
% \david{A detail that can probably be cut:} If the overlapped region is shorter than 4 frames, we filter a larger window of 4 frames around the boundary.

% Mouth closures at \textbackslash m, \textbackslash b, \textbackslash p phonemes are crucial to the perceived realism of the result. \david{Is there a source to cite?}
% However, misalignments of phonemes and the blending procedure can sometimes fail to close the mouth of the 3D head model fully.
% We therefore force the desired mouth closure by linearly blending in a manually-annotated closed-mouth expression from the repository at the beginning of all \textbackslash m, \textbackslash b, \textbackslash p phonemes.
% \david{Should we have a forward-pointer to mouth-closure refinement control? I don't think we should.}

% \david{An attempt at a conclusion sentence}
% In summary, the fast phoneme search and stitching algorithm converts the input edit into a temporally coherent sequence of expression parameters of the source actor, which both conform to the timing specified by the edit and close the mouth at the desired time. It is three orders of magnitude faster compared to the brute-force approach, taking around $5$ seconds to process an edit of $20$ phonemes in an hour-long repository.


% \maneesh{Can you write a version of the paragraph. Once you've done that we can figure out how best to lace into this section. Also where to we insert mouth closure for m b p?}

%which enables our
%interactive editing work flow.

%% \maneesh{Can probably cut last sentence.}
%% The resulting snippets are later
%% stitched together and retargeted to the target actor in subsequent
%% steps of the synthesis pipeline as described in
%% \Cref{sec:synthesis_overview}.

% LocalWords: subsequences subsequence len Levenshtein levenshtein
% LocalWords: viseme visemes pre et al durations misalignments
% LocalWords: preprocessing
'''


Certainly! Based on the methods described in the research paper, I'll provide Python code that re-creates the key components of the system. The system consists of several steps:

1. Preprocessing Pipeline:
- Phoneme Alignment
- 3D Head Model Registration

2. Synthesis Pipeline:
- Fast Phoneme Search and Stitching
- Neural Retargeting
- Expansion to Full Parameters
- Neural Rendering

Given that the preprocessing steps involve external tools (e.g., P2FA for phoneme alignment and specialized software for 3D head model registration), we'll focus on implementing the core algorithms, particularly the Fast Phoneme Search and Stitching and Neural Retargeting steps.

Below is the Python code implementing these components:

---

### Import Necessary Libraries


import numpy as np
import heapq
import json
from collections import defaultdict
from sklearn.model_selection import train_test_split
import tensorflow as tf
from tensorflow.keras import layers, models


---

### Data Structures and Helper Functions

First, we'll define data structures and helper functions to represent phonemes, visemes, and sequences.

# Define a mapping from phonemes to visemes
phoneme_to_viseme = {
    # Phoneme: Viseme group
    'AA': 'V1', 'AE': 'V1', 'AH': 'V1', 'AO': 'V1', 'AW': 'V2',
    'AY': 'V2', 'B': 'V3', 'CH': 'V4', 'D': 'V5', 'DH': 'V5',
    # Add the rest of the mapping...
}

# Helper function to get viseme from phoneme
def get_viseme(phoneme):
    return phoneme_to_viseme.get(phoneme, 'UNK')  # Return 'UNK' if not found

# Define a Phoneme class
class Phoneme:
    def init(self, name, start_time, end_time):
        self.name = name
        self.start_time = start_time
        self.end_time = end_time
        self.viseme = get_viseme(name)

# Define a Sequence class to represent a list of phonemes
class PhonemeSequence:
    def init(self, phonemes):
        self.phonemes = phonemes

    def length(self):
        return len(self.phonemes)

    def viseme_sequence(self):
        return [p.viseme for p in self.phonemes]

# Function to compute substitution cost between two phonemes
def substitution_cost(p1, p2):
    if p1.viseme == p2.viseme:
        return 0
    else:
        return 1  # Cost can be tuned


---

### Fast Phoneme Search and Stitching

Implementing the algorithm described for fast phoneme search.

# Build an index mapping viseme bigrams to their positions in the repository
def build_viseme_bigram_index(repository_sequences):
    index = defaultdict(list)
    for seq_id, seq in enumerate(repository_sequences):
        visemes = seq.viseme_sequence()
        for i in range(len(visemes) - 1):
            bigram = (visemes[i], visemes[i+1])
            index[bigram].append((seq_id, i))
    return index

# Function to find best matching subsequences using the index
def fast_phoneme_search(edit_sequence, repository_sequences, index, max_subseq_length=6):
    matched_sequences = []
    i = 0
    while i < len(edit_sequence.phonemes):
        # Get the next subsequence to match
        max_len = min(max_subseq_length, len(edit_sequence.phonemes) - i)
        found_match = False
        # Try to find the longest possible match
        for l in range(max_len, 1, -1):
            subseq_phonemes = edit_sequence.phonemes[i:i+l]
            subseq = PhonemeSequence(subseq_phonemes)
            # Get viseme bigram key
            visemes = subseq.viseme_sequence()
            bigram = (visemes[0], visemes[1]) if len(visemes) > 1 else (visemes[0],)
            # Search the index
            candidates = index.get(bigram, [])
            # Evaluate candidates
            for candidate in candidates:
                seq_id, pos = candidate
                repo_seq = repository_sequences[seq_id]
                if pos + l <= repo_seq.length():
                    repo_subseq = PhonemeSequence(repo_seq.phonemes[pos:pos+l])
                    # Compute substitution cost
                    total_cost = sum(substitution_cost(p1, p2) for p1, p2 in zip(subseq.phonemes, repo_subseq.phonemes))
                    if total_cost == 0:
                        # Found an exact match
                        matched_sequences.append((repo_subseq, i, i+l))
                        i += l - 1  # Advance index
                        found_match = True
                        break
            if found_match:
                break
        if not found_match:
            # Handle cases where no match is found
            # For simplicity, we can skip or handle appropriately
            # Here we increment i to avoid infinite loop
            i += 1
    return matched_sequences

# Function to stitch matched sequences
def stitch_sequences(matched_sequences, edit_sequence):
    stitched_parameters = []
    for repo_subseq, start_idx, end_idx in matched_sequences:
        # Load expression parameters corresponding to the phonemes
        # For simplicity, assume we have a function that does this
        parameters = get_expression_parameters(repo_subseq)
        # Linearly retime parameters to match the edit sequence timings
        duration = edit_sequence.phonemes[end_idx - 1].end_time - edit_sequence.phonemes[start_idx].start_time
        retimed_parameters = retime_parameters(parameters, duration)
        # Append to the stitched parameters
        stitched_parameters.extend(retimed_parameters)
    return stitched_parameters

# Placeholder functions
def get_expression_parameters(phoneme_sequence):
    # This function should return expression parameters for the given phoneme sequence
    # Placeholder implementation
    return np.random.rand(phoneme_sequence.length(), 64)  # Assume 64 expression parameters

def retime_parameters(parameters, duration):
    # This function retimes the parameters to match the given duration
    num_frames = parameters.shape[0]
    target_num_frames = int(duration * FRAME_RATE)  # Assume a FRAME_RATE defined
    retimed_parameters = np.interp(
        np.linspace(0, num_frames - 1, target_num_frames),
        np.arange(num_frames),
        parameters,
        axis=0
    )
    return retimed_parameters

FRAME_RATE = 30  # Frames per second


---

### Neural Retargeting

Implementing the self-supervised neural retargeting model.

