If you think about mathematical methods, if you think about mathematical methods like

like solving linear equation, like Euler-Lagrosh differential equation or anything like that.

Can you give me an overview of topics where we have introduced certain mathematical concepts

that are useful, as I would say, for medical image processing?

Let me start.

Let me start.

Okay, we have here medical image processing.

Let's say we talk about optimization.

So we have learned a lot about optimization.

Where did we apply optimization?

Well, optimization showed up at all places where we had to solve a medical or an image

processing problem that is reduced to the maximization or minimization of an objective

function.

Yeah.

So we have there the min or max of an objective function.

Can you tell me a few objective functions?

Sabine.

For example, I'm going to use the Lagrange multiplier.

Lagrange multiplier is used for incorporating constraints into an optimization problem or

into the objective function.

I want to know an example for an objective function.

For example, the difference between two images.

It might be an objective function if you want to minimize it.

The difference between two images on a component level.

Okay, and we want to maximize with respect to what?

Or minimize?

With respect to what?

Okay.

Well, and this would get a or would result in a trivial solution, right?

So we need a regularizer.

Yeah.

Can you tell me?

Of G or F?

Of G.

Okay.

How do we solve this optimization problem?

Michael?

You can set it to zero.

Yes, in the discrete case, we can do that.

If we have here an integral, how would you do it then?

Right.

The Euler differential equation.

I tend to write it in German.

So Euler-Lagrange.

You remember Euler-Lagrange was here.

You want to optimize a objective function, I think we called it L of X, F, and F prime.

DX.

Or we call it capital F, I guess.

That was the right name that we have used in the lecture.

Okay.