QuPath: Delauney Clustering

Hi Community, Hi Pete and Associates,

I hope you allow me to ask a possibly very stupid and broad question. Since I have become completely and happily lost in the depths of the QuPath-universe, some issues of very basic nature have come up: Delauney Clustering makes sense, mathematically, but what exactly is the definition of the values that I get? I have done extensive reading, but haven’t come up with consistent explanations. Is there a paper somewhere which sums up this information?

And the most recent/ important question which I haven’t been able to answer yet: What defines a cluster?
I have cells classified as positives and negatives which subsequently become analysed via Delauney Triangulation. Are the clusters defined by negatives and positives? Or is it just everything?
In my data, the Mean Triangle Area for example does not change, while the Mean Triangle Area for the Cluster changes.

Attached is an example image of an area I analyse, as well as the two graphs to which I am referring.

Thanks so much and thanks for all the question-answering and program-improving!!!

Hi @TMM-98

No paper I’m afraid – I haven’t managed to get enough time and space to publish most of the things in QuPath, but hopefully one day (if we can ever get long term funding to help us to work on more things!) :slight_smile:

But it should be possible to visualize most measurements. The number of neighbours will be just the count of lines coming out from the centroid of each cell (nucleus). The distances are then the lengths of these lines – you can check them by using the line tool to replicate some and check if they match. Then the triangles are also what you can see on the image, formed by the line connections (you can replicate them with the polygon tool if you like).

Sometimes the measurements will be missing, i.e. NaN, if you set criteria that blocks a connection being made (e.g. a maximum distance between neighboring cells).

It will depend upon the parameters you set, but basically every cell that is visually connected to another cell (either directly or indirectly, via more connected cells) with a displayed line is part of the same cluster.

If you don’t set any criteria to block cells being connected, you should end up with one big cluster of all the cells that were processed by the command.

I’d expect there to be a correlation between both the mean triangle area and mean distance depending upon how separated the detected cells are.

Okay, thanks for clarifying that!

I am looking forward to your future publications in regard to all these ineresting and complex topics!

Greetings from Germany

1 Like

@petebankhead already answered, but I want to emphasize that the clusters of a certain cell type will mostly be meaningful when you include the checkbox to “Limit edges to same class” of cells. If you want to do clusters between sub-groups of classes, you need to get tricky with scripting.
I have been interested in clusters for a while, so if you have any feedback - here are a few links:
A visual heatmap of the density of a particular class of cell
For more complex cluster analysis, CytoMAP can be used - also does neighborhood analysis.
An older post using another clustering method that could now be run more quickly through CytoMAP - if you set up CytoMAP
Original post discussing hotspots and how to find them

1 Like