| Title | Algebraic Properties of Multilinear Constraints |
| Authors | Anders Heyden, Karl Åström |
| Alternative Location | http://www3.interscience.wi..., Restricted Access |
| Alternative Location | http://dx.doi.org/10.1002/(... |
| Publication | Mathematical Methods in the Applied Scinces |
| Year | 1997 |
| Volume | 20 |
| Issue | 13 |
| Pages | 1135 - 1162 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | JOHN WILEY & SONS |
| Abstract English | 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-n, to work with is the image of P-3 in P-2 x P-2 x ... x P-2 under a corresponding product of projections, (A(1) x A(2) x ... x A(m)).<br> Another descriptor, the variety V-b, is the one generated by all bilinear forms between pairs of views, which consists of all points in P-2 x P-2 x ... x P-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. It has been shown that when m = 3, V-b is a reducible variety with one component corresponding to V-t and another corresponding to the trifocal plane.<br> <br> Furthermore, when m = 3, V-t is generated by the three bilinearities and one trilinearity, when m = 4, V-t is generated by the six bilinearities and when m greater than or equal to 4, V-t can be generated by the ((m)(2)) bilinearities. This shows that four images is the generic case in the algebraic setting, because V-t can be generated by just bilinearities. Furthermore, some of the bilinearities may be omitted when m greater than or equal to 5. (C) 1997 by B. G. Teubner Stuttgart - John Wiley & Sons Ltd. |
| ISBN/ISSN/Other | ISSN: 0170-4214 |
Questions: webmaster
Last update: 2013-04-11
Centre for Mathematical Sciences, Box 118, SE-22100, Lund. Telefon: +46 46-222 00 00 (vx)