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234 Chapter 10. Error Concealment Using Motion Field Interpolation

where
1
k(b)= : (10.4)
1+ e b

The parameter
in Equation (10.3) is used to control the smoothness of the
interpolation kernel. As
varies from 1 to ∞, the interpolation kernel varies
from an approximately linear shape to a brickwall shape, as illustrated in
Figure 10.1.
Once the concealment displacement is estimated, then the damaged pel is
concealed as follows:

ˆ
f(x; y)= f t−:t (x +ˆv x (x; y);y +ˆv y (x; y)): (10.5)
t
In the case where the estimation process produces a subpel accurate displace-
ment, the compensation process will require accessing a pel at a nonsampling
location within the reference frame. Interpolation (e.g., bilinear) of the pels at
surrounding sampling locations can be employed to provide an approximation
to the required pel.

1
γ=1
γ=5
0.9
γ=10
γ=50
0.8
0.7
0.6
h γ (a) 0.5

0.4

0.3

0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
a
Figure 10.1: Interpolation kernel h
(·) with di,erent values of the smoothness parameter