We consider the problem of realization of perspective systems. A perspective system is a linear dynamic system whose output is observed up to a scale factor. For such a system, we are able to characterize the orbit of all parameter sets that produce the observed output as a certain group action on the nominal parameter set. In this way, we are able to determine the extent to which of these parameters are identifiable. We show how perspective systems arise in the study of motion and shape estimation in machine vision. We apply the approach developed in this paper to two problems in machine vision. In these problems, the special structure of the parameter sets enables us to define a subgroup action on the parameters that further characterizes the set of identifiable parameters.