Black and White images are not using the color view of
humans. Complicated information can be coded in colors to provide more
significant pictures with a striking contrast. We experimented many
different color mappings, where the ``jet'' or ``hsv'' color maps in
Matlab provided good contrasts. The ``jet'' color map changes from
blue for the lowest intensity, to green over yellow to red for the
maximum intensity. The ``hsv'' is as follows red 
yellow
green blue purple
magenta. The idea of the different colors is that
domains are easier separable for the human. High activations
represented as red can be spotted immediately.
The 16 bit precision of the intensities is also too wide to display on a screen or print on paper. It is easier to distinguish different areas by using fewer colors. We tried color maps ranging from 2 colors up to 256. Our display function takes the number of different color values to display as an argument. The function is called dspim for display image and can be found in the appendix. We found empirically that 64 colors yielded the best results and this range is used to print all the Sand3 images in this report.
Multiple representation methods of the same image can also show more information about an image. We experimented with surface plots, gradient flow diagrams and contour plots. Figure 11 shows the results. The contour plot can be useful by partitioning the image into multiple areas. Unfortunately, the gradient flow diagram does not reveal much additional information on the entire image, its strengths can be better used when using on smaller subareas of the image. The last diagram uses a very restricted color palette. This is very similar to the contour plot. The different image areas can be better distinguished in this representation.
Figure 11: Different image representations
Another method to improve the contrast of the image was histogram
equalization. Histogram modeling
has been found to be a powerful technique for image enhancement
[Jai89]. The histogram of the original Sand3 image is very
biased (see bottom left diagram in Figure 13 or
14). We can say that the range of the possible
intensities is not well used at all. Most of the image is a specific
gray value. In order to better extract the information in the image
and to improve the contrast, we would like to remap the
intensities. This can be done by applying a function which spreads the
intensities that are close to the highest histogram value apart. For
example, we have 16 bit precision for our intensities. To display
the image, we use a gray scale with 64 entries. We therefore have
intensities which are mapped onto one intensity
value for the display. In the histogram, we can see which one of the
64 values is dominant. If we could also spread those 1024 values
apart, in such a manner that they fall into more different intensity
values, we increased the contrast and use the range better. We found
that a sigmoid transfer function, centered at the dominant histogram
value can well stretch those values apart. The sigmoid function has
the formula
and is plotted in Figure 12. The Matlab code for the histogram stretching is in the file hist_stretch.m in the appendix. In Figure 13 and 14 we can clearly see that the image quality was improved. Many more details become visible and the color range is better used. Figure 13 was created by applying hist_stretch.m 4 times consecutively, in Figure 14, the function was applied 5 times.
Figure 13: Histogram Stretching applied
to Sand3 with horizontal Line removed
Figure 14: Histogram Stretching applied
to Sand3 with background removed
