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).