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ffv1.lyx
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#LyX 1.3 created this file. For more info see http://www.lyx.org/
\lyxformat 221
\textclass article
\language english
\inputencoding auto
\fontscheme default
\graphics default
\paperfontsize default
\spacing single
\papersize Default
\paperpackage a4
\use_geometry 0
\use_amsmath 0
\use_natbib 0
\use_numerical_citations 0
\paperorientation portrait
\secnumdepth 3
\tocdepth 3
\paragraph_separation skip
\defskip medskip
\quotes_language english
\quotes_times 2
\papercolumns 1
\papersides 1
\paperpagestyle default
\layout Title
\noindent
Description of the FFV1 Video Codec
\layout Author
by Michael Niedermayer <michaelni@gmx.at>
\layout Standard
\begin_inset LatexCommand \tableofcontents{}
\end_inset
\layout Section
Introduction
\layout Standard
The FFV1 video codec is a simple lossless intra only codec.
It is still under development and the bitstream might change between versions.
\layout Standard
The latest version of this document is available at http://www.mplayerhq.hu/~micha
el/ffv1.{lyx,txt,html,ps}
\layout Standard
\noindent
This document assumes familiarity with mathematical and coding concepts
such as Arithmetic coding and YCbCr colorspaces.
\layout Section
Terms and Definitions
\layout List
\labelwidthstring 00.00.0000
CABAC Context Adaptive Binary Arithmetic Coder
\begin_inset LatexCommand \cite{H264}
\end_inset
\layout List
\labelwidthstring 00.00.0000
RCT Reversible component transform
\layout Section
High-level Description
\layout Standard
Each frame is split in 3 planes (Y, Cb, Cr).
In the case of the normal YCbCr colorspace the Y plane is coded first followed
by the Cb and Cr planes, in the case of the JPEG2000-RCT colorspace the
lines are interleaved to reduce cache trashing as most likely the RCT will
be immedeatly converted to RGB during decoding, the order of the lines
in the interleaving is again Y,Cb,Cr.
\layout Standard
Samples within a plane are coded in raster scan order (left->right, top->bottom)
, each sample is predicted by the median predictor from samples in the same
plane and the difference is stored
\layout Subsection
Border
\layout Standard
Samples above the coded picture are assumed to be 0, right of the coded
picture are identical to the closest left sample and left of the coded
picture are identical to the top right one
\layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="5">
<features>
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
a
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
b
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
c
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
c
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
a
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
d
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
e
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
e
\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
d
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
f
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
g
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
h
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
h
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\layout Standard
Note, this is identical to
\begin_inset LatexCommand \cite{JPEGLS}
\end_inset
\layout Subsection
Median predictor
\layout Standard
median(left, top, left + top - diag)
\layout Standard
left, top, diag are the left, top and lefttop samples
\layout Standard
Note, this is also used in
\begin_inset LatexCommand \cite{JPEGLS,HuffYuv}
\end_inset
\layout Subsection
Context
\layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="4">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
T
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
tl
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
t
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
tr
\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
L
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
l
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
X
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\layout Standard
The quantized sample differences L-l, l-tl, tl-t, t-T, t-tr are used as
context
\layout Standard
\begin_inset Formula $context=Q_{0}[l-tl]+\left|Q_{0}\right|(Q_{1}[tl-t]+\left|Q_{1}\right|(Q_{2}[t-tr]+\left|Q_{2}\right|(Q_{3}[L-l]+\left|Q_{3}\right|Q_{4}[T-t])))$
\end_inset
\layout Standard
If context < 0 then -context is used and the difference between the sample
and its predicted value is encoded with a flipped sign
\layout Subsection
Quantization
\layout Standard
There are 5 quantization tables for the 5 sample differences, both the number
of quantization steps and their distribution are stored in the bitstream.
Each quantization table has exactly 256 entries, and the 8 least significant
bits of the sample difference are used as index
\layout Standard
\begin_inset Formula $Q_{i}[a-b]=Table_{i}[(a-b)\&255]$
\end_inset
\layout Subsection
Colorspace
\layout Subsubsection
JPEG2000-RCT
\layout Standard
\begin_inset Formula $Cb=b-g$
\end_inset
\layout Standard
\begin_inset Formula $Cr=r-g$
\end_inset
\layout Standard
\begin_inset Formula $Y=g+(Cb+Cr)>>2$
\end_inset
\layout Standard
\begin_inset Formula $g=Y-(Cb+Cr)>>2$
\end_inset
\layout Standard
\begin_inset Formula $r=Cr+g$
\end_inset
\layout Standard
\begin_inset Formula $b=Cb+g$
\end_inset
\layout Standard
\begin_inset LatexCommand \cite{JPEG2000}
\end_inset
\layout Subsection
Coding of the sample difference
\layout Standard
Instead of coding the 9 (or 10 in the case of RCT) bits of the sample difference
with huffman or CABAC coding only the 8 (or 9) least significant bits are
used as thats enough the recover the original sample
\layout Standard
\begin_inset Formula $coder\_ input=\left[\left(sample\_ difference+2^{bits-1}\right)\&\left(2^{bits}-1\right)\right]-2^{bits-1}$
\end_inset
\layout Subsubsection
Arithmetic coding mode
\layout Paragraph
Context Adaptive Binary Arithmetic Coding (CABAC)
\layout Standard
The coder is borrowed from
\begin_inset LatexCommand \cite{H264}
\end_inset
and the reader is referred to that for further information, it is also
noted that the author doesn't know if the coder is patented, so care must
be taken if FFV1 is used in countries where software patents are legal.
