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#LyX 2.0 created this file. For more info see http://www.lyx.org/
\lyxformat 413
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\begin_body
\begin_layout Title
\noindent
FFV1 Video Codec Specification
\end_layout
\begin_layout Author
by Michael Niedermayer <[email protected]>
\end_layout
\begin_layout Standard
\begin_inset CommandInset toc
LatexCommand tableofcontents
\end_inset
\end_layout
\begin_layout Section
Introduction
\end_layout
\begin_layout Standard
The FFV1 video codec is a simple and efficient lossless intra-frame only
codec.
\end_layout
\begin_layout Standard
The latest version of this document is available at
\begin_inset Flex URL
status collapsed
\begin_layout Plain Layout
https://raw.github.com/FFmpeg/FFV1/master/ffv1.lyx
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\noindent
This document assumes familiarity with mathematical and coding concepts
such as Range coding and YCbCr colorspaces.
\end_layout
\begin_layout Section
Terms and Definitions
\end_layout
\begin_layout Labeling
\labelwidthstring 00.00.0000
ESC Escape symbol to indicate that the symbol to be stored is too large
for normal storage and a different method is used to store it.
\end_layout
\begin_layout Labeling
\labelwidthstring 00.00.0000
MSB Most significant bit, the bit that can cause the largest change in magnitude
of the symbol
\end_layout
\begin_layout Labeling
\labelwidthstring 00.00.0000
RCT Reversible Color Transform, a near linear, exactly reversible integer
transform that converts between RGB and YCbCr representations of a sample.
\end_layout
\begin_layout Labeling
\labelwidthstring 00.00.0000
VLC Variable length code
\end_layout
\begin_layout Section
General Description
\end_layout
\begin_layout Standard
Each frame is split in 1 to 4 planes (Y, Cb, Cr, Alpha).
In the case of the normal YCbCr colorspace the Y plane is coded first followed
by the Cb and Cr planes, if an Alpha/transparency plane exists, it is coded
last.
In the case of the JPEG2000-RCT colorspace the lines are interleaved to
improve caching efficiency since it is most likely that the RCT will immediatel
y be converted to RGB during decoding; the interleaved coding order is also
Y,Cb,Cr,Alpha.
\end_layout
\begin_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 see
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Coding-of-the-sample-difference"
\end_inset
.
\end_layout
\begin_layout Subsection
Border
\end_layout
\begin_layout Standard
For the purpose of the predictior and context, samples above the coded slice
are assumed to be 0; samples to the right of the coded slice are identical
to the closest left sample; samples to the left of the coded slice are
identical to the top right sample (if there is one), otherwise 0.
\end_layout
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\begin_layout Subsection
Median predictor
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\begin_layout Standard
median(left, top, left + top - diag)
\end_layout
\begin_layout Standard
left, top, diag are the left, top and left-top samples
\end_layout
\begin_layout Standard
Note, this is also used in JPEG-LS and HuffYuv
\begin_inset CommandInset citation
LatexCommand cite
key "JPEGLS,HuffYuv"
\end_inset
.
\end_layout
\begin_layout Subsection
Context
\end_layout
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\begin_layout Standard
The quantized sample differences L-l, l-tl, tl-t, t-T, t-tr are used as
context:
\end_layout
\begin_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
\end_layout
\begin_layout Standard
If the context is smaller than 0 then -context is used and the difference
between the sample and its predicted value is encoded with a flipped sign.
\end_layout
\begin_layout Subsection
Quantization
\end_layout
\begin_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:
\end_layout
\begin_layout Standard
\begin_inset Formula $Q_{i}[a-b]=Table_{i}[(a-b)\&255]$
\end_inset
\end_layout
\begin_layout Subsection
Colorspace
\end_layout
\begin_layout Subsubsection
JPEG2000-RCT
\end_layout
\begin_layout Standard
\begin_inset Formula $Cb=b-g$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $Cr=r-g$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $Y=g+(Cb+Cr)>>2$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $g=Y-(Cb+Cr)>>2$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $r=Cr+g$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $b=Cb+g$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset citation
LatexCommand cite
key "JPEG2000"
\end_inset
\end_layout
\begin_layout Subsection
\begin_inset CommandInset label
LatexCommand label
name "sub:Coding-of-the-sample-difference"
\end_inset
Coding of the sample difference
\end_layout
\begin_layout Standard
Instead of coding the n+1 bits of the sample difference with Huffman-, or
Range coding (or n+2 bits, in the case of RCT), only the n (or n+1) least
significant bits are used, since this is sufficient to recover the original
sample.
In the equation below, the term
\begin_inset Quotes eld
\end_inset
bits
\begin_inset Quotes erd
\end_inset
represents bits_per_raw_sample+1 for RCT or bits_per_raw_sample otherwise:
\end_layout
\begin_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
\end_layout
\begin_layout Subsubsection
Range coding mode
\end_layout
\begin_layout Standard
Early experimental versions of FFV1 used the CABAC Arithmetic coder from
H.264
\begin_inset CommandInset citation
LatexCommand cite
key "H264"
\end_inset
, but due to the uncertain patent/royality situation, as well as its slightly
worse performance, CABAC was replaced by a range coder based on an algorithm
defined by
\shape italic
G.
