Equi-areal Catadioptric Sensors

A prominent characteristic of most catadioptric sensors is their lack of “uniformity of resolution”. While several sensors previously appearing in the literature have been described as “equi-resolution”, this is not the case, because they do not incorporate the concept of solid angle. We describe catadioptric sensors whose associated projections from the viewing sphere to the image plane are area preserving (equi-areal), and so truly are equi-resolution . We show that in the orthographic case the catoptric component must be a surface of revolution of constant Gaussian curvature. We compare these equi-areal sensors in both the perspective and orthographic cases with other sensors that have been proposed earlier for treating the uniformity-ofresolution problem.