#### Preparing Training Data

# Function to build corresponding parameter sequences for training
def build_training_data(source_sequences, target_sequences):
    X = []  # Source parameters
    Y = []  # Target parameters
    for s_seq in source_sequences:
        s_visemes = s_seq.viseme_sequence()
        # Find matching sequences in target
        for t_seq in target_sequences:
            t_visemes = t_seq.viseme_sequence()
            if s_visemes == t_visemes:
                # Load expression parameters
                s_params = get_expression_parameters(s_seq)
                t_params = get_expression_parameters(t_seq)
                # Retime target parameters to match source
                duration = (s_seq.phonemes[-1].end_time - s_seq.phonemes[0].start_time)
                t_params_retimed = retime_parameters(t_params, duration)
                # Append to training data
                X.append(s_params)
                Y.append(t_params_retimed)
    return np.concatenate(X), np.concatenate(Y)

# Assume we have lists of PhonemeSequence objects for source and target
source_sequences = []  # Filled with PhonemeSequence objects from the repository
target_sequences = []  # Filled with PhonemeSequence objects from the target video

# Build training data
X_train, Y_train = build_training_data(source_sequences, target_sequences)


#### Defining the Neural Network Model

# Define the retargeting neural network
def build_retargeting_model(input_shape, H=2):
    inputs = layers.Input(shape=input_shape)
    # Initialize previous outputs (state)
    previous_outputs = [layers.Input(shape=input_shape) for _ in range(H)]
    x = layers.concatenate([inputs] + previous_outputs)
    x = layers.Dense(1024, activation='relu')(x)
    x = layers.Dropout(0.25)(x)
    x = layers.Dense(1024, activation='relu')(x)
    x = layers.Dropout(0.5)(x)
    x = layers.Dense(1024, activation='relu')(x)
    x = layers.Dropout(0.25)(x)
    residual = layers.Dense(input_shape[-1])(x)
    outputs = layers.Add()([inputs, residual])
    model = models.Model(inputs=[inputs] + previous_outputs, outputs=outputs)
    return model

# Build the model
input_shape = (64,)  # Number of expression parameters
model = build_retargeting_model(input_shape)

# Compile the model with custom loss function
def custom_loss(y_true, y_pred):
    # Data term
    data_term = tf.reduce_mean(tf.abs(y_true - y_pred))
    # Temporal regularization (second difference)
    accel = y_pred[2:, :] - 2 * y_pred[1:-1, :] + y_pred[:-2, :]
    temporal_term = tf.reduce_mean(tf.square(accel))
    # Total loss
    return data_term + 10 * temporal_term

model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.0002), loss=custom_loss)

# Prepare the data for training (assuming T=7 as per the paper)
def prepare_training_sequences(X, Y, T=7, H=2):
    X_sequences = []
    Y_sequences = []
    for i in range(len(X) - T):
        X_seq = X[i:i+T]
        Y_seq = Y[i:i+T]
        X_sequences.append(X_seq)
        Y_sequences.append(Y_seq)
    X_sequences = np.array(X_sequences)
    Y_sequences = np.array(Y_sequences)
    return X_sequences, Y_sequences

X_sequences, Y_sequences = prepare_training_sequences(X_train, Y_train)

# Split into training and validation sets
X_train_seq, X_val_seq, Y_train_seq, Y_val_seq = train_test_split(X_sequences, Y_sequences, test_size=0.1)

# Train the model
model.fit(
    [X_train_seq[:, t, :] for t in range(T)],  # Unrolled inputs
    Y_train_seq,
    epochs=100,
    batch_size=100,
    validation_data=([X_val_seq[:, t, :] for t in range(T)], Y_val_seq)
)


#### Inference

# Function to perform inference using sliding window
def retarget_parameters(source_parameters, model, T=7, H=2):
    num_frames = source_parameters.shape[0]
    predicted_parameters = np.zeros_like(source_parameters)
    counts = np.zeros(num_frames)
    # Pad the source_parameters with zeros at the beginning
    padded_source = np.vstack([np.zeros((H, source_parameters.shape[1])), source_parameters])
    for i in range(num_frames - T + 1):
        window = padded_source[i:i+T+H]
        inputs = [window[H + t].reshape(1, -1) for t in range(T)]
        previous_outputs = [window[H + t - h - 1].reshape(1, -1) for h in range(H) for t in range(T)]
        model_inputs = inputs + previous_outputs[:H]
        prediction = model.predict(model_inputs)
        predicted_parameters[i + T // 2] += prediction[0]
        counts[i + T // 2] += 1
    # Average the predictions
    predicted_parameters /= counts[:, np.newaxis]
    return predicted_parameters


---

### Usage Example

Putting it all together:

# Assume we have an edit_sequence (PhonemeSequence) and repository sequences
edit_sequence = ...  # A PhonemeSequence object representing the edit
repository_sequences = ...  # List of PhonemeSequence objects from the repository

# Step 1: Build the viseme bigram index
index = build_viseme_bigram_index(repository_sequences)

# Step 2: Perform fast phoneme search
matched_sequences = fast_phoneme_search(edit_sequence, repository_sequences, index)

# Step 3: Stitch the sequences
stitched_parameters = stitch_sequences(matched_sequences, edit_sequence)

# Step 4: Retarget the parameters
retargeted_parameters = retarget_parameters(stitched_parameters, model)

# The retargeted_parameters can then be used for further processing (e.g., expansion to full parameters and neural rendering)


---

### Notes:

- Phoneme and Viseme Mapping: You'll need to provide a complete mapping between phonemes and visemes based on your specific application.

- Expression Parameters: The functions get_expression_parameters and retime_parameters are placeholders. You'll need to implement these based on how you store and manipulate expression parameters.

- Data: The code assumes that you have access to the phoneme sequences and corresponding expression parameters for both the repository and target videos.

- Neural Network Training: Training deep learning models requires substantial data. Ensure that you have adequate data and that it is properly preprocessed.

- Error Handling: For simplicity, error handling and edge cases are not fully implemented. You'll need to add appropriate checks and handle exceptions based on your requirements.

- External Tools: Preprocessing steps like phoneme alignment and 3D head model registration rely on external tools that are not implemented here.

