Welcome back to Beyond the Patterns.

So today I have the great pleasure to announce two researchers.

We have Suprasana Sheet, who is a postdoc and also associate researcher at the ETH AI

Center, as well as the University of Zurich.

And we have Chinmay Pragba, who is a PhD candidate also at the University of Zurich

with Björn Menze and an associate researcher as well at the ETH AI Center.

Both of them are very much interested in, of course, deep learning on the one side,

but also graphs.

And in particular, they have discovered a new method how they can generate graphs and

apply that to 3D vascular structures.

So this is really a very, very cool approach because it somehow brings together the continuous

way of diffusion models as well as the symbolic representation that you have in graphs.

So the presentation is entitled 3D Vessel Graph Generation Using Denoising Diffusion.

And without further ado, Chinmay Supra, the stage is yours.

Thank you so much, Professor Meyer, for the very kind introduction.

Look at our proposed solution and look at the efficacy of our solution by using two

real world data sets.

So let's get started.

We need to realize that the vascular graphs we are interested in are an example of a spatial

or geometric graphs.

Unlike normal graphs, which are set of nodes and a connection between these nodes represented

using the adjacency matrix, a spatial graph is also embedded in 3D space.

That implies each of the node has an associated 3D coordinate.

Such spatial graphs are quite abundant and found near us, for example, proteins, molecules,

or even road network supply or power supply graph.

As already mentioned, in medical imaging, we see the spatial graphs in the form of vascular

structures.

On the left, we see the light sheet microscopic images and the associated vascular graph structure.

And on the right, we see the human circle of Willis, whose vascular structure can also

be represented using a 3D spatial graph.

Now, a question arises, why is it of central interest to start generating these synthetic

graph structures?

Turns out, it is quite difficult to obtain a large corpus of such vascular graph structures

for one.

The annotations is quite tedious, requires some special training, thereby making it expensive,

or can even require some specialized tools in order to do the annotation process.

Thus, obtaining a very large corpus is not trivial, and we often require large corpus

to train any data-driven deep learning model.

Thus, it is of interest to start generating synthetic vascular graphs that are very faithful

to the underlying data distribution and can help us in handling this data scarcity issue.

Let us see how the problem has been approached till now.

Turns out, most of the existing work tend to use a rule-based simulation where they

take into account the oxygen concentration or nutrition distribution in order to generate

such vascular graphs.

These methods are mostly heuristic-driven and struggle in capturing the complex topology.

For example, the cyclical structure that are present in capillary beds would be very difficult

to be captured by such rule-based heuristic methods.

On the other hand, we attempt to solve this problem using a data-driven vascular graph

generation approach.

Our hypothesis is, by being data-driven, we get rid of all the heuristics and let the