In this paper we introduce and study a linear dynamical system with a perspective observation function. The study of these systems has been shown to be useful in motion and shape estimation problems in machine vision. We introduce the notion of perspective observability and obtain under a special case a necessary and sufficient condition that would guarantee observability of the initial condition of the linear dynamical system up to a one-parameter magnitude scaling. Subsequently, a new realization theory is introduced which is useful for studying linear systems with perspective observation. Our main result is to show that parameters can be recovered up to orbits of a suitable "perspective group." A new rescaling algorithm is described to identify parameters up to orbits of the perspective system. The identification problem is further analyzed in detail for various problems that are of interest in machine vision.