Graphics Reference
In-Depth Information
mixed lossy/lossless coding of pictures. Such a feature is useful in coding video
sequences with mixed content, e.g. natural video with overlaid text and graphics.
The text and graphics regions can be coded losslessly to maximize readability
whereas the natural content can be coded in a lossy fashion.
In the transform skip mode, only the transform is skipped. This mode was
found to improve compression of screen-content video sequences generated in
applications such as remote desktop, slideshows etc. These video sequences
predominantly contain text and graphics. Transform skip is restricted to only
4
4 transform blocks and its use is signaled at the transform unit level by the
transform_skip_flag
syntax element.
6.5
Complexity Analysis
With straightforward matrix multiplication, the number of operations for the 1D
inverse transform is
N
2
multiplications and
N
(
N
1) additions. For the 2D trans-
form, the number of multiplications required is 2
N
3
and the number of additions
required is 2
N
2
(
N
1). However, by utilizing the (anti-) symmetry properties of
each basis vector inherited from DCT, the number of arithmetic operations can be
significantly reduced. We refer to the algorithm that does this as the Even-Odd
decomposition in this paper (it was also referred to as partial butterfly during HEVC
development) [
14
]. Even-Odd decomposition is illustrated below using the 4- and
8-point inverse transform.
Consider the 4-point forward transform matrix defined in (
6.5
). For notational
simplicity the constants
d
32
i
,0
of Eq. (
6.5
) will be denoted by
d
i
.Usingthenew
notation (
6.5
) becomes
2
4
3
5
d
16
d
16
d
16
d
16
d
8
d
24
d
24
d
8
D
4
D
(6.11)
d
16
d
16
d
24
d
16
d
16
d
8
d
24
d
8
The inverse transform matrix is given by
D
4
.Let
x
D
[
x
0
,
x
1
,
x
2
,
x
3
]
T
be the input
vector and
y
D
[
y
0
,
y
1
,
y
2
,
y
3
]
T
denote the output. The 1D 4-point inverse transform
is given by the following equation:
y
D
D
4
x
(6.12)
The Even-Odd decomposition of the inverse transform of an
N
-point input
consists of the following three steps:
1. Calculate the even part using a
N
/2
N
/2 subset matrix obtained from the even
columns of the inverse transform matrix (
6.13
shows an example).
