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What you call 'hotspots' are better known as 'specular highlights' or 'specularities'. There exist plenty algorithms to remove these. Publicly available code is provided for example by R,Tan et al http://www.staff.science.uu.nl/~tan00109/textureSeparation/results.html . A fast specularity removal method was presented by Yang et. al http://www.cs.cityu.edu.hk/~qiyang/ who also provides code. However note that depending on your application the usage of the both methods may not work on your facial images since faces are highly textured. Imho the most promising method was proposed by Mallick et al http://nguyendangbinh.org/Proceedings/ECCV/2006/CD1/papers/3951/39510550.pdf , unfortunately it is not that easy to implement and they also have a patent on their method.
