Recovery limits in pointwise degradation

Pointwise image formation models appear in a variety of computational vision and photography problems. Prior studies aim to recover visibility or reflectance under the effects of specular or indirect reflections, additive scattering, radiance attenuation in haze and flash, etc. This work considers bounds to recovery from pointwise degradation. The analysis uses a physical model for the acquired signal and noise, and also accounts for potential post-acquisition noise filtering. Linear-systems analysis yields an effective cutoff-frequency, which is induced by noise, despite having no optical blur in the imaging model. We apply this analysis to hazy images. 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. The theory considers the point-wise degradation that exists in the scene during acquisition, which fundamentally limits recovery, even if the parameters of an algorithm are perfectly set.