  Underwater images are degraded by the selective attenuation of light that
distorts colours and reduces contrast. The degradation extent depends on the
water type, the distance between an object and the camera, and the depth under
the water surface the object is at. Underwater image filtering aims to restore
or to enhance the appearance of objects captured in an underwater image.
Restoration methods compensate for the actual degradation, whereas enhancement
methods improve either the perceived image quality or the performance of
computer vision algorithms. The growing interest in underwater image filtering
methods--including learning-based approaches used for both restoration and
enhancement--and the associated challenges call for a comprehensive review of
the state of the art. In this paper, we review the design principles of
filtering methods and revisit the oceanology background that is fundamental to
identify the degradation causes. We discuss image formation models and the
results of restoration methods in various water types. Furthermore, we present
task-dependent enhancement methods and categorise datasets for training neural
networks and for method evaluation. Finally, we discuss evaluation strategies,
including subjective tests and quality assessment measures. We complement this
survey with a platform ( https://puiqe.eecs.qmul.ac.uk/ ), which hosts
state-of-the-art underwater filtering methods and facilitates comparisons.
