Critical Loci for Two Views Reconstruction as Quadratic Transformations Between Images

In this paper, the effect of the existence of a critical set for the projective reconstruction of a scene in P3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {P}}}^{3}$$\end{document} 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.