Given iPhone and derivatives, I was expecting this might be a hot area of research, but a search of 'touch screen authentication' found only an MIT 2004 project called 'distinctive touch'.
The project surrounded building a system called distinctive touch for enabling lightweight authentication using gestures on touchscreen displays. Using this system, users were identified by their passdoodle, a gestural equivalent of a username and password, which consisted of one or more strokes that they drew on the screen with their finger within a short duration of time.
I'd venture that an 'easily memorable' touch screen gesture would manifest as 'obscene'. Or a puppy's face.
In addition to authenticating through gestures, you could use them to perform other identity operations.