If it is a ConstructorCalledByMethodInvocation or a MethodCalledByMethodInvocation you can use getCallingObject().
What about MethodCalledByConstructor?
Basically, when my pointcut matches, I want to invoke a particular method on the caller object. It so happens that one of the calls is made from a constructor. Is there anyway to get to the calling object (the one being constructed) in that case?
I think target object is what you want. You need to treat all invocation subclasses separately, though.