So today we have the last regular lecture, next week we will discuss the exercises.

So today we will have some further topics we have not yet touched.

So far we have been discussing how to deal with images as unknown.

So to like denoise image and we also have seen some other tasks like inpainting or reconstruction

or segmentations.

Today we want to look at one interesting thing that is more related to videos than really

to images, namely the issue of image registration or motion estimation.

So what you could typically think of is you have some video with some moving objects like

a driving car or something like this and you want to detect the motion and you would like

also to estimate the motion.

So for example what parts in the image are moving and at which velocity.

There are several, why is it not working?

Okay let me restart this.

So there is a simple case that is done in many experiments in physics or chemistry.

It's when you have somehow a movie of particles like these little circles or some small well

distinguished objects.

And the simplest thing would be to track through the whole video sequence each of these particles.

So of course it's not very advanced, often done manually.

And there are slightly more advanced topics or methods where you try to find somehow,

you look into a full window of particles and you try in the next time step, if you think

you have discrete time steps you would look okay where do I find somehow a window of the

same particles.

So you could, for example this is what is called particle image velocimetry.

So this is kind of a pure statistical thing.

You try to compute some correlation between different parts in the image and you try to

find somehow the one which has the best correlation and then you say okay this has moved there

and this has moved there.

Okay this is of course not what we want to do because we want to do some PDEs.

Okay we need to restart again.

This will work at some point.

Maybe I can use something from here as well.

Where is it?

Okay good.

So if you think about a very general thing you would say okay I have two images like

the left and the right in the simplest case.

In Moriwan's case you have more than two so you have a whole sequence but to start with

you say okay the first thing I want to have is from one time step to the next.

Or the same problem happens in many other applications where for example you take an

image from different lighting conditions or you take an image from like in medicine with

different devices and so on.

So you have like two tomography scans of the same patient but with different tomographs

and then you want to match them to align them and so on.

Okay so here of course if you take images like this there are absolutely no particles

so it's not so easy to track if you how to get the motion.

Okay what you could do is to say I try to do the same as I have in continuum mechanics.

Of course if you look at this image it's somehow just a deformation of the left.

This was very simply constructed it's just somehow blowing up the whole thing that I

have on the left.

So what I could try to find is some kind of deformation vector.

So you would say okay I start maybe with identity would be just for the visualization would