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Good afternoon everybody. Last week we considered the problem of super resolution and let me

briefly summarize where we are currently and what we did so far including the topics on

super resolution. So in summer semester we talk about interventional medical image processing.

I did that on purpose. That's the Franconian way of doing things. And we talked about the

structure tensor which appeared a little bit difficult for you at the beginning but nowadays

it should be fine with you. We compute gradients, we compute the covariance matrices based on the

outer product of gradients and we compute the eigenvalues and eigenvectors and we found out

that these eigenvalues and eigenvectors of the structure tensor can be used for classifying

regions, corners and edges. And then we considered an important class of features, the SIFT features

and the HOC features that can be used for image processing and we will see in a few sessions in

a few lectures from now that SIFT features are heavily used for many interventional procedures

and that they are very crucial to find point features in an image. Then we looked a little

bit on pre-processing and here in particular we have learned about the bilateral filter which

is basically a filtering operation that does edge dependent or edge preserving filtering. That means

smoothing is just applied to regions where we have a good chance that there is no edge and if there

is an edge then the smearing, the smoothing procedure is way weaker than in homogeneous

regions. Then we looked into shutter segmentation in X-ray images. We have used the Huff-Transform

to do the line detection and we also have seen a global objective function which takes into

account the geometry of shutter regions with respect to having a rectangle shaped structure

and this can be of course used for the segmentation process and will improve the segmentation process.

In general this idea supported the intuition, the more information we have about the things we are

looking for the better the algorithms actually work if we incorporate this knowledge into the

algorithms. Then we had a few very important sections and we learned very important algorithms

that you usually will also see in standard computer vision lectures but they are so crucial that you

have to know these methods. We talked about magnetic navigation and we have seen that for

magnetic navigation we need an interface that allows us to use the image information and to

adjust the three-dimensional orientation of the magnetic field and in this context we learned

about the epipolar geometry. That was basically developed end of the 80s beginning of the 90s.

This was the driving force in computer vision and today we have a very good understanding of

epipolar geometry and associated algorithms. The epipolar geometry is characterized by a

single illustration that is basically using the fact that 2D images, 2D image planes are

considered as 2D subspaces in 3D and once you look at images in terms of a three-dimensional plane

you come up with all the methods that we have discussed right away by just looking at the

geometric relationships of the points and translation vector and rotations we are considering.

We have seen the essential matrix and the fundamental matrix. The difference between

the essential matrix and the fundamental matrix was, Matthias? Unit? Right, it carries the intrinsic

camera parameters from the left and from the right with the original matrix and the inverse

of this matrix. We also learned about the eight-point algorithm. What was the core idea

of the eight-point algorithm? What was your name Matthias? Michael? Yes. You don't know

the answer to my first question or to the second one? It's Christoph. Still Christoph. Hasn't

changed since then. Okay. If you watch the videos you will notice that I'm asking over and over

his name and I forget it over and over which tells you something about the importance or about

my dementia or something like that. You can conclude whatever you want out of that. I

don't care. Right, Csuk? Of course. The simple ones I remember. His name was? No?

Tongsik. Tongsik. Okay. Csuk, Tongsik and I don't remember. Good. Apipolar geometry and

then we talked about structure for motion approaches and this was motivated by the problem

that we have an ultrasound device with some markers and we observe how the ultrasound

device is moved within the three-dimensional space and once we know where the ultrasound

probe is and where the images were acquired we can use the two-dimensional images and