spec.tex

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 a more detailed specification of the standards from which its parameters are
 derived.
Some standards do not specify all the parameters necessary.
For these unspecified parameters, this document serves as the definition of
 what should be used when encoding or decoding Theora video.

\subsection{Rec.~470M (Rec.~ITU-R~BT.470-6 System M/NTSC with
 Rec.~ITU-R~BT.601-5)}
\label{sec:470m}

This color space is used by broadcast television and DVDs in much of the
 Americas, Japan, Korea, and the Union of Myanmar \cite{rec470}.
This color space may also be used for System M/PAL (Brazil), with an
 appropriate conversion supplied by the encoder to compensate for the
 different gamma value.
See Section~\ref{sec:470bg} for an appropriate gamma value to assume for M/PAL
 input.

In the US, studio monitors are adjusted to a D65 white point
 ($x_w,y_w=0.313,0.329$).
In Japan, studio monitors are adjusted to a D white of 9300K
 ($x_w,y_w=0.285,0.293$).

Rec.~470 does not specify a digital encoding of the color signals.
For Theora, Rec.~ITU-R~BT.601-5 \cite{rec601} is used, starting from the
 $R'G'B'$ signals specified by Rec.~470.

Rec.~470 does not specify an input gamma function.
For Theora, the Rec.~709 \cite{rec709} input function is assumed.
This is the same as that specified by SMPTE 170M \cite{smpte170m}, which claims
 to reflect modern practice in the creation of NTSC signals circa 1994.

The parameters for all the color transformations defined in
 Section~\ref{sec:color-xforms} are given in Table~\ref{tab:470m}.

\begin{table}[htb]
\begin{align*}
\mathrm{Offset}_{Y,C_b,C_r}    & = (16, 128, 128)  \\
\mathrm{Excursion}_{Y,C_b,C_r} & = (219, 224, 224) \\
K_r                            & = 0.299           \\
K_b                            & = 0.114           \\
\gamma                         & = 2.2             \\
\beta                          & = 0.45            \\
\alpha                         & = 4.5             \\
\delta                         & = 0.018           \\
\epsilon                       & = 0.099           \\
x_r,y_r                        & = 0.67, 0.33      \\
x_g,y_g                        & = 0.21, 0.71      \\
x_b,y_b                        & = 0.14, 0.08      \\
\text{(Illuminant C) } x_w,y_w & = 0.310, 0.316    \\
\end{align*}
\caption{Rec.~470M Parameters}
\label{tab:470m}
\end{table}

\subsection{Rec.~470BG (Rec.~ITU-R~BT.470-6 Systems B and G with
 Rec.~ITU-R~BT.601-5)}
\label{sec:470bg}

This color space is used by the PAL and SECAM systems in much of the rest of
 the world \cite{rec470}
This can be used directly by systems (B, B1, D, D1, G, H, I, K, N)/PAL and (B,
 D, G, H, K, K1, L)/SECAM\@.

\begin{verse}
{\bf Note:} the Rec.~470BG chromaticity values are different from those
 specified in Rec.~470M\@.
When PAL and SECAM systems were first designed, they were based upon the same
 primaries as NTSC\@.
However, as methods of making color picture tubes have changed, the primaries
 used have changed as well.
The U.S. recommends using correction circuitry to approximate the existing,
 standard NTSC primaries.
Current PAL and SECAM systems have standardized on primaries in accord with
 more recent technology.
\end{verse}

Rec.~470 provisionally permits the use of the NTSC chromaticity values (given
 in Section~\ref{sec:470m}) with legacy PAL and SECAM equipment.
In Theora, material must be decoded assuming the new PAL and SECAM primaries.
Material intended for display on old legacy devices should be converted by the
 decoder.

The official Rec.~470BG specifies a gamma value of $\gamma=2.8$.
However, in practice this value is unrealistically high \cite{Poyn97}.
Rec.~470BG states that the overall system gamma should be approximately
 $\gamma\beta=1.2$.
Since most cameras pre-correct with a gamma value of $\beta=0.45$,
 this suggests an output device gamma of approximately $\gamma=2.67$.
This is the value recommended for use with PAL systems in Theora.

