I have developped a perl script which transforms .m (Matlab files) into .cpp files.
I have then defined the EXTENSION_MAPPING (in the Doxyfile) as described in the documentation, that is :
EXTENSION_MAPPING=m=C++

Unfortunately, this syntax was not working.

Looking into the code, I discover that .m files are associated with objective-c language (see the file util.cpp, line 6484 in the initDefaultExtensionMapping function) :
updateLanguageMapping(".m",     "objective-c");

If the EXTENSION_MAPPING is redefined, the updateLanguageMapping function is called but without the dot in the extension (see the file doxygen.cpp, line 9560). Setting EXTENSION_MAPPING to m=C++ leads to :
updateLanguageMapping("m", "C++") (note the missing dot in the "m")

The preceding association between .m file and objective-c won't be replaced by the new one as expected, because extension .m and m are not considered to be the same extension : the map g_extLookup (see function updateLanguageMapping in file util.cpp) will contain for m files :
{
...
{'.m', SrcLangExt_ObjC},
{'m', SrcLangExt_Cpp}
...
}

And following calls to getLanguageFromFileName will still lead to associate .m files with Objective-C.

As a workaround, we can modify the EXTENSION_MAPPING that way :
EXTENSION_MAPPING=.m=C++ (note the dot before the 'm')

Doxygen behaves then as expected but :
- this is not correct regarding to the documentation
- Doxygen outputs : "Adding custom extension mapping: ..m will be treated as language c++" (note the two dots before the 'm')

See also bug #567774 describing a similar problem.