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I'm trying to find the positions of crabs in a bunch of images, and I'm having annotators click on all the crabs they see in an image. Naturally, annotators won't click in the exact same places for the same crabs, and they might not see all the same crabs.

In order to infer the real positions of all the crabs, I was thinking of doing some clustering, but my problem is that I'd have to cluster across annotators.

I'm making the assumption that for a given annotator each click per image represents a unique crab, so I don't want to cluster points within an annotator's judgments for an image.

This has got to be a thing other people have faced, but I can't find any information about it.

Can anybody point me in the right direction?

(I also think the problem could be conceptualized as annotators randomly sampling from the set of real crab positions and clicking these positions with some simple random error in the positioning. This seems like a relatively straightforward inference problem, but I can't make heads or tails of it.)

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Define an appropriate distance. E.g.

sqrt((x1-x2)²+(y1-y2)²) + 1000000 if a1==a2 else 0

Then do hierarchical clustering.

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  • $\begingroup$ But what if annotator A has two points that are close to each other, but also close to a cluster of points from annotators B, C, and D? They'd each be close to the cluster, but hugely far apart from each other. Also, how does one go from a cluster hierarchy to getting an estimate of the number of clusters and the positions? $\endgroup$
    – Zeke
    Commented Jun 26, 2017 at 17:17
  • $\begingroup$ If you do anything but single linkage, the penalty term will prevent this from happening. I'd define a threshold in pixels to find clusters. Hen maybe discard all the 1-element clusters. $\endgroup$
    – Has QUIT--Anony-Mousse
    Commented Jun 26, 2017 at 18:07

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