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multiresolution framework, which is common approach in motion calculations (to
enable computation of large flows).
1.5
Benchmarking in Testing
When presenting a new solution to a problem, any claims of improved results or
performance should be supported by a reasonable validation of the claims. In most
cases the other methods used to compare ones own method to are rather simple,
as authors often have to balance the effort between improving one's own method
and implementing other advanced methods for comparison. A common benchmark
for testing TSR algorithms would make it easy to compare performances and re-
sults, but none exist. Even with a data set for benchmarking generally agreed upon,
the question of how to evaluate the results remains—should it be done objectively
and/or subjectively and what exact method(s) of evaluation should be used.
1.6
Outline
The rest of this chapter is organized as follows. In the next section, a generic energy
formulation for TSR is proposed, and we study in more details the case of frame
doubling proposing two algorithms. Then in Section 3 we evaluate our two frame
doubling methods through a series of experiments before drawing our conclusions
in section 4.
2
Energy Minimization Formulation
We use a probabilistic formulation to get to our energy formulation. This formu-
lation was first proposed in [22] for image sequence inpainting and then used for
deinterlacing in [23] and well as video (spatial) super resolution in [24].
2.1
Variational Temporal Super Resolution
We assume we are given an “degradation process”
D
which produces a “low-
resolution” observed output from an hypothetical high-resolution input, as well as
such a low resolution observation
u
0
. Following [22], the probability that a high-
resolution input
u
andmotionfield
v
produces the output
u
0
via
D
,
p
(
u
,
v
|
u
0
,
D
),is
factored as
p
(
u
,
v
|
u
0
,
D
)
∝
u
,
D
)
P
0
p
(
u
0
|
p
(
u
s
)
P
1
u
s
,
v
)
P
2
p
(
u
t
|
p
(
v
)
P
3
.
(1)
where
u
s
and
u
t
are the spatial and temporal distribution of intensities respectively.
On the left hand side we have the a posteriori distribution from which we wish to
extract a maximum a posteriori (MAP) estimate. The right side terms are:
P
0
,the
image sequence likelihood,
P
1
the spatial prior on image sequences,
P
3
the prior on
