Can Calder 2022 find boundaries of multiple connected components? Calder et al. 2022 (version 2) shows an interesting method for estimating the boundary from a point cloud. One of the impressive aspects of this is the algorithm should be able to find non-convex boundaries, thus in theory could provide a better boundary estimate on many datasets compared to finding the minimum convex hull.
What they do not show, and I have yet to figure out from their paper, is whether their method requires that the boundary be for a single connected component or not. If a single connected component is assumed, then a combination of mapper and persistent homology might be an essential exploratory step, followed by partitioning the data by connected components as a preprocessing step, before this boundary estimation step can be used.

A quick simulation ($n=5000$) on some blobs visually suggests that it should handle multiple components. But it also looks messy due to noise.

Here is a similar example with $n=10^5$.

And here are some examples with two components where some of the boundaries are non-convex.


Their implementation will tell you which points are estimated to be boundary points, but it does not tell you which connected component a given boundary point is from. This approach could be made more useful if combined with the results of certain forms of topological data analysis including persistent homology and mapper. Or perhaps connected components could be estimated with a suitable clustering algorithm.
