We present a framework capable of tackilng the problem of continual object recognition in a setting which resembles that under whichhumans see and learn. This setting has a set of unique characteristics:it assumes an egocentric point-of-view bound to the needs of a singleperson, which implies a relatively low diversity of data and a coldstart with no data; it requires to operate in an open world, where newobjects can be encounteredat any time; supervision is scarce and hasto be solicited to the user, and completelyunsupervised recognitionof new objects should be possible. Note that this setting differs fromthe one addressed in the open world recognition literature, where supervised feedback is always requested to be able to incorporate newobjects. We propose a first solution to this problem in the form ofa memory-based incremental framework that is capable of storinginformation of each and any object it encounters, while using the supervision of the user to learn to discriminate between known and unknown objects. Our approach is based on four main features: the useof time and space persistence (i.e., the appearance of objects changesrelatively slowly), the use of similarity as the main driving principlefor object recognition and novelty detection, the progressive introduction of new objects in a developmental fashion and the selectiveelicitation of user feedback in an online active learning fashion. Experimental results show the feasibility of open world, generic objectrecognition, the ability to recognize, memorize and re-identify newobjects even in complete absence of user supervision, and the utilityof persistence and incrementality in boosting performance.