A considerable part of the imitation problem is finding mechanisms that link the recognition of actions that are being demonstrated to the execution of the same actions by the imitator. In a situation where a human is instructing a robot, the problem is made more complicated by the difference in morphology. In this paper we present an imitation framework that allows a robot to recognise and imitate object-directed actions performed by a human demonstrator by solving the correspondence problem. The recognition is achieved using an abstraction mechanism that focuses on the features of the demonstration that are important to the imitator. The abstraction mechanism is applied to experimental scenarios in which a robot imitates human- demonstrated tasks of transporting objects be- tween tables.