Results
1 Influence of the training set
(a) (b) (c)
(d) (e)
Figure
1 : Different Training Set images used in this section.
Figure
2 : Input image, at its original size, and up sampled
with
bilinear interpolation. The last image is the
mid-band
of the interpolated image.
Here the training set images were chosen to verify their influence on the result. The horizontal, vertical and diagonal examples show how the style of the training set can be seen in the result. In figure 14 (using the circle image), the leaves are all rounded, but the edges are sharp. When these four images are used together, the result is much better, much more realistic. This shows that instead of using one big image as training data, it is better to use a diversified set of smaller images.
The test with the “text image” shows how different parts of the training set (here different characters) are combined to create edges.
Figure 3 : Super-resolution
using the “vertical” image (a). On the right is shown the
high-frequency band generated by the program.
Figure 4 : Super-resolution
using the “horizontal” image (b).
Figure 5 : Super-resolution
using the “diagonal” image (d).
Figure 6 : Super-resolution
using the “circle” image (c).
Figure 7 : Super-resolution
using the four images (a), (b), (c) and (d).
Figure 8 : Super-resolution
using the “text” image (e). Note that the algorithm tries to “create” edges
with the characters.
2 Influence of the a parameter
·
: the overlap does
not affect the matching process, only frequential effects are taken into
account. (here the images are displayed four times bigger than their real
size).
Figure 9 : a = 0
On the left is the
result of super-resolution with and on the right with
. Here the result is not as bad as Freeman said, but we can
see some artefacts when
, due to the discontinuity of the high-frequency band. The
artefacts are 4 pixel-large (the size of the high-frequency patches (5 px)
minus the overlap (1 px)).
·
: this is the value recommended by Freeman. The quality is
good.
Figure 10 : a = 0,5
On the left is the bilinearly
interpolated image, and on the right the result of super-resolution. Note that
with super-resolution we get a foreground (the two big flowers) and a
background (on the top-right and
on the bottom-left), which
we cannot really see with bilinear
interpolation.
·
: the overlap has a more important influence in the matching
process.
Figure 11 : a = 5
On the left is shown the generated
image with a = 0,5 and on
the right with
a = 5. We can see that some artefacts
appear, even in smooth parts (on the bottom-right).
·
: the frequential effects are hardly taken into account.
Figure 12 : a = 500
Here are displayed on the top, the
results with (left) and
(right), and on the
bottom the corresponding high-frequency bands generated by super-resolution.
The high-frequency band does not look
like the image itself, and thus, once added to the interpolated image, it
creates many artefacts.
3 Textures
Wall.
Figure 13 a 52x52 wall texture,
zoomed in by a factor 2 and 4 with super-resolution (top), cubic B-Spline
interpolation (center) and bilinear interpolation (bottom). On
the bottom-right is the training set image used in super-resolution.
Corrugated iron.
Figure 14 a 65x50 corrugated iron
texture, zoomed in by a factor 2 and 4 with super-resolution (top), cubic
B-Spline interpolation (center) and bilinear interpolation (bottom). Up-left
is the training image used in super-resolution.
Palm tree trunk.
Figure 15 : palm tree trunk
(left), zoomed in by a factor 2 with super-resolution (center-left), cubic
B-Spline interpolation (center-right) and bilinear interpolation (right). Down-left
is the training image used in super-resolution.
Coloured circles.
Figure 16 : Training set image.
Figure 17 : coloured circles
texture, zoomed in by a factor 2 and 4 with super-resolution (top), cubic
B-Spline interpolation (center) and bilinear interpolation (bottom).
4 Others results.
Corcovado.
Figure 18 : detail of the
Corcovado, zoomed in by a factor 2 and 4 with super-resolution. Note
that the jpeg artefacts from the original image are amplified by
super-resolution.
Stone wall.
Figure 19 : detail of a stone
wall, zoomed in by a factor 2 with bilinear interpolation (left) and with
super-resolution (right).
Branches.
Figure 20 : Branches, zoomed in
by a factor 2 with bilinear interpolation (left) and with super-resolution
(right).
Desert plant.
Figure 30 : Desert plant :
original image (center) sharpened with super-resolution (left), and up
sampled with bilinear interpolation (right).
Jaguar.
Figure 11 : Jaguar, zoomed in by
a factor 2 with bilinear interpolation (top) and with super-resolution
(bottom).