---

I hope this code provides a solid starting point for your research project. Let me know if you need further assistance or clarification on any part of the implementation!

can you provide a step by step for me to follow and report back to you with the result of that action . I'm a beginner at this . and the research project should stick to the criteria given in the method section of research paper


Absolutely! I'll provide a detailed step-by-step guide to help you implement the Python code described in the methods section of the research paper. Since you're a beginner, I'll explain each step thoroughly and include code snippets that you can follow along with.

Objective: Re-create the Python code described in the methods section of the research paper, focusing on the Fast Phoneme Search and Stitching, and the Neural Retargeting components.

---

## Table of Contents

1. Understanding the Project Structure
2. Setting Up the Environment
3. Defining Data Structures
4. Implementing Fast Phoneme Search and Stitching
- Building the Viseme Bigram Index
- Fast Phoneme Search
- Stitching Sequences
5. Implementing Neural Retargeting
- Preparing Training Data
- Building the Neural Network Model
- Training the Model
- Inference (Retargeting)
6. Putting It All Together
7. Next Steps

---

<a name="1"></a>
## 1. Understanding the Project Structure

Before we dive into coding, it's important to understand what we're building:

- Input:
- Edit Sequence: A sequence of phonemes representing the desired speech edit.
- Repository Video: A large collection of phoneme sequences from a source actor.

- Output:
- A sequence of facial expression parameters for the target actor that match the edit sequence.

- Main Components:
- Fast Phoneme Search and Stitching: Finds matching phoneme sequences in the repository and stitches them together to form the edit.
- Neural Retargeting: Transforms the source actor's facial expression parameters to match the target actor.

<a name="2"></a>
## 2. Setting Up the Environment

Let's set up your Python environment:

1. Install Python: Make sure you have Python 3.6 or later installed. You can download it from python.org.

2. Create a Virtual Environment (optional but recommended):


    python -m venv myenv
    source myenv/bin/activate  # On Windows use: myenv\Scripts\activate


3. Install Required Libraries:

    pip install numpy tensorflow==2.4.1


    > Note: We're using TensorFlow 2.4.1 for this project. Adjust the version if necessary.

<a name="3"></a>
## 3. Defining Data Structures

We'll start by defining the basic data structures to represent phonemes and visemes.

#### Step 1: Import Libraries

import numpy as np
import tensorflow as tf
from collections import defaultdict


#### Step 2: Define Phoneme to Viseme Mapping

# Define a mapping from phonemes to visemes (simplified example)
phoneme_to_viseme = {
    'AA': 'V1', 'AE': 'V1', 'AH': 'V1', 'AO': 'V1',
    'EY': 'V2', 'AY': 'V2', 'OW': 'V2',
    'B': 'V3', 'P': 'V3', 'M': 'V3',
    'CH': 'V4', 'JH': 'V4',
    'D': 'V5', 'T': 'V5',
    # ... (Include all phonemes needed)
}


#### Step 3: Define the Phoneme Class

class Phoneme:
    def init(self, name, start_time, end_time):
        self.name = name
        self.start_time = start_time
        self.end_time = end_time
        self.viseme = phoneme_to_viseme.get(name, 'UNK')  # Default to 'UNK' if not found


#### Step 4: Define the PhonemeSequence Class

class PhonemeSequence:
    def init(self, phonemes):
        self.phonemes = phonemes  # List of Phoneme objects
    
    def length(self):
        return len(self.phonemes)
    
    def viseme_sequence(self):
        return [phoneme.viseme for phoneme in self.phonemes]


<a name="4"></a>
## 4. Implementing Fast Phoneme Search and Stitching

The goal is to find matching sequences in the repository that correspond to segments of our edit sequence.

<a name="4.1"></a>
### Building the Viseme Bigram Index

#### Step 5: Build the Index

def build_viseme_bigram_index(repository_sequences):
    index = defaultdict(list)
    for seq_id, seq in enumerate(repository_sequences):
        visemes = seq.viseme_sequence()
        for i in range(len(visemes) - 1):
            bigram = (visemes[i], visemes[i + 1])
            index[bigram].append((seq_id, i))
    return index


- Explanation: 
    - We create an index where each key is a viseme bigram (pair).
    - The value is a list of positions (sequence ID and index) where this bigram occurs in the repository.

#### Step 6: Prepare Repository Sequences

- Load or Define Repository Sequences:
    - For this example, let's assume you have a list of PhonemeSequence objects in repository_sequences.
    - Each PhonemeSequence should be a sequence from your repository video, already processed into phonemes.

<a name="4.2"></a>
### Fast Phoneme Search

#### Step 7: Define Substitution Cost Function

def substitution_cost(p1, p2):
    return 0 if p1.viseme == p2.viseme else 1  # 0 if visemes match, else 1


#### Step 8: Implement the Search Function

def fast_phoneme_search(edit_seq, repository_sequences, index, max_subseq_length=6):
    matched_sequences = []
    i = 0
    while i < edit_seq.length():
        max_len = min(max_subseq_length, edit_seq.length() - i)
        found_match = False
        for l in range(max_len, 1, -1):
            subseq = PhonemeSequence(edit_seq.phonemes[i:i + l])
            visemes = subseq.viseme_sequence()
            bigram = tuple(visemes[:2])  # First two visemes
            candidates = index.get(bigram, [])
            for seq_id, pos in candidates:
                repo_seq = repository_sequences[seq_id]
                if pos + l <= repo_seq.length():
                    repo_subseq = PhonemeSequence(repo_seq.phonemes[pos:pos + l])
                    total_cost = sum(
                        substitution_cost(p1, p2)
                        for p1, p2 in zip(subseq.phonemes, repo_subseq.phonemes)
                    )
                    if total_cost == 0:
                        matched_sequences.append((repo_subseq, i, i + l))
                        i += l - 1  # Advance index
                        found_match = True
                        break
            if found_match:
                break
        if not found_match:
            # Handle cases where no match is found
            # For simplicity, we'll skip this phoneme
            i += 1
    return matched_sequences


- Explanation:
    - We iterate over the edit sequence and try to find the longest matching subsequence in the repository.
    - We use the viseme bigram index to quickly find candidates.
    - If a match is found (total cost is 0), we add it to matched_sequences.

<a name="4.3"></a>
### Stitching Sequences

#### Step 9: Define Functions to Get and Retime Expression Parameters

For simplicity, we'll create placeholder functions:

FRAME_RATE = 30  # Frames per second

def get_expression_parameters(phoneme_sequence):
    # Placeholder: Return random parameters
    num_frames = int(
        (phoneme_sequence.phonemes[-1].end_time - phoneme_sequence.phonemes[0].start_time) * FRAME_RATE
    )
    return np.random.rand(num_frames, 64)  # Assume 64 expression parameters

def retime_parameters(parameters, target_duration):
    num_frames = parameters.shape[0]
    target_num_frames = int(target_duration * FRAME_RATE)
    retimed_parameters = np.zeros((target_num_frames, parameters.shape[1]))
    for i in range(parameters.shape[1]):  # For each parameter
        retimed_parameters[:, i] = np.interp(
            np.linspace(0, num_frames - 1, target_num_frames),
            np.arange(num_frames),
            parameters[:, i]
        )
    return retimed_parameters


- Explanation:
    - get_expression_parameters simulates retrieving expression parameters for a phoneme sequence.
    - retime_parameters adjusts the timing of the parameters to match the target duration.

