Instance segmentation of edge image

Question

I have a dataset consisting of height data of broken objects (rocks), bounded by a box (the tray). I want to find and label each broken piece - possibly bigger than a minimum size - in the image, to be able to extract some physical dimensions for it. Ideally I also would label the tray surrounding the objects. Using sample data for training the model is not an option, the method has to work without prior examples.

Running the Canny edge detection on the ooriginal data works well, and running it on a gradient magnitude and/or gradient direction data produecs even better edge images outlining the objects. Some linking of the edges and fine-tuning the algorithm is still needed. See image below for an example of the result from Canny.

I am at a loss now on how to proceed with the actual instance segmentation and what (Python) algorithms to use. I have been looking, using litterature and the net, into Hough transforms, watershed-based segmentation and other edge-base segmentation methods but can't see a clear way to achieve what I want to do and what to do with the data.