Panoramic images as optimizing projections from the unit sphere to the plane

Resumo: In this work, we address the problem of obtaining perceptually acceptable panoramic images which are images of wide fields of view (FOVs). To achieve this goal, we first model the visible information of a scene as a unit sphere and then model the panoramic images as projections from this sphere to an image plane. Desirable properties in panoramic images are transformed in properties that this projections should have, such as conformality and smoothness. Energies that measure how distorted a panoramic image is are obtained and the problem becomes optimizing all these energies. This work is strongly based in [1], where all the distortions we consider are suggested. The contribution of this work is the formal geometric analysis of these distortions and the details about the optimization methods, which were briefly mentioned in [1].