Welcome to the Monday session. We are now in the last chapter of this winter semester

course and the last chapter is about image registration and basically we will focus on

the rigid image registration. What does that mean? That means that we want to capture one

and the same object using two different modalities, using one and the same modalities and capture

the object at different time points and we want to take the pictures we have acquired

and move them into a joint coordinate system. And rigid means there is no deformation. So

you take the skull, nothing is deformed, it's just a rotation and translation. So how many

parameters can characterize rigid transformation in 3D? Six! X, Y, Z. And then you have phi

X, phi Y and that's one, right? The roll. And we allow no deformation. And we all know

that this is not true. I mean, if somebody you know moves around on the table, the belly

is wobbling around and you have nonlinear deformations, right? So how we deal with nonlinear

deformations is something that we will consider in summer semester. We need a little more

mathematics to do that. We need variational calculus to do that. Here we just can brute

force use these square estimators to compute the rotation and translation parameters. And

today I will briefly motivate this problem and tell you how you can efficiently solve

this in 2D. So I will motivate it and I will explain how that works in 2D. That's the program

for today. I also should welcome all the audience in the world because I received emails this

weekend. I'm watching pattern analysis and it's real fun. That's nice. But if people

start to start to send emails with questions, I always have to reply, I have no idea. I

don't know. So image registration, and we have a formal definition. Image registration.

I mean, if I ask you what is image registration. So you have to learn these three lines, right?

Image registration is the process of transforming the different images into one common coordinate

system. The registration of volume is also subsumed by the term image registration. You

We don't say volume registration, we just register volumes.

You might hear we register, we compute a registration,

or we perform a registration,

nic cocoa if anything else,

but transforming in some way the images.

And we have a research team in our lab that focuses

on image registration problems.

So, dependent on the properties, that was a non-rigid transformation.

Oh, that was extremely non-rigid.

It's tax money, so be careful.

The term rigid registration subsumes the process of computing a rigid transform.

Rigid means it doesn't deform.

It just rotates and translates.

Non-rigid means we allow for deformations.

These are the two terms.

The question is how can we compute?

Now it's interesting, we are close to blood, right?

That motivates.

It's like my little son with nice comments on his sister.

Blood motivates.

That's my experience.

Blood motivates.

How can we compute the transformation?

The best thing is that I have some points, and I have points in image number one, points

in image number two, then I have the point correspondences, and based on the point correspondences

I estimate the transformation.

That's the idea.