Critical Loci for Two Views Reconstruction as Quadratic Transformations Between Images

Marina Bertolini, Luca Magri, Cristina Turrini

Abstract: In this paper, the effect of the existence of a critical set for the projective reconstruction of a scene in $${{\mathbb {P}}}^{3}$$ P 3 from two views is analyzed directly on the image planes. Corresponding points, which are images of critical points, are linked by a birational map between the two planes which is a quadratic transformation. This transformation is explicitly described and used to investigate the instability phenomena for reconstruction with a new approach.