Projective reconstruction of approximately planar scenes

The fundamental theorem of projective geometry states that the transformation mapping coplanar points from an object onto an image plane can be determined given the correspondence between four or more object points and their projections in the image. This theorem can be used to predict where other features in the object plane will appear in the image, and conversely, to project new image features back onto the object plane. In this paper we examine what happens when these mathematical results are applied to real-world data containing random sensor noise and deviations from coplanarity.