Information Technology Reference
In-Depth Information
2.2.3
Initialization
At the coarsest level at the top of the pyramid we do not have a
k
+ 1levelto
initialize our data from and thus have to use temporal initialization (inferior to
k
+ 1
initialization). For the flow calculation we have chosen to do frame averaging of
both flow and intensities. If the new frame is located at time
n
and the two know
frames are at times
n
1
/
2then
v
(
x
,
n
)=
v
0
(
x
,
n
1
/
2)+
v
0
(
x
,
n
+ 1
/
2)
/
2and
±
−
u
(
x
,
n
)=
u
0
(
x
,
n
1
/
2)+
u
0
(
x
,
n
+ 1
/
2)
/
2
.
Even though the flow we compute
at the top level is (almost) of subpixel size due to the downscaling, we still use
it to re-initialize the intensities by simple interpolation along the flow
u
(
x
,
n
)=
−
u
0
(
x
+
v
b
,
n
1
/
2)+
u
0
(
x
+
v
f
,
n
+ 1
/
2)
/
2 before we minimize
E
i
(
u
).
−
3
Experiments
We have implemented our frame doubling algorithm in such a way that we can test
it in two versions: With and without the gradient constancy assumption on the flow.
With GCA on the flow, we expect the most correct results as both flow and intensities
are subject to minimal blurring. Without GCA on the flow, a more blurred flow is
expected and thus also a more blurred intensity output.
The tests conducted have focused on the major problem of having too low a frame
rate in image sequences: Unnatural, jerky motion, which is typically most promi-
nent when the camera pans on scenes containing high contrast (vertical) edges. By
doubling the frame rate we will aim at reestablishing the phi-effect. The images
sequences chosen for testing all have the problem of perceived jerky, unnatural mo-
tion. The sequences are a mix of homemade and cutouts of real world motions pic-
tures on standard PAL 25 fps DVDs originating from film. All inputs and results
discussed are also given as video files (*.avi) online at:
http://image.diku.
dk/sunebio/TSR/TSR.zip
[32]. The shareware AVI video viewer/editor Vir-
tualDub is included in the material, and we would like to stress the importance of
viewing the results as video: The effects, artifacts and improvements discussed are
mainly temporal and not seen in stills.
3.1
Parameters
There are eleven parameters to tune in our algorithm and we have focused on op-
timizing the output quality, not speed (yet). Through extensive empirical parameter
testing we have optimized two sets of parameters for variational frame doubling
TSR; with and without GCA in the flow. The settings found to be optimal are given
in Table 1 for both versions of our algorithm. We see that settings for the intensity
energy minimization is the same for both algorithm versions, but the given values
proved optimal with both flow energy minimizations. The temporal to spatial dif-
fusion weight ratio,
λ
s
, is high, favoring temporal diffusion, which ensures that
spatial diffusion is only used when temporal information is highly unreliable. Low-
ering the ratio from 50:1 to 20:1 gave similar results when evaluating on video, but
λ
t
:
