Image recovery under noise is widely studied. However, there is little emphasis on performance as a function of object size. In this work we analyze the probability of recovery as a function of object spatial frequency. The analysis uses a physical model for the acquired signal and noise, and also accounts for potential postacquisition noise filtering. Linear-systems analysis yields an effective cutoff frequency, which is induced by noise, despite having no optical blur in the imaging model. This means that a low signal-to-noise ratio (SNR) in images causes resolution loss, similar to image blur. We further consider the effect on SNR of pointwise image formation models, such as added specular or indirect reflections, additive scattering, radiance attenuation in haze, and flash photography. The result is a tool that assesses the ability to recover (within a desirable success rate) an object or feature having a certain size, distance from the camera, and radiance difference from its nearby background, per attenuation coefficient of the medium. The bounds rely on the camera specifications.