Okay. Welcome back to Interventional Medical Image Processing. Sorry, I was a bit late

So so far, we have discussed intervention

of medical image processing and different topics.

So both you remember you can follow the cloud in your head now.

So this is the summary of our lecture.

So far, we have been discussing some tools.

We've been discussing the preprocessing, and

we were looking in to different feature descriptors and

how to improve image quality, so we did edge preserving filtering and we were also interested

in performing all of these steps in real time, so we also looked into things like the guided

filter that could be very efficiently solve the edge preserving filtering problem using

box filters.

And after that we stepped further ahead to a topic that we called image analysis and

we started first with describing epipolar geometry, we figured out that epipolar geometry

is very useful if you are looking for point correspondences in two camera or x-ray images,

we also looked into the extension that if you use epipolar planes that you essentially

have identical plane integrals in two projections and how this can be used to establish consistency

conditions and then we went ahead and talked about the factorization algorithm, so Tomasi's

famous factorization algorithm that allows you to reconstruct 3D point correspondences

from a series of camera images, so that you could reconstruct really 3D geometry and camera

parameters from a sequence of tracked images.

Good, the topic now we will stay in the field of image analysis and what we will be talking

about today is a first approach for image segmentation and what we will discuss today

is data driven image segmentation.

So we will look into a segmentation method that does not require a very sophisticated

modeling of the image itself, we will do everything with low level descriptors, with low level

features for the segmentation and a very popular algorithm is the random walker and the nice

thing with the random walker is that you don't have this very sophisticated model and the

other thing is you can compute it very quickly so it's also suitable for interactive application

and the way it works is you have an image and you place seed points, so you have some

semi-automatic approach, so you have a user that is marking some areas in the image as

belonging to one class and to another class, so you could do foreground, background or

you could have heart and lung, so these would be the tissue classes that you assign, so

it also works with multiple labels and based on these labels on the input, so then you

have a couple of points in the image where you know the class for sure and what you do

next is you try to derive a segmentation from those initial points and this is what we are

going to discuss about today.

So the nice thing is if your segmentation fails and sometimes the segmentation fails

and you don't get the right result, then if you have this interactive approach that you

can recompute, you can place additional labels close to the decision boundary, close to the

segmentation boundary and then you can readjust your segmentation and for 2D this works very

efficiently and it can be done really in an iterative way that you update your label masks.

By the way generally when we speak about segmentation we mean the process of delineating a boundary

of a certain object, so you would be interested in figuring out where the boundary of the

liver is or a specific organ, a tissue class, so this is generally the process of segmentation.

And after we derive the method we will look into a couple of examples how the method behaves

with different inputs because the inputs are very important for this method here.

So first we will look into the problem statement, so we need some way of formalizing the mathematical

description of the image segmentation problem and then we will derive an algorithm and based

on the algorithm we will then look into its properties and a couple of details on the