Geometry of Eye Design: Biology and Technology

Natural or artificial vision systems process the images that they collect with their eyes or cameras in order to derive information for performing tasks related to navigation and recognition. Since the way images are acquired determines how dificult it is to perform a visual task, and since systems have to cope with limited resources, the eyes used by a specific system should be designed to optimize subsequent image processing as it relates to particular tasks. Different ways of sampling light, i.e., different eyes, may be less or more powerful with respect to particular competences. This seems intuitively evident in view of the variety of eye designs in the biological world. It is shown here that a spherical eye (an eye or system of eyes providing panoramic vision) is superior to a camera-type eye (an eye with restricted field of view) as regards the competence of three-dimensional motion estimation. This result is derived from a statistical analysis of all the possible computational models that can be used for estimating 3D motion from an image sequence. The findings explain biological design in a mathematical manner, by showing that systems that fly and thus need good estimates of 3D motion gain advantages from panoramic vision. Also, insights obtained from this study point to new ways of constructing powerful imaging devices that suit particular tasks in robotics, visualization and virtual reality better than conventional cameras, thus leading to a new camera technology.