Trying to use SAM to segment engineering rock samples, but I need to solve two issues

Hello, I am trying to use SAM to segment engineering rock samples as follows:
Here's a photo that contains a box of rock samples, and what I need to do is segment all the rocks and then choose the ones that is longer than a specific length(as we know the length of the box, we can easily calculate the length of each rock based on its pixel size).

By using SAM SamAutomaticMaskGenerator, I can get the segmented elements of this photo as follows:

However, there're two issues which I think should be solved first so that my final target can be reached:
The first one is the overlapping elements. As SAM may have **overlapping segment elements**, I may count **repeated** rocks. Is it possible to make SAM generate all non-overlapping elements?
The second one is how to separate the rocks from backgrounds. SAM segments everything including photo background, and is it possible so that I can only segment rocks?

I appreciate if anyone could help solve this issue. Thank you !

Start with the SamAutomaticMaskGenerator entry point and the provided rock-sample images. Determine whether the requested non-overlapping masks and rock-only filtering are supported by the current interface, and define the expected mask output for both cases before assessing a change.

Written by the indexing model from the issue text.