Geometric derivations of minimal sets of sufficient multiview constraints
Photogrammetric Record
By: Orrin H. Thomas and Edward R. Oshel
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Abstract
Geometric interpretations of four of the most common determinant formulations of multiview constraints are given, showing that they all enforce the same geometry and that all of the forms commonly in use in the machine vision community are a subset of a more general form. Generalising the work of Yi Ma yields a new general 2 x 2 determinant trilinear and 3 x 3 determinant quadlinear. Geometric descriptions of degenerate multiview constraints are given, showing that it is necessary, but insufficient, that the determinant equals zero. Understanding the degeneracies leads naturally into proofs for minimum sufficient sets of bilinear, trilinear and quadlinear constraints for arbitrary numbers of conjugate observations.
Suggested Citation
Thomas, O.H., and Oshel, E.R., 2012, Geometric derivations of minimal sets of sufficient multiview constraints: Photogrammetric Record, v. 27, no. 137, p. 74-93, https://doi.org/10.1111/j.1477-9730.2011.00653.x.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Geometric derivations of minimal sets of sufficient multiview constraints |
| Series title | Photogrammetric Record |
| DOI | 10.1111/j.1477-9730.2011.00653.x |
| Volume | 27 |
| Issue | 137 |
| Publication Date | December 12, 2011 |
| Year Published | 2012 |
| Language | English |
| Publisher | Wiley |
| Publisher location | Hoboken, NJ |
| Contributing office(s) | Astrogeology Science Center |
| Description | 20 p. |
| Larger Work Type | Article |
| Larger Work Subtype | Journal Article |
| Larger Work Title | Photogrammetric Record |
| First page | 74 |
| Last page | 93 |