Rec.~470 does not specify a digital encoding of the color signals.
For Theora, Rec.~ITU-R~BT.601-5 \cite{rec601} is used, starting from the
 $R'G'B'$ signals specified by Rec.~470.

Rec.~470 does not specify an input gamma function.
For Theora, the Rec 709 \cite{rec709} input function is assumed.

The parameters for all the color transformations defined in
 Section~\ref{sec:color-xforms} are given in Table~\ref{tab:470bg}.

\begin{table}[htb]
\begin{align*}
\mathrm{Offset}_{Y,C_b,C_r}    & = (16, 128, 128)  \\
\mathrm{Excursion}_{Y,C_b,C_r} & = (219, 224, 224) \\
K_r                            & = 0.299           \\
K_b                            & = 0.114           \\
\gamma                         & = 2.67            \\
\beta                          & = 0.45            \\
\alpha                         & = 4.5             \\
\delta                         & = 0.018           \\
\epsilon                       & = 0.099           \\
x_r,y_r                        & = 0.64, 0.33      \\
x_g,y_g                        & = 0.29, 0.60      \\
x_b,y_b                        & = 0.15, 0.06      \\
\text{(D65) } x_w,y_w          & = 0.313, 0.329    \\
\end{align*}
\caption{Rec.~470BG Parameters}
\label{tab:470bg}
\end{table}

\section{Pixel Formats}
\label{sec:pixfmts}

Theora supports several different pixel formats, each of which uses different
 subsampling for the chroma planes relative to the luma plane.

\subsection{4:4:4 Subsampling}
\label{sec:444}

All three color planes are stored at full resolution - each pixel has a $Y'$,
 a $C_b$ and a $C_r$ value (see Figure~\ref{fig:pixel444}).
The samples in the different planes are all at co-located sites.

\begin{figure}[htbp]
\begin{center}
\includegraphics{pixel444}
\end{center}
\caption{Pixels encoded 4:4:4}
\label{fig:pixel444}
\end{figure}

% Figure.
%YRB         YRB
%
%
%
%YRB         YRB
%
%
%


\subsection{4:2:2 Subsampling}
\label{sec:422}

The $C_b$ and $C_r$ planes are stored with half the horizontal resolution of
 the $Y'$ plane.
Thus, each of these planes has half the number of horizontal blocks as the luma
 plane (see Figure~\ref{fig:pixel422}).
Similarly, they have half the number of horizontal super blocks, rounded up.
Macro blocks are defined across color planes, and so their number does not
 change, but each macro block contains half as many chroma blocks.

The chroma samples are vertically aligned with the luma samples, but
 horizontally centered between two luma samples.
Thus, each luma sample has a unique closest chroma sample.
A horizontal phase shift may be required to produce signals which use different
 horizontal chroma sampling locations for compatibility with different systems.

\begin{figure}[htbp]
\begin{center}
\includegraphics{pixel422}
\end{center}
\caption{Pixels encoded 4:2:2}
\label{fig:pixel422}
\end{figure}

% Figure.
%Y     RB    Y           Y     RB    Y
%
%
%
%Y     RB    Y           Y     RB    Y
%
%
%

\subsection{4:2:0 Subsampling}
\label{sec:420}

The $C_b$ and $C_r$ planes are stored with half the horizontal and half the
 vertical resolution of the $Y'$ plane.
Thus, each of these planes has half the number of horizontal blocks and half
 the number of vertical blocks as the luma plane, for a total of one quarter
 the number of blocks (see Figure~\ref{fig:pixel420}).
Similarly, they have half the number of horizontal super blocks and half the
 number of vertical super blocks, rounded up.
Macro blocks are defined across color planes, and so their number does not
 change, but each macro block contains within it one quarter as many 
 chroma blocks.