#### Step 10: Stitch the Matched Sequences

def stitch_sequences(matched_sequences, edit_sequence):
    stitched_parameters = []
    for repo_subseq, start_idx, end_idx in matched_sequences:
        # Get parameters from the repository subsequence
        parameters = get_expression_parameters(repo_subseq)
        # Calculate the target duration from the edit sequence
        target_duration = edit_sequence.phonemes[end_idx - 1].end_time - edit_sequence.phonemes[start_idx].start_time
        # Retime the parameters
        retimed_params = retime_parameters(parameters, target_duration)
        # Append to stitched parameters
        stitched_parameters.append(retimed_params)
    # Concatenate all parameters
    stitched_parameters = np.vstack(stitched_parameters)
    return stitched_parameters


- Explanation:
    - We process each matched sequence, retrieve and retime parameters, and append them to the final list.
    - Finally, we concatenate all parameters into a single array.

<a name="5"></a>
## 5. Implementing Neural Retargeting

We will create a neural network model that takes the stitched parameters (from the source actor) and outputs retargeted parameters for the target actor.

<a name="5.1"></a>
### Preparing Training Data

#### Step 11: Build Training Data

def build_training_data(repository_sequences, target_sequences):
    X = []  # Source parameters
    Y = []  # Target parameters
    for repo_seq in repository_sequences:
        repo_visemes = repo_seq.viseme_sequence()
        for target_seq in target_sequences:
            target_visemes = target_seq.viseme_sequence()
            if repo_visemes == target_visemes:
                # Get parameters
                repo_params = get_expression_parameters(repo_seq)
                target_params = get_expression_parameters(target_seq)
                # Retime target parameters to match repository duration
                duration = (
                    repo_seq.phonemes[-1].end_time - repo_seq.phonemes[0].start_time
                )
                target_params_retimed = retime_parameters(target_params, duration)
                # Ensure same number of frames
                if repo_params.shape[0] == target_params_retimed.shape[0]:
                    X.append(repo_params)
                    Y.append(target_params_retimed)
    # Concatenate all data
    X_train = np.vstack(X)
    Y_train = np.vstack(Y)
    return X_train, Y_train


- Explanation:
    - We find sequences in the repository and target that have the same viseme sequences.
    - We retrieve and retime their parameters to have the same duration and frames.
    - We collect these pairs into training datasets X_train and Y_train.

#### Note:

- Data Requirement:
    - You'll need to have processed sequences from the target actor.
    - This requires the target actor's video to be processed into phonemes and expression parameters.

<a name="5.2"></a>
### Building the Neural Network Model

#### Step 12: Define the Model

from tensorflow.keras import layers, models

def build_retargeting_model(input_dim, H=2):
    inputs = layers.Input(shape=(input_dim,))
    # Previous outputs (state)
    prev_outputs = [layers.Input(shape=(input_dim,)) for _ in range(H)]
    # Concatenate inputs and previous outputs
    x = layers.Concatenate()([inputs] + prev_outputs)
    # Recurrent unit
    x = layers.Dense(1024, activation='relu')(x)
    x = layers.Dropout(0.25)(x)
    x = layers.Dense(1024, activation='relu')(x)
    x = layers.Dropout(0.5)(x)
    x = layers.Dense(1024, activation='relu')(x)
    x = layers.Dropout(0.25)(x)
    # Output layer (residual)
    residual = layers.Dense(input_dim)(x)
    outputs = layers.Add()([inputs, residual])
    model = models.Model(inputs=[inputs] + prev_outputs, outputs=outputs)
    return model


- Explanation:
    - The model takes the current input and previous H outputs.
    - It predicts the residual to add to the input to get the output.
    - Here, input_dim is the number of expression parameters (e.g., 64).

<a name="5.3"></a>
### Training the Model

#### Step 13: Prepare Training Sequences

def prepare_training_sequences(X, Y, H=2):
    X_sequences = []
    Y_sequences = []
    for i in range(H, len(X)):
        input_seq = [X[i]] + [Y[i - h - 1] for h in range(H)]
        X_sequences.append(input_seq)
        Y_sequences.append(Y[i])
    return np.array(X_sequences), np.array(Y_sequences)


- Explanation:
    - We prepare the data so that for each time step, the model gets the current input and H previous outputs.

#### Step 14: Compile the Model

model = build_retargeting_model(input_dim=64, H=2)

# Define custom loss function
def custom_loss(y_true, y_pred):
    data_term = tf.reduce_mean(tf.abs(y_true - y_pred))
    # Compute acceleration (second difference)
    accel = y_pred[2:] - 2 * y_pred[1:-1] + y_pred[:-2]
    temporal_term = tf.reduce_mean(tf.square(accel))
    return data_term + 10 * temporal_term

model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.0002), loss=custom_loss)


#### Step 15: Train the Model

# Prepare sequences
X_train_seq, Y_train_seq = prepare_training_sequences(X_train, Y_train)

# Split into training and validation sets (optional)
split_idx = int(0.9 * len(X_train_seq))
X_train_seq, X_val_seq = X_train_seq[:split_idx], X_train_seq[split_idx:]
Y_train_seq, Y_val_seq = Y_train_seq[:split_idx], Y_train_seq[split_idx:]

# Train the model
model.fit(
    [X_train_seq[:, i] for i in range(3)],  # inputs + H previous outputs
    Y_train_seq,
    epochs=100,
    batch_size=100,
    validation_data=(
        [X_val_seq[:, i] for i in range(3)],
        Y_val_seq
    )
)


- Explanation:
    - We unroll the inputs for the current time step and H previous outputs.
    - We train the model for 100 epochs. Adjust as needed based on performance.

<a name="5.4"></a>
### Inference (Retargeting)

#### Step 16: Define the Inference Function

def retarget_parameters(source_parameters, model, H=2):
    num_frames, input_dim = source_parameters.shape
    predicted_parameters = []
    prev_outputs = [np.zeros((input_dim,)) for _ in range(H)]  # Initialize previous outputs
    for i in range(num_frames):
        inputs = [source_parameters[i]] + prev_outputs
        # Reshape for model input
        inputs = [inp.reshape(1, -1) for inp in inputs]
        pred = model.predict(inputs)
        predicted_parameters.append(pred[0])
        # Update previous outputs
        prev_outputs = [pred[0]] + prev_outputs[:-1]
    predicted_parameters = np.array(predicted_parameters)
    return predicted_parameters


- Explanation:
    - We loop over each frame and predict the retargeted parameters.
    - We keep track of the previous outputs as the model's state.

