Good.

So we are currently in the chapter, and that's the last package of the lecture.

We talk about image fusion and registration.

Then we look at the rigid situation, rigid registration, where we just allow for rotation

and translation but no deformation.

Deformations will be considered in summer semester in interventional medical image processing.

We look at rigid registration, and Dieter has just shown to you a video where you have

seen how, for instance, the skull is rigid, is registered using an MR and then CT image.

Registration means compute the transformation such that both datasets or multiple datasets

end up to sit in a joint coordinate system, and fusion is the process of computing the

transform and visualizing the multimodal dataset.

Fusion means bring them all together and visualize it.

So it's a little more in terms of expressing the situation.

Good.

And last week we ended the chapter on point correspondence-based registration, where we

use features, points, point correspondencies, and compute out of point correspondencies

the transformation, the rigid transformation.

For the 2D-2D case, it's a linear estimation problem using complex numbers.

For the 3D-2D estimation problem, it's a linear problem using homogeneous coordinates.

And for the 3D-3D point cloud registration, it's also a linear problem using quaternions.

So that was the big picture that we now have in mind while thinking about point-based registration.

Then on Thursday we looked at intensity-based rigid registration.

And the steps for this is as follows.

What do we have to solve?

First of all, we need to define a similarity measure.

That means you take the original image, you take the target image, you map the two images

using transformation T on each other, and then you have a number telling you how well

the two images fit to each other.

Similarity measure.

We will talk about this in a few minutes again in more detail.

Once we have a similarity measure, we need to parameterize our transformation.

We have to characterize what is the type of transformation we look at, and then we basically

define our search space.

So define the parameterization of the transform.

I will give you a few examples then.

And then you get a similarity measure, you incorporate the parameterization of the transform,

and then you try to optimize or to maximize the similarity, or the dissimilarity has to

be minimized in terms of the parameters.

And then you have to walk through the search space and you have to find the extreme values

of your similarity measure.

What's important in this context is the optimization algorithm.

The optimization algorithm that has to be considered.

And if you know these three steps, then you are basically set up to implement a...

Let me just switch that off to implement a registration routine.

Let me just try to switch that off here.

So let's use an example.

How can I switch that off?

Let's look at the registration of two CT datasets first.

So we have one, two.

So this is our source image, and this is our reference image, or that's another name for