The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
FGb: a library for computing Gröbner bases
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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We study how an irreducible smooth and closed algebraic surface X embedded in CP4, can be recovered using its projections from two points onto embedded projective hyperplanes. The different embeddings are unknown. The only input is the defining equation of each projected surface. We show how both the embeddings and the surface in CP4 can be recovered modulo some action of the group of projective transformations of CP4. We show how in a generic situation, a characteristic matrix of the pair of embeddings can be recovered. Then we use this matrix to recover the class of the couple of maps and as a consequence to recover the surface. For a generic situation, two projections define a surface with two irreducible components. One component has degree d(d-1) and the other has degree d, being the original surface.