Welcome to the Tuesday morning session.

We are currently in the chapter on image registration.

And we are considering the problem

of registering images from different modalities.

So think about the situation that you have a PET scan,

for instance, and an MR scan.

And these two volumes, they have to be mapped

into a joint coordinate system, T.

And the overall structure of registration algorithms

is always the same.

What you basically do is you define a transform, a type of,

or define a type of T. I say it's a polynomial,

as we have had it in the case of image undistortion.

That was basically already some kind of registration problem.

Or we say it's a rotation and translation,

and no deformation is allowed.

That's a constraint on the possible transformations.

Or you say I approximate the transformation

by B-spline functions, or any other type of function,

or a deformation vector field.

So I have to decide at the beginning which type of transform

I want to consider.

That's a very basic decision in the registration process,

and basically defines the way we go with our algorithm.

Rigid registration means rotation translation.

If you allow for deformations, you

can start with polynomials, B-splines, up

to displacement vector fields, where

you compute a vector for each and every voxel that tells us

from where to where you have to move the voxel to map it

into the joint coordinate system.

So that's an important design decision.

I would say a very crucial one.

Then second, you have to define a similarity measure.

Similarity measure of source, I would say,

of the transformed source and the target image.

There are different names for the two images.

In the literature, one called it template and reference image.

I personally prefer, now after many years, the terms source

and target image.

One is the target, and this is the source,

and I want to transform the source image to the target

image such that both of them match perfectly

or as good as possible.

So we need a similarity measure, and the similarity measure

can be, for instance, if you just compute features

like points, you compute the point correspondences,

and then you compute the sum of squared distances

of the corresponding points as a similarity measure

that you want to minimize.