One approach to super-resolution fluorescence microscopy, termed stochastic localization microscopy, relies on the nanometer scale spatial localization of individual fluorescent emitters that stochastically label specific features of the specimen. The precision of emitter localization is an important determinant of the resulting image resolution but is insufficient to specify how well the derived images capture the structure of the specimen. We address this deficiency by considering the inference of specimen structure based on the estimated emitter locations. By using estimation theory, we develop a measure of spatial resolution that jointly depends on the density of the emitter labels, the precision of emitter localization, and prior information regarding the spatial frequency content of the labeled object. The Nyquist criterion does not set the scaling of this measure with emitter number. Given prior information and a fixed emitter labeling density, our resolution measure asymptotes to a finite value as the precision of emitter localization improves. By considering the present experimental capabilities, this asymptotic behavior implies that further resolution improvements require increases in labeling density above typical current values. Our treatment also yields algorithms to enhance reliable image features. Overall, our formalism facilitates the rigorous statistical interpretation of the data produced by stochastic localization imaging techniques.