But even if CABAC turns out to be patent free there is still some risk
that other parts of FFV1 are covered by patents.
By just looking at the very long list of patents which cover other relatively
simple standards it is shown that the patent offices seem to pass nearly
everything.
In many cases the patents cover basic operations like subtraction or taking
the median of 3 integers in a specific case like motion vectors.
\layout Paragraph
Non binary values
\layout Standard
\begin_inset LatexCommand \label{sub:Non-binary-values}
\end_inset
To encode 8 or 9bit numbers as is needed in our case, we could simply encode
each bit separately and use the past bits as context, but that would mean
255 contexts per 8bit symbol which is not only a waste of memory but also
requires more past data to reach reasonable good estimate of the probabilities.
Alternatively simply assuming a laplacian distribution and only dealing
with its variance and mean like we do in huffman coding mode would be another
possibility, but due to flexibility and simplicity, another method was
chosen, which simply uses a single symbol to encode if a number is 0 and
if not encodes the number using its exponent,mantisse and sign, the exact
contexts which are used can probably better be described by the following
code then by some english text
\layout LyX-Code
put_symbol(CABACContext *c, uint8_t *state, int v, int is_signed, int max_exp){
\layout LyX-Code
int i;
\layout LyX-Code
if(v){
\layout LyX-Code
const int a= ABS(v);
\layout LyX-Code
const int e= av_log2(a);
\layout LyX-Code
put_cabac(c, state+0, 0);
\layout LyX-Code
for(i=0; i<e; i++){
\layout LyX-Code
put_cabac(c, state+1+i, 1); //1..8
\layout LyX-Code
}
\layout LyX-Code
if(e<max_exp){
\layout LyX-Code
put_cabac(c, state+1+i, 0); //1..8
\layout LyX-Code
for(i=e-1; i>=0; i--){
\layout LyX-Code
put_cabac(c, state+16+e+i, (a>>i)&1); //17..29
\layout LyX-Code
}
\layout LyX-Code
if(is_signed)
\layout LyX-Code
put_cabac(c, state+9 + e, v < 0); //9..16
\layout LyX-Code
}
\layout LyX-Code
}else{
\layout LyX-Code
put_cabac(c, state+0, 1);
\layout LyX-Code
}
\layout LyX-Code
}
\layout LyX-Code
\layout Standard
max_exp is 7 unless the RCT is used, in which case it is 8 for the samples
in a plane and 7 for the elements in the header
\layout Standard
is_signed is 1 for encoding of the samples within a plane or line, and 0
for the elements of the header
\layout Paragraph
Initial values for the context model
\layout Standard
At keyframes all CABAC state variables are set to 0 except number 7 which
is set to 124, number 7 is used to select between -127..-64,64..127 and -128
which should explain the strong favoring of the earlier
\layout Subsubsection
Huffman coding mode
\layout Standard
Uses golomb rice codes.
The VLC code is split in 2 parts, the prefix stores the most significant
bits, the suffix stores the k least significant bits or stores the whole
number in the ESC case
\layout Paragraph
Prefix
\layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
bits
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
value
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
1
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
01
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
1
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
...
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
...
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0000 0000 0001
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
11
\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0000 0000 0000
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
ESC
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\layout Paragraph
Suffix
\layout List
\labelwidthstring 00.00.0000
non\SpecialChar ~
ESC the k least significant bits MSB first
\layout List
\labelwidthstring 00.00.0000
ESC the value - 11, in MSB first order, ESC may only be used if the value
cannot be coded as non ESC
\layout Paragraph
Examples
\layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="3">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
k
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
bits
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
value
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
1
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
001
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
2
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
2
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
1 00
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
0
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
2
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
1 10
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
2
\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
2
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
01 01
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
5
\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
any
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\layout Standard
000000000000 10000000
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\layout Standard
139
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\layout Paragraph
run mode
\layout Standard
run mode is entered when the context is 0, and left as soon as a non 0 differenc
e is found, the level is identical to the predicted one, the run and the
first different level is coded