So, good morning everybody.

As you can notice, Vincent is not here today.

He's away this week.

He will be back next week.

And if I'm not mistaken, in two weeks I will also have to replace him.

Okay, some microphone balancing issues.

Just a second.

Okay, it should work like that.

The beamer should be turning on.

Yes, good.

Okay, so it seems to be working.

So today we'll start the lecture with the part about non-linear filtering.

Ah, yeah, by the way, I think you saw me already a few weeks ago.

I'm Mathias Sore.

I'm working with Vincent in the pattern recognition lab, computer vision group.

I will replace him at least once more until the end of the semester.

So today we'll see some non-linear filtering methods.

So some recursive filters, homomorphic filtering, and morphological operators, which are actually

quite amusing in my opinion.

So filtering is applied in the pre-processed...

I think I have the wrong slides without animation.

Yes, give me a second.

I will switch them.

Okay, sorry for this small issue.

So filtering is applied during the pre-processing phase.

So you remember the pipeline.

First you record the data.

Then you pre-process it to make it into something that is easier to process for the classification

task or at least for a feature extraction.

And if you pre-process the data in a correct way, then feature extraction will be way easier,

more stable, and you will get data that you can actually work much better with.

So, so far you've seen histogram equalization, so how to correct the luminosity in images,

thresholding, which is typically used for binarization.

So when you want to have the pixels of an input image either white or black, and you

also saw some linear filtering.

So today we go one step further with nonlinear filtering, and we'll start with recursive

filters.

So recursive filters are filters which can be computed based on a previous value of the

filter.

So for example, if you compute a moving average, which is illustrated here on the left, to

compute a moving average you will take a part of the signal, you make the sum of the values

along this part of the signal, and you divide by the length of the signal, and that gives

you the average for a specific part of the signal.

Then you offset your filter by one step, and you could do the same.

So that means you could again compute the sum of all values and divide by the length

of the signal, and again go one more step, make the sum, divide, and so on.

However, if you think about it, when you compute the moving average, the sum contains a lot

of similar operations between two neighbor locations.

Instead of recomputing every time a whole sum, it might be more efficient to instead

compute the differences compared to the previous step.