Thank you for the introduction. So, starting off, so I joined the lab in May 2016 and it's

the 6th PIF, meanwhile, if you don't count the CT reconstruction workshop. Now, since last time

a few things got published, notably for this one archive paper, which I consider a valid publication

because we won a prize on it, and my medical physics paper about the beam hardening correction,

and a paper at ICCV, which I will talk about in the following 10 minutes. Now, I have submitted

another paper which will also be part of this talk. It's the projective reconstruction for

out-point correspondences, and I currently prepare a larger work on all my research in the past years,

which you can find over here. So, what am I talking about about acquisition geometry? What

is this? So, for CT reconstruction, we need raw data which we measure, but what we also need is

calibration data on the geometry of our CT system, and that calibration data specifies how our operator

which we need to invert is actually built up. So, this geometry is usually built up by projection

matrices and specifies how source and detector move. Now, if we don't get this calibrated data

right, like there can be two cases which is this curse, for example, there's involuntary patient

motion, you can see that our reconstruction which should look like this will get degraded by

artifacts like streaking artifacts which you see on the right side. Now, this is not only about

patient motion, it is also about non-reproducible scanner trajectories. So, if your scanner which

you calibrate is not able to reconstruct, so to use the same trajectory again, you get the same

problems. Both artifacts are in the end caused by your projection matrix not matching your

projection data. Now, if you look to a related field which is the field of computer vision,

we can actually find that, for example, you see this reconstruction of the coliseum, and they did

this reconstruction based on random images of people who uploaded in on the internet. Now,

they can do this because their algorithms, they often termed like structure for motion,

they estimate the 3D reconstruction and the acquisition geometry at the same time. The

working horse for this to actually work is they establish point correspondences. So,

I sampled two random images from the coliseum and what you can see here is that for some points in

those images, you can actually find corresponding points in other images. Those things are called

point correspondences and those computer vision algorithms rely heavily on them. The reason why

they rely heavily on them is they often use it to build up the relative geometry of projections

in the beginning. So, what you see here is that a corresponding point like X1 here will actually

is the projection of the same 3D point in the 3D reconstruction. Now, there's another thing. So,

if you connect the source of the X-ray projections, you get a thing called the baseline and where

the space line intersects the detectors, there will be the so-called epipoles which I will refer

to later. Now, the epipoles and any point can be used to define a line which is called an epipolar

line. Now, any point has to lie on a corresponding epipolar line in the other projection and this

geometry is fully described by a single matrix called the fundamental matrix. Now, if we want to

apply this to, if we want to transfer this to X-ray images, we started with the problem of like

having to determine corresponding points. Now, I brought you an example here of a phantom. So,

there is some metal beads with the different densities in here and you're now tasked with

finding correspondences. So, some of them are literally impossible because they are in the air,

but even for those it's kind of really, really hard. So, we can apply the computer vision algorithm

and we can estimate a fundamental matrix which gives us this result. Is it correct? Well, I don't

know, but let's look at the ground truth. So, on the left side, the estimated epipolar geometry,

on the right side, the ground truth. So, what you see is it's kind of random result and that's not

surprising because the point matching fails completely. So, that leads me to the topic of

this talk. I want to estimate fundamental matrices without point correspondences. How do I do this? I

refer back to the epipolar geometry which is in before and I've just highlighted the so-called

epipolar plane here. The idea is since we are working in X-ray imaging, what we want to reconstruct

is the 3D distribution of the linear attenuation coefficient. Now, if we think about this epipolar

plane and all the attenuation contained in this plane, if we have an integral over this whole plane

accumulating all the attenuation, it should be the same no matter from which detector we measure all