Scenes where hierarchical objects dynamically form and dissolve

[iyildirim]

Just registering here so that we think about it. This is when you have a bird of flocks but then half of the birds separate to their own way. Or when you have two rectangles moving together part ways halfway. etc. Fig. 5 in Balaban et al. 2019 is an example.

[iyildirim]

Initial Proposal:

• Composite objects move like the other singular objects (that is, they only have linear velocity and no angular momentum).

• When two objects touch, with a low probability they stick together and start moving together.

• A given composite object might break apart with a low probability at any of its joints on a given time point.

What is the most efficient way of going about implementing this? I am happy to give it a try if people are busy. Let me know.

[iyildirim]

We would like to model such clusters of beads using Chinese Restaurant Process. We will utilize Pakman & Paninski approach here too using their Neural Clustering Process. This will enable us with a data-driven smart proposal distribution to sample cluster assignments based on the velocities and positions.

[belledon]

I think the data generative procedure is rather elegant

1. initialize k objects
2. each object moves using the dynamics from Vul
3. As objects approach one another the probability increases as a sigmoid peaking to some low value (say 0.1) where distance between two dots is measured as distance from the closest points along the circumference (distance between centers + 2*radius)
4. given that probability, at each time step, for each dot, the probability of being attached is a multinomial with those weights
5. If true, then the unordered set of attached objects now moves with the same dynamics applied to its centroid

We can play with clusters have N > 2.. I think it would be cool

[iyildirim]

Let me know if you guys can take a stab at this. I would think it shouldn't be too complicated.