A Monte Carlo Study of Gray-Level—Depth Mapping in Underwater Images

Abstract

Conventional underwater images offer an accessible means of observing vertical light attenuation, but interpreting their gray-level trends requires a link between optical transport and digital image formation. This study derives conditions under which a log-linear gray-level–depth relationship is retained and evaluates trend preservation using a Monte Carlo model coupling photon transport, camera response, and 8-bit quantization. The framework provides a physical basis for interpreting the empirical gray-level attenuation slope, kG, and identifies low-signal conditions that compromise its interpretation. In the numerical experiment, the mean relative slope difference between the virtual-camera response and an unscattered direct downwelling irradiance reference was 0.5091%, indicating agreement within the model. Field application in the freshwater Danjiangkou Reservoir identified log-linear gray-level–depth trends in four signal-qualified image sequences, whereas low-signal sequences exhibited pronounced compression of the available gray-level range. These findings support conventional cameras as a potentially low-cost complement to radiometric profiling for relative optical-attenuation monitoring.