<a name="6"></a>
## 6. Putting It All Together

Let's combine all the steps to process an edit sequence:

#### Step 17: Process the Edit Sequence

# Assume we have an edit sequence
edit_sequence = PhonemeSequence([
    Phoneme('B', 0.00, 0.10),
    Phoneme('AE', 0.10, 0.20),
    Phoneme('T', 0.20, 0.30),
    # ... (Add more phonemes as per your edit)
])

# Build the viseme bigram index from the repository
index = build_viseme_bigram_index(repository_sequences)

# Perform fast phoneme search
matched_sequences = fast_phoneme_search(edit_sequence, repository_sequences, index)

# Stitch the sequences to get source parameters
stitched_parameters = stitch_sequences(matched_sequences, edit_sequence)

# Retarget the parameters to get target actor parameters
retargeted_parameters = retarget_parameters(stitched_parameters, model)

# retargeted_parameters now contains the expression parameters for the target actor


<a name="7"></a>
## 7. Next Steps

At this point, you have:

- Implemented the fast phoneme search and stitching algorithm.
- Built and trained a neural retargeting model.
- Applied the model to retarget parameters for an edit sequence.

To proceed further:

1. Expand Phoneme and Viseme Definitions:
    - Make sure to include all necessary phonemes in your mapping.
    - Adjust the viseme groups as per your application's needs.

2. Implement Preprocessing Steps:
    - Use tools like P2FA or Montreal Forced Aligner for phoneme alignment.
    - Use facial tracking software or libraries to obtain expression parameters.
    - Ensure that both the repository and target videos are processed similarly.

3. Enhance Data Handling:
    - Implement proper data loading and handling.
    - Use real expression parameters instead of placeholders.

4. Implement Neural Rendering:
    - After obtaining the retargeted parameters, you'll need to render them into video frames.
    - This involves using a GAN or other rendering techniques, which can be a complex task.

5. Error Handling and Optimization:
    - Add error checks and handle edge cases.
    - Optimize code for performance if necessary.

6. Testing and Evaluation:
    - Test the entire pipeline with real data.
    - Evaluate the results and adjust parameters or models as needed.

---

Feel free to reach out if you have any questions or need further clarification on any of the steps. I'm here to help you through the process!

---

Note: The code provided is a simplified representation to illustrate the concepts described in the methods section. Implementing a fully functional system would require integrating several external tools and handling detailed aspects of data processing, model training, and rendering.


can we do one step at a time and then move one to next step in detailed way that replicates research paper method section . i need guidance for everything from basic level to complete the step and report back to you with the result.


Absolutely, I'd be happy to guide you through each step in detail. We'll proceed one step at a time, replicating the methods described in the research paper's method section. I'll ensure that each step is explained thoroughly, starting from the basics, so you can follow along comfortably.

Please feel free to ask any questions at any point, and once you've completed a step, you can report back with the results or any issues you encountered.

---

## Overview

Our goal is to implement key components from the research paper, focusing on:

1. Fast Phoneme Search and Stitching
2. Neural Retargeting

We'll start by setting up the necessary environment and then proceed step by step.

---

## Step 1: Setting Up the Environment

Before we dive into coding, we need to set up our programming environment.

### 1.1 Install Python

First, ensure you have Python installed on your computer.

- Check if Python is installed:
- Open a terminal or command prompt.
- Type python --version or python3 --version.
- If Python is installed, it will display the version number (e.g., Python 3.8.5).

- If Python is not installed:
- Download and install Python 3.6 or later from the official website.
- Follow the installation instructions for your operating system.

### 1.2 Install an Integrated Development Environment (IDE)

An IDE can make coding easier.

- Recommended IDEs:
- Visual Studio Code
- PyCharm Community Edition
- Anaconda Navigator (comes with Spyder IDE)

### 1.3 Create a Project Folder

- Create a new folder on your computer where you'll save all your project files. For example, TalkingHeadProject.

### 1.4 Set Up a Virtual Environment (Optional but Recommended)

A virtual environment helps manage project-specific dependencies without affecting your system-wide Python installation.

- Create a virtual environment:
- Open your terminal or command prompt.
- Navigate to your project folder:


    cd path_to_your_project_folder

  - Create a virtual environment:

    python -m venv myenv

  - Activate the virtual environment:
    - On Windows:

      myenv\Scripts\activate

    - On macOS/Linux:

      source myenv/bin/activate

    - You should see (myenv) at the beginning of your command line, indicating the virtual environment is active.

### 1.5 Install Required Libraries

We'll need a few Python libraries for our project.

- In your terminal, make sure your virtual environment is activated.
- Install the libraries:

  pip install numpy tensorflow

  - numpy: A library for numerical computations.
  - tensorflow: A library for building and training neural networks.

---

### Action for You:

1. Set up your programming environment by following the steps above.
2. Once you have Python installed, an IDE set up, and the necessary libraries installed, please let me know so we can proceed to the next step.

If you encounter any issues or have questions during this setup, feel free to ask, and I'll help you through it.


yes i was able to complete the step and encountered no issues


Great! Since you've successfully set up your environment, let's proceed to the next step.

---

## Step 2: Defining Data Structures

In this step, we'll define the basic data structures needed to represent phonemes, visemes, and sequences. These structures form the foundation for the algorithms we'll implement later.

### 2.1 Create a New Python File

- Action: Open your IDE and create a new Python file in your project folder.
- Suggested name: main.py

### 2.2 Import Necessary Libraries

At the top of your Python file, we'll import the necessary Python libraries.


import numpy as np
from collections import defaultdict


- Explanation:
- numpy: A library for numerical computations in Python.
- collections.defaultdict: A dictionary subclass that calls a factory function to supply missing values. We'll use it to build our viseme index.

### 2.3 Define Phoneme to Viseme Mapping

In speech processing, phonemes are the smallest units of sound, and visemes are groups of phonemes that look similar when spoken (they produce the same visual mouth shape). Mapping phonemes to visemes helps us focus on visual aspects of speech.

#### 2.3.1 Create the Mapping Dictionary

We'll define a dictionary that maps phonemes to visemes.

# Define a mapping from phonemes to visemes
phoneme_to_viseme = {
    'AA': 'V1', 'AE': 'V1', 'AH': 'V1', 'AO': 'V1', 'AW': 'V2', 'AY': 'V2',
    'B': 'V3', 'P': 'V3', 'M': 'V3',
    'CH': 'V4', 'JH': 'V4', 'SH': 'V4', 'ZH': 'V4',
    'D': 'V5', 'T': 'V5',
    'EH': 'V6', 'EY': 'V6', 'IH': 'V6', 'IY': 'V6',
    'F': 'V7', 'V': 'V7',
    'G': 'V8', 'K': 'V8', 'NG': 'V8',
    'L': 'V9', 'R': 'V9',
    'N': 'V10', 'S': 'V10', 'Z': 'V10',
    'OW': 'V11', 'UH': 'V11', 'UW': 'V11',
    'TH': 'V12', 'DH': 'V12',
    'HH': 'V13',
    'ER': 'V14',
    # Add any additional phonemes as needed
}


- Note: This mapping is an example. If you have a specific phoneme set or a different viseme grouping, please adjust the phoneme_to_viseme dictionary accordingly.

