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3. Inter PU motion parameters and reference list index or indices, for motion
estimation;
4. Rate-distortion optimized quantization (RDOQ), for quantization process.
The key function and differentiation point of a “good” encoder is the selection
of the “best” coding parameters (or so-called syntax element values), for improved
coding efficiency. Finding the “best” coding parameters is traditionally performed in
a rate-distortion (R-D) sense: it enables tradeoffs between the numbers of bits used
to encode a block of the picture vs. the resulting distortion that is produced by using
that number of bits. An R-D optimization problem can in general be formulated as:
. coding parameters / .D/ subject to
min
R R T
(9.1)
where
D D Distortion ;
R D Rate . number of bits required to signal coding parameters /
R T D Ta rg e t R a t e
The above minimization is over a combined set of coding parameters and the dis-
tortion term is used to quantify the fidelity between original and reconstructed block.
In principal, distortion can be measured either by relying on a mathematical distance
or by taking into account perception mechanisms. Perceptual metrics correlate well
with viewers' perceptual experience but defining them is challenging because of the
complexity of modeling various physiological components involved in human visual
system. Objective quality measures based on mathematical distances, on the other
hand, are easier to derive and under many circumstances they can still provide good
tradeoffs between subjective quality and rate used. They are, moreover, “content-
agnostic”. That is, the same error distribution on different content could yield
similar objective quality metrics. Examples of distance based objective quality
metrics include mean-squared error (MSE), peak-signal-to-noise (PSNR), and sum
of absolute differences (SAD).
Constrained optimization problem in ( 9.1 ) can be turned into an unconstrained
optimization problem by the introduction of non-negative Lagrangian multiplier œ
which combines R and D into a so-called Lagrangian cost function [ 20 , 22 ], namely:
. coding parameters / J D .D C œ R/
min
(9.2)
Note that œ acts, in a sense, as a “knob”: changing the value of œ enables
tradeoffs between rate decreases vs. distortion increases. For example, œ D 0, in
( 9.2 ), corresponds to minimizing distortion; conversely, choosing a large value for
œ corresponds to rate minimization. A natural question that arises is what value to
choose for œ? Sullivan and Wiegand [ 22 ]andOhmetal.[ 19 ] address this question
by establishing a relationship between œ and quantization step size Q .
œ D c Q 2
(9.3)
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