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200 10 Edge-Based Inpainting
The first term presents smooth continuation demand on
ˆ
θ
Ω
, where a and b are
positive constants, and k is a smoothing kernel. It is the integral of the divergence
(in L
p
function space) of the vector field
ˆ
θ
Ω
, with respect to the gradients of the
smoothed
ˆ
f
Ω
(x). The second term is a constraint between
ˆ
θ
Ω
and
ˆ
f
Ω
(x), where α
is a positive weighting factor.
ˆ
θ
Ω
should be related to
ˆ
f
Ω
(x) by trying to impose
ˆ
θ
Ω
·5
ˆ
f
Ω
= |5
ˆ
f
Ω
|. The use of the vector field θ is the main point of the model
given in Eq. (10.3). Thus, it enables image inpainting to restore missing regions by
continuing both the geometric and photometric regularities of images.
However, the model in Eq. (10.3) assumes that the parameter
ˆ
θ
Ω
can be inferred
from θ under ...