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Welcome to the Tuesday morning session. I have to apologize that I couldn't teach yesterday.

If I was explaining to you a very nice algorithm and very important algorithm that also tackles the problem of point correspondences

and how to find proper point correspondences in combination with the estimation of rotation and translation.

The ICP concept is something that we use heavily for many applications.

And Eva has shown to you, I think, a few examples what we did in our lab regarding this.

So what is the general context? I will not do an overview of the complete lecture today

because I just learned that next week is the last week for teaching.

I'm very surprised. I was expecting that we have one week more.

And so I will just summarize what we are currently considering on image registration and fusion

because, as I said, this is also one important subtopic of this lecture.

Image fusion basically means bring images acquired at different time points, acquired by different modalities,

into a joint common coordinate system such that the doctor can just fade from one image to the other image

or can do some pixel-by-pixel computations with a merged data set.

It's also called sensor data fusion, fusion system, image registration.

These are the terms we usually use.

And the process of image registration is basically nothing else but the computation of the transform of the two images onto each other.

And now we have seen that there are different taxonomies of registration algorithms.

You can look into the dimension of the image data. You can consider 3D by 3D image registration,

2D by 2D image registration, 3D 2D image registration, and many more.

So the dimension is one criterion.

And then we have seen that we can also allow for different mappings between the images.

For instance, rigid transforms, that means that you just rotate and translate, and you allow no deformations.

In this case, we talk about rigid registration.

If deformations are allowed, we talk about non-rigid or deformable registration or flexible registration,

which will be part of the lecture in summer semester.

So rigid versus non-rigid.

And then we have also started to consider two different classes of registration algorithms.

One are using features and feature correspondences.

The other subset of algorithms is just using the intensity information.

And we call this either feature-based registration,

or we call it intensity-based, where we just use the image intensities.

Okay, so these are the different types we have considered so far.

And using point features, we have seen a triple of really nice methods.

One method was the 2D or related to 2D 2D using complex numbers

that you might have learned in the first semester, mathematics.

Then 3D, 3D, we learned about quaternions for rotations.

Three different types of representations of rotations, Euler angles, axis angle, and the quaternions.

Quaternions lead surprisingly to a linear estimator like complex numbers to estimate rotation.

And then we have seen 2D, 3D, where we used homogeneous coordinates.

So we have a very, very good understanding.

Once point correspondences are given, we can compute the rigid transformation between the two sets of points.

And this can be done by basically three lines of MATLAB code.

And that's amazing. That's amazing.

It's very harder to explain these things instead of just implementing it.

Once you are understood how that works, it's easy to implement.

And then we started to look into intensity-based registration.

And that's where I want to continue today.

Intensity-based registration, where we basically use the SSD as a similarity measure

if we want to merge or register images acquired by one and the same modality.