So, welcome to the Tuesday session.

We are currently discussing 3D ultrasound.

3D ultrasound, meaning what can we do to get 3D volume data sets using a standard ultrasound

device.

And 3D reconstruction in ultrasound imaging is completely different from what we know

from CT or MR imaging, for instance.

Because the ultrasound probe already computes a slice through the body by just putting the

ultrasound probe on the skin or on the surface and then you get some reflections and reflection

properties.

So, it can look along one slice in one plane into the human body.

And the problem is how can I compute the position and orientation of these slices in 3D and

then how can I use this information to do a proper sorting and arrangement of the 2D

slices in a 3D cube.

That's the idea.

And I also pointed out that there are mechanical devices that provide tools for 3D imaging.

For instance, here we have the axial rotation.

Here we have a rotation around an axis that is here laterally.

And then we have the elevation.

So just lateral, the movement here parallel to the surface.

Then we have the rotation around a lateral axis.

And here we have a rotation around this axis.

And if you go to the hospital or to a high-end doctor and if you have a look at modern ultrasound

devices, usually they don't have just a single probe, they have several probes.

If you go to our women's hospital, they have a huge probe of that size and you know immediately

if you look at it what happens there.

You have just the motion along the surface or the elevation is implemented there.

So modern scanners usually provide the 3D option.

We are currently at a point where we say, well, mechanics is fine, mechanical devices

are good, but can we also develop some computer vision methods to allow for 3D ultrasound

imaging?

And the idea is as follows, we have here our markers and here we have our ultrasound probe

and here we have a camera looking at the scene capturing the markers.

And what we are currently looking at is how can I compute the rotation and translation

of these markers here according to a world coordinate system.

We also have a project with Adidas for instance where people have markers here and here, I

don't know whether you have mentioned this, and you track them and then you compute motion

parameters and things like that out of the point correspondences.

So the methods we are characterizing here are very general and applied to many other

problems in the field of computer vision.

So the estimation of this transform here.

And another problem that we have is that we have to consider today, this is the image

plane here.

So that's the image that is generated by our ultrasound device.

And here we have an image coordinate system to address for instance the pixels in the

ultrasound image.

And what is also important to do a 3D reconstruction is take this coordinate system here of our

markers and estimate the transform from this coordinate system to our image coordinate

system.

That's also something that we have to compute.

This is usually called X, this transformation.