Novel methods for estimating surface normals from affine transformations

Abstract

The aim of this paper is to describe different estimation techniques in order to deal with point-wise surface normal estimation from calibrated stereo configuration. We show here that the knowledge of the affine transformation between two projections is sufficient for computing the normal vector unequivocally. The formula which describes the relationship among the cameras, normal vectors and affine transformations is general, since it works for every kind of cameras, not only for the pinhole one. However, as it is proved in this study, the normal estimation can optimally be solved for the perspective camera. Other non-optimal solutions are also proposed for the problem. The methods are tested both on synthesized data and real-world images. The source codes of the discussed algorithms are available on the web.