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Background removal with changing light

I've got a project where I have a camera mounted on the ceiling pointing to a map on a table.

Before any pieces are placed on the map, I train a background subtractor to know what's background and what's not, and segment those pieces, so that I can get their shape & colors.

However, whenever the lighting changes (ie. you're playing inside next to a window and it starts getting darker) the whole thing falls apart.

This is the only way I've found to correctly identify moving parts within a "game board", but the lighting changes are basically throwing it in the wind.

Any ideas of what I can do to periodically adapt to the lighting conditions without having my pieces becoming part of the background? Any help would be appreciated.