### 2.4 Define the Phoneme Class

We'll create a Phoneme class to represent individual phonemes along with their attributes.

class Phoneme:
    def init(self, name, start_time, end_time):
        self.name = name                      # Phoneme label (e.g., 'AH', 'T', 'B', etc.)
        self.start_time = start_time          # Start time of the phoneme in the audio/video
        self.end_time = end_time              # End time of the phoneme in the audio/video
        self.viseme = phoneme_to_viseme.get(name, 'UNK')  # Corresponding viseme; 'UNK' if not found


- Explanation:
- Constructor (__init__) Parameters:
- name: The phoneme symbol.
- start_time: The time when the phoneme starts.
- end_time: The time when the phoneme ends.
- Attributes:
- viseme: Retrieved from the phoneme_to_viseme mapping. If the phoneme isn't in the mapping, it defaults to 'UNK' (unknown).

### 2.5 Define the PhonemeSequence Class

We'll create a PhonemeSequence class to manage sequences of phonemes.

class PhonemeSequence:
    def init(self, phonemes):
        self.phonemes = phonemes  # A list of Phoneme objects

    def length(self):
        return len(self.phonemes)

    def viseme_sequence(self):
        return [phoneme.viseme for phoneme in self.phonemes]


- Methods:
- length(): Returns the number of phonemes in the sequence.
- viseme_sequence(): Returns a list of visemes corresponding to the phonemes in the sequence.

### 2.6 Example Usage

Let's create an example to see how these classes work.

# Example phonemes for a word (e.g., "BAT")
phoneme_list = [
    Phoneme('B', 0.0, 0.1),
    Phoneme('AE', 0.1, 0.2),
    Phoneme('T', 0.2, 0.3)
]

# Create a PhonemeSequence
sequence = PhonemeSequence(phoneme_list)

# Get the length of the sequence
print("Sequence Length:", sequence.length())

# Get the viseme sequence
print("Viseme Sequence:", sequence.viseme_sequence())


- Expected Output:

  Sequence Length: 3
  Viseme Sequence: ['V3', 'V1', 'V5']


### Action for You:

1. Copy the Code:

   - Copy the code snippets from sections 2.2 to 2.5 into your Python file after the imports.

2. Adjust the Phoneme-to-Viseme Mapping:

   - Review the phoneme_to_viseme dictionary.
   - If your project uses additional phonemes, add them to the dictionary with appropriate viseme groups.

3. Test the Code:

   - Use the example in 2.6 to test if everything is working.
   - Run your Python script and verify that the output matches the expected output.

4. Save Your Work:

   - Save the Python file in your project folder.

5. Let Me Know:

   - Once you've completed these steps, please let me know.
   - If you encounter any issues or have questions, feel free to ask, and I'll help you resolve them.

---

Additional Notes:

- Understanding the Classes:
  - These classes will help us organize phoneme data and easily access attributes like visemes and timings.
  - We'll use instances of these classes throughout the implementation of the algorithms.

- Next Steps:
  - After this, we'll proceed to implement the Fast Phoneme Search and Stitching algorithm, building upon these data structures.

---

Feel free to reach out if you need any clarification or assistance with this step!


PS C:\Users\pc\Desktop\project> & c:/Users/pc/Desktop/project/myenv/Scripts/python.exe c:/Users/pc/Desktop/project/main.py
Traceback (most recent call last):
File "c:\Users\pc\Desktop\project\main.py", line 42, in <module>
if name == "main":
^^^^
NameError: name 'name' is not defined


Certainly! I'm happy to help you troubleshoot this error and guide you through the next steps.

---

### Understanding the Error

From the error message you provided:

Traceback (most recent call last):
File "c:\Users\pc\Desktop\project\main.py", line 42, in <module>
if name == "main":
^^^^
NameError: name 'name' is not defined

The error is a NameError stating that the name 'name' is not defined at line 42 in your main.py file.

### Cause of the Error

In Python, when you want to check if your script is being run directly (and not imported as a module), you use the special variable __name__ (with double underscores before and after). The correct way to write this check is:


if name == "main":
    # Your code here


In your code, name is missing the double underscores, so Python doesn't recognize it as a predefined variable, resulting in a NameError.

### Solution

Please update line 42 of your main.py file to use the correct __name__ variable. Here's how you can fix it:

if name == "main":
    # Your code here


### Explanation

- __name__ is a special built-in variable in Python that represents the name of the module.
- When a Python script is run directly, __name__ is set to "__main__".
- When a script is imported as a module in another script, __name__ is set to the module's name.
- Therefore, the condition if __name__ == "__main__": checks whether the script is being run directly.

### Next Steps

1. Update Your Code

- Open main.py and locate line 42.
- Replace:

     if name == "main":

     With:

     if name == "main":


2. Add Code to the Main Block (if needed)

   - If you haven't already, you can add test code or function calls inside this block to execute when the script is run directly.
   - For example, using the test code from the earlier example:

     if name == "main":
         # Example phonemes for a word (e.g., "BAT")
         phoneme_list = [
             Phoneme('B', 0.0, 0.1),
             Phoneme('AE', 0.1, 0.2),
             Phoneme('T', 0.2, 0.3)
         ]

         # Create a PhonemeSequence
         sequence = PhonemeSequence(phoneme_list)

         # Get the length of the sequence
         print("Sequence Length:", sequence.length())

         # Get the viseme sequence
         print("Viseme Sequence:", sequence.viseme_sequence())


3. Run Your Script Again

   - Save the changes to main.py.
   - Run your script from the terminal:

     python main.py


     (Make sure you're in the correct directory and your virtual environment is activated.)

4. Verify the Output

   - If everything is working correctly, you should see the following output:

     Sequence Length: 3
     Viseme Sequence: ['V3', 'V1', 'V5']


   - This confirms that your classes are defined correctly and that the test code is executing.

### Confirm Completion

Please try these steps and let me know if the error is resolved. If you encounter any other issues or have questions about the code, feel free to ask, and I'll be happy to assist further.

---

### Understanding the Main Block

Just to provide additional context:

- The if __name__ == "__main__": block is a common Python idiom.
- It allows you to run some code only when the script is executed directly, and not when it's imported as a module in another script.
- This is useful for testing or running examples.

### Additional Notes

- Indentation: Ensure that the code following the if statement is properly indented.
- Consistency: Be consistent with the use of underscores in variable names and special variables like __name__.

