Thanks, I was not aware of Otsu's method.

From the Wikipedia article, "Otsu's method performs badly in case of heavy noise, small objects size, inhomogeneous lighting and larger intra-class than inter-class variance." (Emphasis mine.)

Right now my solution is at the stage of local thresholds with a configurable block size.

Thanks to your pointer, I know now that my next steps will be to review the Niblack or the Bernsen algorithms. (Or just integrate ImageJ.)