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TitleAlgebraic Varieties in Multiple View Geometry
Author(s) Kalle Astrom, Anders Heyden
TypeArticle in Conference Proceedings
AbstractIn this paper we will investigate the different algebraic varieties that can be generated from multiple view geometry with uncalibrated cameras. The natural descriptor, Vn , to work with is the image of IP 3 in IP 2 Theta IP 2 Theta Delta Delta Delta Theta IP 2 under a corresponding product of projections, (A1 Theta A2 Theta : : : Theta Am). Another descriptor, the variety Vb , is the one generated by all bilinear forms between pairs of views, which consists of all points in IP 2 Theta IP 2 Theta Delta Delta Delta Theta IP 2 where all bilinear forms vanish. Yet another descriptor, the variety V t , is the variety generated by all trilinear forms between triplets of views. We will show that when m = 3, Vb is a reducible variety with one component corresponding to V t and another corresponding to the trifocal plane. Furthermore, we will show that when m = 3, V t is generated by the three bilinearities and one trilinearity, when m = 4, V t is generated by th...
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Refereed No