Die folgende Content wurde von der Universität Erlangen-Nürnberg verwendet.

Der hat in medizinischer Bildverarbeitung promoviert und kann damit alles.

Er sucht auch sehr gute Studenten, die bei ihm im Lab mitarbeiten möchten

oder vielleicht auch eine Masterarbeit oder Bachelorarbeit schreiben möchten.

Also wenn jemand von Ihnen Interesse hat, dann möge er sich bitte an mich wenden.

Das ist sicher ganz spannend.

Die Techniken, die wir hier lernen, sind auch übertragbar.

Ob ich jetzt Eckpunkte finde auf einer Straße oder Eckpunkte in einem medizinischen Bild,

das ist letztlich völlig egal.

Okay, so, let's continue in the text.

We are currently considering one application in an intervention environment

that is called magnetic navigation.

The core idea is we have a catheter that is in the vessel trees

and we want to apply an external magnetic field

and we want to pull the catheter tip into the right direction.

In terms of algorithms, we are required to build an interface for the user

that allows him to find a proper or to select the proper orientation

for the magnetic field that is pulling or pushing the catheter into the right direction.

So that's the story so far and I have motivated this

and we started out with the most important figure for this.

This is the so-called key figure.

When I ask you in the oral exam about magnetic navigation, this is the image to draw.

This is the picture to draw.

So the idea is, and that is very important,

we have left the imagination that an image is just a matrix.

We consider in the following and all the upcoming lectures images as 2D planes in 3D space.

So this is more or less the detector plane, one, and this is the second detector plane,

and this is our optical center, and this is our point.

We do a perspective projection of the point into the image plane, get this projection,

we do a second projection, and we get this projection,

and this here is basically the translation of the camera,

the translation of the camera we have performed.

This figure shows that there is a triangle and this triangle defines a plane,

and this is the third plane.

We have the two image planes and we have the so-called ap-polar plane.

So if I give you this point in the optical center and you know how the camera has translated,

you can compute this plane because it's spanned by these two vectors.

You can intersect this plane with this image and you can compute the ap-polar plane,

the ap-polar line, sorry, the ap-polar line, which is the intersection of the two planes in 3D.

And there is an interesting observation here.

The fact that you have an intersecting line here and the fact that you know that this point is also projected on this image plane,

you know that the point that corresponds to this projection has to lie on this line here.

If I give you two image planes, I tell you where they are in space,

and if I give to you one projection point, you know that all the possible 3D points that will lead to this projection point,

they have to lie on this projection line somewhere.

The second image will also have a picture of this point,

and the question is where are the possible projections of the point?

And the possible projections lie on a line.

So that's a one-dimensional search problem.

Finding corresponding points once the geometry is known is a one-dimensional search problem.