Assignment P1
Student: Jan Hendrik Dithmar, 2031259, jadi5003@stud.uni-saarland.de


Problem 1

(a)
The standard deviation of the noisy images increase by a small value while increasing the noise level.

(b)
Suitable values I found:
couple10.pgm: sigma = 0.3
couple20.pgm: sigma = 0.65
couple40.pgm: sigma = 0.8

The standard deviation after the convolution is much higher (about 70).


Problem 2

(a)
You get a three-point spectrum because you have the average grey value in the middle and because the Fourier Transformation
is always point-symmetric, you get the other two points.
It is located this way because you have a change in frequencies in this way while in the other way the signal is constant.

(b)
Usually, the Fourier Transform of a Gaussian is again a Gaussian. The Gaussian in gauss3.pgm is too big, it goes over the
boundaries of the image. That is why this Gaussian doen't become a Gaussian again.

(c)
Yes, I can find aliasing artifacts. These are located in the middle of the spectrum from left to right where a lot of lines
overlap. (This can be seen in file tile_fs.pgm)


Problem 3

The naming of the files is like the following:
<imagename>_fft.pgm is the Fourier spectrum where you can see how the filter is applied.
<imagename>_filter.pgm is the actual filtered image.