Imperial is now publishing Phd theses online; as part of this, the library are now worried about copyright on figures and images reproduced from the literature. So there is now a requirement on PhD students at the time of submission to certify that they have copyright clearance for images used in PhD theses. This is because there is no doctrine of fair use in the UK, and our government has been captured by rights holders. So: redraw everything you can. Actually this will be good for you, as it will mean that you synthesise more and summarise less. Also, NB that we can and should recycle original figures made within this group – I have a library of past theses.
But, for micrographs there is no getting around the requirement to ask permission. Actually this isn’t so bad; mostly there are webforms for this, mostly using an online service called rightslink, via the article webpage “rights and permissions” link;
Maney (IOM3) are also the same.
The exception is PhysRev (APS), who basically say yes, but you should ask the author too: http://publish.aps.org/help_faq.html
Nevertheless, source should still be acknowledged by reference, e.g. redrawn from [X], After [X] or from [X].