Simple auto-geometric correction for non-planar projection

This paper presents a simple approach for automatic correcting the distorted image displayed on a non-planar surface of unknown geometry with one or more projectors placed casually. With an un-calibrated camera capturing the viewer´s perspective of the projection surface, a simple checkerboard pattern is used to build the mapping of the correspondence pixels of the projector image to the camera image. Unlike the method using homograpy to represent the mapping, we use perspective projection invariant rational Bezier patches to approximately represent the mapping from projector to camera, which also considers the non-linearities of projector or camera to achieve better registration. Compared to the method using many structured light pattern, our method saves a lot of computing time and become easier. The achieved mapping can be used for texture mapping to pre-warp the rendered images for projection. As a result, a layman user can get a corrected image displayed on a non-planar surface for the point of view of the camera easily.