Nigel N.
Martin
\shape default
in 1979
\begin_inset CommandInset citation
LatexCommand cite
key "RangeCoder"
\end_inset
.
\end_layout
\begin_layout Paragraph
Binary values
\end_layout
\begin_layout Standard
To encode binary digits efficiently a range coder is used.
\begin_inset Formula $C_{i}$
\end_inset
is the i-th Context.
\begin_inset Formula $B_{i}$
\end_inset
is the i-th byte of the bytestream.
\begin_inset Formula $b_{i}$
\end_inset
is the i-th range coded binary value,
\begin_inset Formula $S_{0,i}$
\end_inset
is the i-th initial state, which is 128.
The length of the bytestream encoding n binary symbols is
\begin_inset Formula $j_{n}$
\end_inset
bytes.
\end_layout
\begin_layout Standard
\begin_inset Formula $r_{i}=\left\lfloor \frac{R_{i}S_{i,C_{i}}}{2^{8}}\right\rfloor $
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $\begin{array}{ccccccccc}
S_{i+1,C_{i}}=zero\_state_{S_{i,C_{i}}} & \wedge & l{}_{i}=L_{i} & \wedge & t_{i}=R_{i}-r_{i} & \Longleftarrow & b_{i}=0 & \Longleftrightarrow & L_{i}<R_{i}-r_{i}\\
S_{i+1,C_{i}}=one\_state_{S_{i,C_{i}}} & \wedge & l_{i}=L_{i}-R_{i}+r_{i} & \wedge & t_{i}=r_{i} & \Longleftarrow & b_{i}=1 & \Longleftrightarrow & L_{i}\geq R_{i}-r_{i}
\end{array}$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $\begin{array}{ccc}
S_{i+1,k}=S_{i,k} & \Longleftarrow & C_{i}\neq k\end{array}$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $\begin{array}{ccccccc}
R_{i+1}=2^{8}t_{i} & \wedge & L_{i+1}=2^{8}l_{i}+B_{j_{i}} & \wedge & j_{i+1}=j_{i}+1 & \Longleftarrow & t_{i}<2^{8}\\
R_{i+1}=t_{i} & \wedge & L_{i+1}=l_{i} & \wedge & j_{i+1}=j_{i} & \Longleftarrow & t_{i}\geq2^{8}
\end{array}$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $R_{0}=65280$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $L_{0}=2^{8}B_{0}+B_{1}$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $j_{0}=2$
\end_inset
\end_layout
\begin_layout Paragraph
Non binary values
\end_layout
\begin_layout Standard
\begin_inset CommandInset label
LatexCommand label
name "sub:Non-binary-values"
\end_inset
To encode scalar integers it would be possible to encode each bit separately
and use the past bits as context.
However that would mean 255 contexts per 8-bit symbol which is not only
a waste of memory but also requires more past data to reach a reasonably
good estimate of the probabilities.
Alternatively assuming a Laplacian distribution and only dealing with its
variance and mean (as in Huffman coding) would also be possible, however,
for maximum flexibility and simplicity, the chosen method uses a single
symbol to encode if a number is 0 and if not encodes the number using its
exponent, mantissa and sign.
The exact contexts used are best described by the following code, followed
by some comments.
\end_layout
\begin_layout LyX-Code
void put_symbol(RangeCoder *c, uint8_t *state, int v, int is_signed) {
\end_layout
\begin_layout LyX-Code
int i;
\end_layout
\begin_layout LyX-Code
put_rac(c, state+0, !v);
\end_layout
\begin_layout LyX-Code
if (v) {
\end_layout
\begin_layout LyX-Code
int a= ABS(v);
\end_layout
\begin_layout LyX-Code
int e= log2(a);
\end_layout
\begin_layout LyX-Code
\end_layout
\begin_layout LyX-Code
for (i=0; i<e; i++)
\end_layout
\begin_layout LyX-Code
put_rac(c, state+1+MIN(i,9), 1); //1..10
\end_layout
\begin_layout LyX-Code
\end_layout
\begin_layout LyX-Code
put_rac(c, state+1+MIN(i,9), 0);
\end_layout
\begin_layout LyX-Code
for (i=e-1; i>=0; i--)
\end_layout
\begin_layout LyX-Code
put_rac(c, state+22+MIN(i,9), (a>>i)&1); //22..31
\end_layout
\begin_layout LyX-Code
\end_layout
\begin_layout LyX-Code
if (is_signed)
\end_layout
\begin_layout LyX-Code
put_rac(c, state+11 + MIN(e, 10), v < 0); //11..21
\end_layout
\begin_layout LyX-Code
}
\end_layout
\begin_layout LyX-Code
}
\end_layout
\begin_layout Paragraph
Initial values for the context model
\end_layout
\begin_layout Standard
At keyframes all range coder state variables are set to their initial state.
\end_layout
\begin_layout Paragraph
State transition table
\end_layout
\begin_layout Standard
\begin_inset space ~
\end_inset
\begin_inset Newline newline
\end_inset
\begin_inset Formula $one\_state_{i}=default\_state\_transition_{i}+state\_transition\_delta_{i}$
\end_inset
\begin_inset Newline newline
\end_inset