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where
N
t
−
Δ
t
is the average intensity in the neighborhood of
x
t
−
Δ
t
and
T
I
is an in-
tensity difference threshold for detecting the disagreement between intensities of
the corresponding original frame locations, and hence, avoiding the formation of
blur and halo effects (i.e. ghosting artifacts around motion boundaries). The above
equation states that if the layer label at a transformed location
x
t
−
1
or
x
t
is different
than the layer label at the source location
x
t
−
Δ
t
, then the intensity at the transformed
location should not be taken into account, since the layer is occluded at that point.
All the remaining cases that are not covered by the first three pieces of the function
are mainly caused by the errors in the estimation process and modeling. In these de-
generate cases, smoothness is enforced by using only the intensity that is closer to
the average intensity
N
t
−
Δ
t
in the neighborhood of the interpolation frame location
x
t
−
Δ
t
.
Finally, another special degenerate case occurs when both of the transformed
locations fall outside the frame boundaries. A similar strategy can be followed in this
case in order to enforce smoothness in the results. As an example, such boundary
pixels can be interpolated with the intensity values of the closest locations in the
interpolation frame.
3.5
Results
Fig. 5 and Fig. 7 present some sample results of the algorithm tested on several well-
known video sequences, where bicubic interpolation is used in obtaining intensities
at sub-pixel locations. In order to evaluate the performance of the method both qual-
itatively and quantitatively, only odd frames of the inputted sequences are processed
and a single frame corresponding to
t
= 0
.
5 is interpolated between each pair of
odd frames. The interpolation frames are then compared with the even frames of the
original sequences both objectively and subjectively.
The algorithm achieves visually pleasing results without apparent blur or halo
effects and with sharpness preserved at object boundaries. For objective evalua-
tion, peak signal-to-noise ratio (PSNR) between the even frames of the original
sequences and the interpolated frames are computed. Fig. 6 provides a comparison
between the proposed method and a simple frame averaging scheme for the
Flower
Garden
sequence. The plot suggests a significant improvement in PSNR as well as
an enhanced robustness to changes in motion complexity.
It worths noting that the performance of the proposed technique is closely tied to
the quality of the segmentation estimates (both segmentation maps and correspond-
ing motion models). However, the method is observed to be tolerant to changes in
the number of layers, provided that the corresponding motion model estimates are
reasonably accurate.
Δ
