Polarization distance: a framework for modelling object detection by polarization vision systems

The discrimination of polarized light is widespread in the natural world. Its use for specific, large-field tasks, such as navigation and the detection of water bodies, has been well documented. Some species of cephalopod and crustacean have polarization receptors distributed across the whole visual field and are thought to use polarized light cues for object detection. Both object-based polarization vision systems and large field detectors rely, at least initially, on an orthogonal, two-channel receptor organization. This may increase to three-directional analysis at subsequent interneuronal levels. In object-based and some of the large-field tasks, the dominant e-vector detection axes are often aligned (through eye, head and body stabilization mechanisms) horizontally and vertically relative to the outside world. We develop Bernard and Wehner's 1977 model of polarization receptor dynamics to apply it to the detection and discrimination of polarized objects against differently polarized backgrounds. We propose a measure of 'polarization distance' (roughly analogous to 'colour distance') for estimating the discriminability of objects in polarized light, and conclude that horizontal/vertical arrays are optimally designed for detecting differences in the degree, and not the e-vector axis, of polarized light under natural conditions.