Algebraic properties of multilinear constraints

✍ Scribed by Anders Heyden; Kalle Åström

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 235 KB
• Volume: 20
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19970910)20:13<1135::aid-mma908>3.0.co;2-9

✦ Synopsis

In this paper the different algebraic varieties that can be generated from multiple view geometry with uncalibrated cameras have been investigated. The natural descriptor, V

, to work with is the image of / in /;/;2;/ under a corresponding product of projections, (A ;A ;2;A K ). Another descriptor, the variety V , is the one generated by all bilinear forms between pairs of views, which consists of all points in /;/;2;/ where all bilinear forms vanish. Yet another descriptor, the variety V

, is the variety generated by all trilinear forms between triplets of views. It has been shown that when m"3, V is a reducible variety with one component corresponding to V and another corresponding to the trifocal plane.

Furthermore, when m"3, V is generated by the three bilinearities and one trilinearity, when m"4, V is generated by the six bilinearities and when m*4, V can be generated by the (K ) bilinearities. This shows that four images is the generic case in the algebraic setting, because V can be generated by just bilinearities. Furthermore, some of the bilinearities may be omitted when m*5.