Loss function for 1d segment estimation

My problem is as follows:

I have a long segment [say, 100000 samples] as input.

Regardless of the method, I need to output a partition of this segment into k sub segments, which do not overlap, and whose union can but doesn't have to be the entire segment.

For instance, for the segment [0, 1000], a valid output can be the list [[0, 10], [20, 50], [500, 900], [950, 970]].

I have a ground truth of the "correct" partition, for example

[[0, 15], [25, 40], [400, 650], [950, 975]].

Notice the number and length of the "truth" segments doesn't have to even resemble the number and length of the actual segments.

I need a measurement for the error.

I would like something "standard", although I know that is not well defined.

Currently, I don't have any special requirements from that error function, so I would just like one that makes sense, a trivial one is fine too, as I can't come up even with that.

If some error functions for such problem exist, please let me know of them, or even what that problem is called, so I can search for something.

Thanks

Also, if this belongs in another stack exchange, please let me know.