---

Once you've updated the code and confirmed it's working, we can proceed to the next step, which involves implementing the Fast Phoneme Search and Stitching algorithm.

Let me know how it goes!


yes it added the underscores like you said and i got output
(myenv) PS C:\Users\pc\Desktop\project> python main.py
Sequence Length: 3
Viseme Sequence: ['V3', 'V1', 'V5']
(myenv) PS C:\Users\pc\Desktop\project>

we can move on to the next step


Fantastic! I'm glad you were able to resolve the error and see the expected output.

---

## Step 3: Implementing Fast Phoneme Search and Stitching

In this step, we'll implement the Fast Phoneme Search and Stitching component as described in the methods section of the research paper.

Objective:

- Fast Phoneme Search: Efficiently find matching phoneme sequences in the repository that correspond to segments of our edit sequence.
- Stitching: Combine the matched sequences to form a continuous sequence of expression parameters, ready for retargeting.

---

### Overview of This Step

- 3.1 Build the Viseme Bigram Index
- 3.2 Implement the Fast Phoneme Search Function
- 3.3 Stitch the Matched Sequences

We'll go through each sub-step in detail, with explanations and code examples.

---

### Prerequisites

- Understanding:

- You should be familiar with the classes we defined earlier (Phoneme and PhonemeSequence).
- Basic understanding of dictionaries and lists in Python.

- Data:

- For this step, we'll need:

- Edit Sequence: The sequence of phonemes representing the edit you want to achieve.
- Repository Sequences: A collection of phoneme sequences from the repository video.

- Assumptions:

- Since we don't have actual data, we'll create hypothetical data for demonstration purposes.
- In a real scenario, you would replace these with actual phoneme sequences from your edit and repository.

---

### 3.1 Build the Viseme Bigram Index

Purpose: To create an index that maps viseme bigrams (pairs of visemes) to their locations in the repository, allowing for efficient search.

#### Step 3.1.1: Import Necessary Libraries

At the top of your Python file, make sure you have:


from collections import defaultdict


We've already imported this earlier, but ensure it's there.

#### Step 3.1.2: Define the Index Building Function

Add the following function to your code:

def build_viseme_bigram_index(repository_sequences):
    index = defaultdict(list)
    for seq_id, seq in enumerate(repository_sequences):
        visemes = seq.viseme_sequence()
        for i in range(len(visemes) - 1):
            bigram = (visemes[i], visemes[i + 1])
            index[bigram].append((seq_id, i))
    return index


Explanation:

- index: A dictionary where each key is a viseme bigram (tuple of two visemes), and the value is a list of positions (sequence ID and index) where this bigram occurs in the repository.
- seq_id: An identifier for each sequence in the repository (using its index in the list).
- Process:

- For each sequence in the repository:
- Extract the viseme sequence.
- Iterate through the visemes to form bigrams.
- Add the bigram and its location to the index.

#### Step 3.1.3: Prepare Repository Sequences

For demonstration purposes, we'll create some hypothetical repository sequences.

# Hypothetical repository sequences (you would replace these with actual data)
repository_sequences = [
    PhonemeSequence([
        Phoneme('B', 0.0, 0.1),
        Phoneme('AE', 0.1, 0.2),
        Phoneme('T', 0.2, 0.3)
    ]),
    PhonemeSequence([
        Phoneme('D', 0.0, 0.1),
        Phoneme('AH', 0.1, 0.2),
        Phoneme('G', 0.2, 0.3)
    ]),
    # Add more sequences as needed
]


Action for You:

- If you have actual repository data, replace the hypothetical sequences with your actual PhonemeSequence instances.
- If not, you can use these examples for testing.

#### Step 3.1.4: Build the Index

Now, let's build the viseme bigram index:

# Build the index
viseme_bigram_index = build_viseme_bigram_index(repository_sequences)


Action for You:

- Add this code to your main.py file.
- You can print the index to see what it looks like:

  print("Viseme Bigram Index:")
  for bigram, locations in viseme_bigram_index.items():
      print(f"{bigram}: {locations}")


- Run your script to see the output.

Expected Output Example (will vary based on your data):

Viseme Bigram Index:
('V3', 'V1'): [(0, 0)]
('V1', 'V5'): [(0, 1)]
('V5', 'V1'): [(1, 0)]
('V1', 'V8'): [(1, 1)]


---

### 3.2 Implement the Fast Phoneme Search Function

Purpose: To efficiently find matching subsequences in the repository that correspond to segments of the edit sequence.

#### Step 3.2.1: Define the Substitution Cost Function

Add the following function:

def substitution_cost(p1, p2):
    return 0 if p1.viseme == p2.viseme else 1  # Cost is 0 if visemes match, else 1


Explanation:

- This function computes the cost of substituting one phoneme for another based on their visemes.
- Since we're focusing on visemes (visual similarity), the cost is zero if the visemes match and one if they don't.

#### Step 3.2.2: Implement the Search Function

Add the following function:

def fast_phoneme_search(edit_seq, repository_sequences, index, max_subseq_length=6):
    matched_sequences = []
    i = 0  # Start index in the edit sequence
    while i < edit_seq.length():
        max_len = min(max_subseq_length, edit_seq.length() - i)
        found_match = False
        # Try to find the longest possible match
        for l in range(max_len, 1, -1):
            subseq = PhonemeSequence(edit_seq.phonemes[i:i + l])
            visemes = subseq.viseme_sequence()
            if len(visemes) < 2:
                continue  # Need at least two visemes for a bigram
            bigram = (visemes[0], visemes[1])
            candidates = index.get(bigram, [])
            for seq_id, pos in candidates:
                repo_seq = repository_sequences[seq_id]
                if pos + l <= repo_seq.length():
                    repo_subseq = PhonemeSequence(repo_seq.phonemes[pos:pos + l])
                    # Compute total substitution cost
                    total_cost = sum(
                        substitution_cost(p1, p2)
                        for p1, p2 in zip(subseq.phonemes, repo_subseq.phonemes)
                    )
                    if total_cost == 0:
                        # Found an exact viseme match
                        matched_sequences.append((repo_subseq, i, i + l))
                        i += l  # Advance index
                        found_match = True
                        break
            if found_match:
                break
        if not found_match:
            # No match found, advance by one phoneme
            i += 1
    return matched_sequences


Explanation:

- Variables:
- matched_sequences: A list to store the matched sequences along with their positions.
- i: The current index in the edit sequence.
- Process:
- While we haven't reached the end of the edit sequence:
- Determine the maximum possible length for a subsequence starting at index i.
- Try to find the longest matching subsequence (from max_len down to 2).
- For each length l:
- Extract a subsequence subseq from the edit sequence.
- Get the viseme bigram (first two visemes).
- Look up candidates in the index.
- For each candidate:
- Check if the subsequence in the repository is long enough.
- Compute the substitution cost between the edit subsequence and the repository subsequence.
- If the total cost is zero (perfect match), add it to matched_sequences and update i.
- If a match is found, break out of the loops to continue with the next part of the edit sequence.
- If no match is found, we advance i by one to try matching the next phoneme.