The chroma samples are vertically and horizontally centered between four luma
 samples.
Thus, each luma sample has a unique closest chroma sample.
This is the same sub-sampling pattern used with JPEG, MJPEG, and MPEG-1, and
 was inherited from VP3.
A horizontal or vertical phase shift may be required to produce signals which
 use different chroma sampling locations for compatibility with different
 systems.

\begin{figure}[htbp]
\begin{center}
\includegraphics{pixel420}
\end{center}
\caption{Pixels encoded 4:2:0}
\label{fig:pixel420}
\end{figure}

% Figure.
%Y           Y           Y           Y
%
%      RB                      RB
%
%Y           Y           Y           Y
%
%
%
%Y           Y           Y           Y
%
%      RB                      RB
%
%Y           Y           Y           Y
%
%
%

\subsection{Subsampling and the Picture Region}

Although the frame size must be an integral number of macro blocks, and thus
 both the number of pixels and the number of blocks in each direction must be
 even, no such requirement is made of the picture region.
Thus, when using subsampled pixel formats, careful attention must be paid to
 which chroma samples correspond to which luma samples.

As mentioned above, for each pixel format, there is a unique chroma sample that
 is the closest to each luma sample.
When cropping the chroma planes to the picture region, all the chroma samples
 corresponding to a luma sample in the cropped picture region must be included.
Thus, when dividing the width or height of the picture region by two to obtain
 the size of the subsampled chroma planes, they must be rounded up.

Furthermore, the sampling locations are defined relative to the frame,
 {\em not} the picture region.
When using the 4:2:2 and 4:2:0 formats, the locations of chroma samples
 relative to the luma samples depends on whether or not the X offset of the
 picture region is odd.
If the offset is even, each column of chroma samples corresponds to two columns
 of luma samples (see Figure~\ref{fig:pic_even} for an example).
The only exception is if the width is odd, in which case the last column
 corresponds to only one column of luma samples (see Figure~\ref{fig:pic_even_odd}).
If the offset is odd, then the first column of chroma samples corresponds to
 only one column of luma samples, while the remaining columns each correspond
 to two (see Figure~\ref{fig:pic_odd}).
In this case, if the width is even, the last column again corresponds to only
 one column of luma samples (see Figure~\ref{fig:pic_odd_even}).

A similar process is followed with the rows of a picture region of odd height
 encoded in the 4:2:0 format.
If the Y offset is even, each row of chroma samples corresponds to two rows of
 luma samples (see Figure~\ref{fig:pic_even}), except with an odd height, where
 the last row corresponds to one row of chroma luna samples only (see 
 Figure~\ref{fig:pic_even_odd}).
If the offset is odd, then it is the first row of chroma samples which
 corresponds to only one row of luma samples, while the remaining rows each
 correspond to two (Figure~\ref{fig:pic_odd}), except with an even height, 
 where the last row also corresponds to one (Figure~\ref{fig:pic_odd_even}).

Encoders should be aware of these differences in the subsampling when using an
 even or odd offset.
In the typical case, with an even width and height, where one expects two rows
 or columns of luma samples for every row or column of chroma samples, the
 encoder must take care to ensure that the offsets used are both even.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth]{pic_even}
\end{center}
\caption{Pixel correspondence between color planes with even picture 
 offset and even picture size}
\label{fig:pic_even}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth]{pic_even_odd}
\end{center}
\caption{Pixel correspondence with even picture offset and 
 odd picture size}
\label{fig:pic_even_odd}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth]{pic_odd}
\end{center}
\caption{Pixel correspondence with odd picture offset and 
 odd picture size}
\label{fig:pic_odd}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth]{pic_odd_even}
\end{center}
\caption{Pixel correspondence with odd picture offset and 
 even picture size}
\label{fig:pic_odd_even}
\end{figure}


\chapter{Bitpacking Convention}
\label{sec:bitpacking}

\section{Overview}

The Theora codec uses relatively unstructured raw packets containing
 binary integer fields of arbitrary width.
Logically, each packet is a bitstream in which bits are written one-by-one by