## What Elke is doing in Sweden

My sister is currently studying in Sweden. I think she attends a course on image processing, because these are some pictures which she sent around. You see my father’s edges and my own skin. Good job, Elke, I like them! :-)

When Elke sent me those pictures, I got interested in the convolution matrices she used for finding the edges. Therefore I did a few experiments myself, just for refreshing my knowledge.

So, let’s take an arbitrary image. For example Lena Söderberg (or Lenna), a 57 years old woman from Sweden. That’s just fine for today’s blog post. Here is the original picture which I used:

As a first step, I calculated the 1st derivative of this image. Consider the color of every pixel of the image as a function which depends on the coordinates of the pixel. Therefore, I actually have to calculate two first derivatives in orthogonal directions. I chose the two diagonals as my directions. Here are the convolution matrices and the results:

You’ll notice that the first convolution emphazises lines from the lower left-hand side to the upper right-hand side very well, while the second convolution does just the opposite.

The next thing I was interested in was the size of the convolution matrix, and the distance between the pixels I chose for calculating the difference quotient. Once again, here are my convolution matrices and the results:

Well, not to much of a difference. The lines in the resulting picture just get a bit wider. Especially in the third picture one can also see that those lines which go from the upper left-hand side diagonally to the lower right-hand side somehow split up. You’ll notice it if you look at the contour of Lena’s hat. So, these matrices are not very useful.

Next step: Let’s consider applying the Laplace operator to the original image. We can approximate it as the sum over both second difference quotients. Similarly, I will calculate the sums over the difference quotients which approximate the third and the fourth derivative.

Conclusion: Higher derivatives will give little new information about an image, but they are very good in amplifying the image noise of the JPEG image which I originally took. Why on earth do they have a JPEG compressed image on a website about image processing? Isn’t that like promoting an Alfa Romeo on a website about reliable cars? *g*

Annesaid, on March 4, 2009 at 1:22 amDu hast echt lange Weihle Ulf.

Aber coole Sache. Wusste ich alles noch nicht, muss ich zugegeben…. 0:)