Multihypothesis Motion-Compensated Prediction
with Forward-Adaptive Hypothesis Switching
Markus Flierl
Telecommunications Laboratory
University of Erlangen-Nuremberg
Bernd Girod
Information Systems Laboratory
Stanford University
[email protected]
[email protected]
Forward-Adaptive Hypothesis Switching
Introduction
Goal
• Improved motion-compensated prediction for efficient video
compression
Approaches
• Linear combination of motion-compensated signals
• Forward-adaptive selection of reference frames for motioncompensated prediction
I1
MH2
MH3
Selection of One Motion-Compensated Signal
s[l ]
-
e[l ]
+
Hypothesis with minimum
squared prediction error is
selected
c1[l ]
c 2 [l ]
MH4
Minimizing the Radial Displacement Error
pû x û y ( x, y ) =
 x2 + y 2  ûr =
1

exp −
 2σ 2 
2πσ û2 x
ûx 

û x2 + û y2
pû r (r ) =
 r2
r
exp − 2
 2σ û
σ û2 x

x




Advantage
• More than “additive” gains can be achieved by combining both
approaches
Mobile & Calendar
QCIF, 10 fps
@34 dB PSNR
Multihypothesis Motion-Compensated
Prediction
Multihypothesis Motion Compensation
current frame signal s[l ]
+
1
µ-th hypothesis
c1[l ]
1
c 2 [l ]
e[l ]
-
2
+
prediction error
σ û2
M
x
=
σ û2 x
pû M û M ( x, y) =
x
y
ûr M
M
 x2 + y 2 
1

exp −
2
 2σ 2 M 
2πσ û M
ûx 
x

= min{û r1 ,..., û rM }
pû M (r ) =
r
r
σû M
2
x

r2
exp − 2
 2σ M
ûx

Equivalent Predictor
• Individual and minimum radial displacement errors are
Rayleigh distributed
• This suggests an equivalent predictor with reduced
displacement error variance
Multihypothesis Prediction with
Forward-Adaptive Hypothesis Switching
Combine both predictors and superimpose N hypotheses
where each hypothesis is obtained by switching among M
motion-compensated signals
Theoretical Result
2
• All hypotheses c are shifted versions of the current frame
signal
• The shift is determined by the displacement error
û ~ 0, C∆∆ )
• The ideal reconstruction of the band-limited signal s[l ] is
shifted by the continuous valued displacement error and resampled on the original orthogonal grid
Rate difference when compared to optimum intra-frame encoding:
Φ ee (ω ) N + 1
N −1
=
− 2 P (ω , σ û2 ) +
P (ω ,2σ û2 (1 − ρ û ))
Φ ss (ω )
N
N
P (ω , σ û2 ) = exp(− 12 ω T ωσ û2 )
with
ω = (ω x , ω y )
Optimal Multihypothesis Motion Estimation
min σ e2 ⇒ ρ û =
1
1− N
∆R =
References
1
4π 2
π π
1
∫ ∫ 2 log
−π −π
2
 Φ ee (ω ) 

dω
 Φ ss (ω ) 
[1] B. Girod, “Efficiency Analysis of Multihypothesis Motion-Compensated
Prediction for Video Coding,” IEEE Tr. on Image Processing, vol. 9, no.
2, pp. 173-183, Feb. 2000.
[2] M. Flierl and B. Girod, “Multihypothesis Motion Estimation for Video
Coding,” in Proc. DCC, Snowbird, Utha, Mar. 2001.



