Resolution invariant surfaces for panoramic vision systems

A family of axially symmetric mirror shapes are proposed for panoramic imaging. These shapes keep the resolution in the image invariant to changes in elevation in the scene. In other words, this family of shapes achieves solid angle pixel density invariance. An analysis of range finding using two coaxial axially symmetric resolution invariant mirrors in a coaxial pair is presented. The resolution invariance property of these mirrors mean that when the image captured is unwarped the resultant image will not suffer from variable image quality. This problem is present in unwarped images captured with any mirror shape not designed for resolution invariance. The resolution invariance of these mirrors is especially important in the case of stereo panoramic mirrors where one view of the scene is captured within the other and thus will have lower resolution. It is necessary to clearly identify two was of an object to undertake range-finding. The proposed mirror shapes will be useful for mobile robotics and machine vision. Other applications areas such as visual sensing for control of traffic lights at street intersections could be considered.