#### Step 3.2.3: Prepare an Edit Sequence

Create an example edit sequence:

# Hypothetical edit sequence (the sequence you want to synthesize)
edit_sequence = PhonemeSequence([
    Phoneme('B', 0.0, 0.1),
    Phoneme('AE', 0.1, 0.2),
    Phoneme('T', 0.2, 0.3)
])


Action for You:

- Replace the hypothetical edit sequence with your actual desired sequence if you have one.
- Ensure that the phonemes are in Phoneme objects within a PhonemeSequence.

#### Step 3.2.4: Perform the Search

Add the following code:

# Perform fast phoneme search
matched_sequences = fast_phoneme_search(edit_sequence, repository_sequences, viseme_bigram_index)

# Print matched sequences
print("Matched Sequences:")
for repo_subseq, start_idx, end_idx in matched_sequences:
    visemes = repo_subseq.viseme_sequence()
    print(f"Edit positions {start_idx}-{end_idx}: Repository Sequence Visemes: {visemes}")


Expected Output Example (will vary based on data):

Matched Sequences:
Edit positions 0-3: Repository Sequence Visemes: ['V3', 'V1', 'V5']

---

### 3.3 Stitch the Matched Sequences

Purpose: To combine the matched repository sequences into a continuous sequence of expression parameters, aligned with the timings of the edit sequence.

#### Step 3.3.1: Define Placeholder Functions

Since we don't have actual expression parameters, we'll define placeholder functions.

FRAME_RATE = 30  # Frames per second (adjust if needed)

def get_expression_parameters(phoneme_sequence):
    # Placeholder: Generate random parameters
    duration = phoneme_sequence.phonemes[-1].end_time - phoneme_sequence.phonemes[0].start_time
    num_frames = int(duration * FRAME_RATE)
    # Assume 64 expression parameters per frame
    return np.random.rand(num_frames, 64)

def retime_parameters(parameters, target_num_frames):
    # Retime parameters to match the target number of frames
    num_frames = parameters.shape[0]
    retimed_params = np.zeros((target_num_frames, parameters.shape[1]))
    for i in range(parameters.shape[1]):
        retimed_params[:, i] = np.interp(
            np.linspace(0, num_frames - 1, target_num_frames),
            np.arange(num_frames),
            parameters[:, i]
        )
    return retimed_params


Explanation:

- get_expression_parameters:

- Generates a random array to simulate expression parameters.
- In practice, you'd retrieve actual parameters from your data.

- retime_parameters:

- Adjusts the parameters to match a target number of frames.
- Uses linear interpolation.

#### Step 3.3.2: Implement the Stitching Function

Add the following function:

def stitch_sequences(matched_sequences, edit_sequence):
    stitched_parameters = []
    for repo_subseq, start_idx, end_idx in matched_sequences:
        # Get expression parameters for the repository subsequence
        source_params = get_expression_parameters(repo_subseq)
        # Calculate the target duration from the edit sequence
        start_time = edit_sequence.phonemes[start_idx].start_time
        end_time = edit_sequence.phonemes[end_idx - 1].end_time
        target_duration = end_time - start_time
        target_num_frames = int(target_duration * FRAME_RATE)
        # Retime source parameters to match the target number of frames
        retimed_params = retime_parameters(source_params, target_num_frames)
        # Append to the stitched parameters
        stitched_parameters.append(retimed_params)
    # Concatenate all parameters into one sequence
    if stitched_parameters:
        stitched_parameters = np.vstack(stitched_parameters)
    else:
        stitched_parameters = np.array([])  # Empty array if no matches
    return stitched_parameters


Explanation:

- For each matched sequence:
- Retrieve the source expression parameters.
- Determine the target duration and number of frames based on the edit sequence timings.
- Retime the source parameters to align with the target frames.
- Append the retimed parameters to stitched_parameters.
- Finally, concatenate all parameters to form a continuous sequence.

#### Step 3.3.3: Perform Stitching

Add the following code:

# Stitch the matched sequences to get source expression parameters
stitched_parameters = stitch_sequences(matched_sequences, edit_sequence)

# Print the shape of the stitched parameters
print("Stitched Parameters Shape:", stitched_parameters.shape)


Expected Output (will vary):

Stitched Parameters Shape: (9, 64)

- Explanation: If the total duration corresponds to 9 frames at 30 FPS, and we have 64 parameters per frame.

---

### Action for You:

1. Add the Code:

- Copy and paste the code snippets from 3.1 to 3.3 into your main.py file, in the appropriate locations.

2. Understand Each Step:

- Read through the code and comments to understand what's happening.
- Ask questions if anything is unclear.

3. Run the Code:

- Save your main.py file.
- Run the script from your terminal:

     python main.py


4. Observe the Output:

   - Check the outputs printed to the console.
   - Ensure that the viseme bigram index is built, matches are found, and the stitched parameters are generated.

5. Use Real Data (if available):

   - If you have actual data for the edit sequence and repository sequences, use it instead of the hypothetical data.
   - Update the Phoneme and PhonemeSequence instances accordingly.

6. Let Me Know:

   - Once you've completed these steps, please let me know how it went.
   - If you encountered any issues or have questions, I'm here to help.

---

### Understanding How This Replicates the Research Paper's Method

- Fast Phoneme Search:

  - We're implementing an efficient search algorithm that leverages a viseme-based index.
  - By focusing on viseme bigrams, we reduce the search space and improve performance.

- Stitching Sequences:

  - By retiming and concatenating the matched source parameters, we create a continuous sequence that matches the edit.
  - The methods align with the description in the research paper's method section.

---

### Next Steps (After Completion)

- Once we've successfully implemented and tested the Fast Phoneme Search and Stitching, we can proceed to Step 4: Implementing Neural Retargeting.
- In that step, we'll create and train a neural network to retarget the stitched source parameters to match the target actor's expressions.

---

I'm excited to hear about your progress! Feel free to share any outputs or specific questions you might have.

i got this as output (myenv) PS C:\Users\pc\Desktop\project> python main2.py

Viseme Bigram Index:
('V3', 'V1'): [(0, 0), (2, 0)]
('V1', 'V5'): [(0, 1), (2, 1)]
('V5', 'V1'): [(1, 0)]
('V1', 'V8'): [(1, 1)]
('V5', 'V14'): [(2, 2)]
Sequence Length: 4
Viseme Sequence: ['V3', 'V1', 'V5', 'V14']

Matched Sequences:
Edit positions 0-4: Repository Sequence Visemes: ['V3', 'V1', 'V5', 'V14'].
lets move on to next step