Three-Dimensional Camouflage: Exploiting Photons to Conceal Form

Abstract

Many animals have a gradation of body color, termed "countershading," where the areas that are typically exposed to more light are darker. One hypothesis is that this patterning enhances visual camouflage by making the retinal image of the animal match that of the background, a fundamentally two-dimensional theory. More controversially, countershading may also obliterate cues to three-dimensional (3D) shape delivered by shading. Despite relying on distinct cognitive mechanisms, these two potential functions hitherto have been amalgamated in the literature. It has previously not been possible to validate either hypothesis empirically, because there has been no general theory of optimal countershading that allows quantitative predictions to be made about the many environmental parameters involved. Here we unpack the logical distinction between using countershading for background matching and using it to obliterate 3D shape. We use computational modeling to determine the optimal coloration for the camouflage of 3D shape. Our model of 3D concealment is derived from the physics of light and informed by perceptual psychology: we simulate a 3D world that incorporates naturalistic lighting environments. The model allows us to predict countershading coloration for terrestrial environments, for any body shape and a wide range of ecologically relevant parameters. The approach can be generalized to any light distribution, including those underwater.

Optimizing countershading camouflage

“…Theory (25) suggests that correct orientation, and thus mobility, is less important under diffuse illumination. This reduced constraint would suggest that the appropriate countershading for camouflage will be more widespread in animals living under a leaf canopy or routinely overcast skies.…”

“…Predictions for the optimal countershading both to obliterate self-shadow and to match the average background radiance from the vegetation on which the targets were placed followed Penacchio et al (25). Illumination patterns were modeled using RADIANCE (28), which is raytracing software that enables 3D modeling of scenes under realistic illumination conditions, with the position of the sun and presence/absence of clouds, as well as the reflectance of objects and backgrounds, under control of the user.…”

“…The cylinder was assumed to be Lambertian, reflecting the light equally in every direction (i.e., matte with no specular reflection). Following Penacchio et al (25), if irrðxÞ is the irradiance falling onto the cylinder at location x and rad background is the radiance of the background, the reflectance of the body at the same location, reflðxÞ, which both cancels out the gradient of illumination and matches the background exactly is given by reflðxÞ = π.rad background irrðxÞ.…”

“…We have recently filled this important gap by using a general theory of optimal countershading to derive the predicted optimal patterns for different weather conditions at a specific location, time of year and day (25). Modeling of the light field shows that a sharp transition between dark and light, as used in previous experimental studies, provides optimal countershading only in direct, overhead sunlight (25).…”

“…We have recently filled this important gap by using a general theory of optimal countershading to derive the predicted optimal patterns for different weather conditions at a specific location, time of year and day (25). Modeling of the light field shows that a sharp transition between dark and light, as used in previous experimental studies, provides optimal countershading only in direct, overhead sunlight (25). Only one of the previous experimental studies (24) was carried out under conditions where direct sun was a plausible illuminant, the others taking place in woodland (22) or including trials with overcast or rainy weather (21), or carried out in winter (21,23).…”