The following content has been provided by the University of Erlangen-Nürnberg.

Good. So, welcome back to Interventional Medical Image Processing.

So, last lecture we were talking about random walker and a local segmentation method

was using edges and very local features of an image in order to derive semi-automatically a shape from a given image.

And today we want to look at a method that is very much the contrary because here we want to start from a shape model and then fit it to our image.

And this method is called statistical shape models.

So, general segmentation, we've already seen that in the last lecture, is very difficult in the presence of noise and artifact.

So, we've seen that if you have noise and you have fine edges that you're trying to trace, they will be disrupted by the noise and you may lose track of the edge.

So, if we had some kind of prior knowledge, that would be extremely helpful.

So, if we already know how the kind of object that we want to segment looks like, then we can have a much more constrained search for that specific boundary.

So, in an extreme case, let's say you have a machinery part and you have been, say, you're in material testing and you are imaging a part of known dimensions,

then you would be able to use a computer model to drive the segmentation.

So, if you had some kind of CAD model, you could use it to drive your segmentation.

However, we can't do that in the general case.

We can't do that in the case of humans because typically the organs or the kind of objects that we're interested in in the human body, they vary.

So, if we just had a single shape that is describing how a liver looks like, that would probably not be a very good model to detect livers in all humans

because the shape of the liver varies in different humans and in particular here in the abdomen,

it may just be a difference in how you lie on the table that introduces some deformation and you will have a different shape that you decide to segment.

So, our conclusion is it would be good not to have a single model,

but to have something that is able to describe those variations and still help us to guide the segmentation process.

Actually, such model-based methods have been applied already in the 1990s in 2D and later they have been expanded to 3D and were also applied successfully.

And you can define a model to describe the expected shape and appearance.

So, instead of just having a single shape, you describe the expected shape. So, you could, for example, use a mean shape, the average shape of the organ,

and the first variations of the shape and then try to fit it to your current observation.

And in contrast to what we've seen in the last lecture, we will do that in a top-down approach.

So, we start with our model and then we try to fit our model to the data.

Previously, we were very close to the data and we're trying to derive the boundary directly from the data.

So, this was a bottom-up approach and here we have the top-down approach.

Yeah, and of course, if we have such prior knowledge, then we will definitely get much more stable results.

So, if we have, for example, a liver model, our segmentation result will be within the expected range of liver variations.

But of course, if you just supply a different data set and you have a head scan and you're trying to segment a liver,

you will still fit a liver model to your head scan.

So, you have to be careful with the degree of prior knowledge that you're introducing.

And if you just look for something that looks like a liver, you will always find a liver.

So, if you have a hammer, the world looks like a nail. Be careful about that.

Today, single template models are only useful in industrial applications, so where we expect no variations,

where we are producing the machinery up to specification and they're actually expected to not vary from the shape.

And if it actually varies from the shape, there must have been a problem and you need to do something about that.

So, you can use it, for example, for fault detection in industrial applications.

In our medical applications, of course, we need to model our variation.

In fact, there is many different approaches to incorporate prior knowledge into segmentation,

but we will only discuss the statistical shape models here.

But you can also see that, for example, seminal snakes that introduce a smoothness and an image fit

or a deformable simplex mesh are different methods that will also allow some variation in the segmentation.

So, you have a template shape here and some image fit.

In general, those models can be adopted to specific shapes, but they do not model the variation intrinsically.

And this is what we want to do here. Here, we want to derive a mean shape and expect the variations.

And once we do the segmentation, we can also find a kind of goodness of fit,

how well this observed observation will actually fit our expectance model.

In general, the slides that you are talking about today, they are based on a paper by Tobias Heimann,