Polarization: Beneficial for visibility enhancement?

When imaging in scattering media there is a need to enhance visibility. Some approaches have used polarized images in this context with apparent success. These methods take advantage of the fact that the path radiance (airlight) is partially polarized. However, mounting a polarizer attenuates the signal associated with the object. This attenuation degrades the image quality. Thus, a question arises: is the use of a polarizer worth the mentioned loss? The ability to see objects is limited by noise. Therefore, in this work we analyze the change in signal to noise ratio (SNR) following the use of a polarizer or a dehazing process. Typically, methods use either one polarized image (with minimum path radiance) or two polarized images corresponding to extrema of the path radiance. We show that if the only goal is signal discrimination over noise (and not color or radiance recovery) in haze, the use of polarization in both approaches is unnecessary: polarization rarely improves the SNR over an average of unpolarized images acquired under the same acquisition time. Nevertheless, under a single frame constraint, the use of a single polarized image is beneficial.