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Good morning everybody, welcome to the Tuesday morning session on interventional medical

image processing.

Before we start with the factorization method using perspective projection models, let's

repeat a few general things that we have discussed so far.

If you are required to find corners in an image, what do you do?

With a structure tensor.

What is the core idea of the structure tensor?

Yes?

And once you have the gradients, what do you do with it?

How they are?

You compute basically the covariance matrix of the gradient vectors and the principal axis.

That's the idea.

So we have detected points.

We need point correspondences for magnetic navigation where we have considered the problem

how can we orient the external magnetic fields such that the catheter is pushed into the

right direction.

We have used two images for building an interface, two images acquired from different viewpoints

and we have introduced in this context the epipolar geometry.

What is the core idea of epipolar geometry?

And where does this point in this corresponding point in the second image lie?

How do you compute the epipolar line roughly?

Right.

Translation vector.

Perfect.

Okay.

How do we call the point where all the epipolar lines intersect?

The epipole?

Okay.

The epipole is computed how?

How would you compute the epipole?

I think this is the section for the transition.

Perfect.

Geometric intuition for that.

You can have an infinite number of epipolar planes but the rotation axis of these epipolar

planes is defined by the translation vector and that's exactly the intersection with the

two planes and it leads to the epipoles.

How would you compute the essential matrix given a set of point correspondencies?

How would you estimate the essential matrix?

The eight point algorithm.

What is the core idea?

One two three four five.

Measurement matrix.

The properties, the important properties of the essential matrix, I don't ask for them.

Okay.

And then we can compute the essential matrix out of that.

How many points do we need to compute a 3D point?

How many 2D points in the projection do we need to compute the 3D coordinates of a point?

No.

Let me ask it in a different way.