So we can start talking about pattern, no, interventional medical image processing.

Okay.

And yesterday we have seen that we can do a 3D reconstruction of objects from orthographic

projections by building up measurement matrices.

The measurement matrix is just giving us the x11, x12 up to x1 number of points and then

we have y11, y12 up to y1 and p and so on.

So we just take the x and the y coordinates, put them into a measurement matrix usually

and that's something we should really do by heart in the future.

We normalize our point features in a way that the centroid of the coordinate system, that

the centroid of the point set coincides with the origin of the coordinate system.

And if we do that, we get this type of matrix and we have seen yesterday that this matrix

can be factorized using the singular value decomposition where this here holds the structure

or no, the other way around, where this here holds the motion parameters and this here

holds the structure of the scene.

And we have seen a powerful algorithm that allows us to compute this initial factorization

and we also have seen that the singular value decomposition does a very good job to enforce

the rank criterion.

Which rank does the measurement matrix have?

What's the rank of it?

Three?

Why?

Because three is the minimum point of the Bethorns product.

Well, this is basically a product of the base vectors multiplied with the point vectors

in a proper configuration, and so we have rank 3 matrix multiplied

with another matrix and that's clear where that rank deficiency comes from.

So we can enforce this rank criterion by looking at the signal of elixir positions,

setting all the signal of values that are sigma four or sigma five and so on.

We set them to zero and we get the closest rank deficient matrix.

Hello, this is, okay.

Where is my wallet?

Okay, good.

Perfect.

So, and then we have discussed one problem

that we know from engineering mathematics

or from pure mathematics,

that the ring of matrices does not allow

a unique factorization.

And we came up with additional constraints

saying that the base vectors are required

to have unit length and that the base vectors

are required to be orthogonal.

And we enforced these two constraints

into the objective function and ended up

with a quadratic optimization problem.

Now that is not very difficult and quite easy to handle,

but it's non-linear.

Okay, so this method I like very much.

And what is the implication that I like it very much?

I ask it quite often in the oral accent.

Yeah, so you should really put here