Existence of Two View Chiral Reconstructions

Pryhuber, Andrew; Sinn, Rainer; Thomas, Rekha R.

doi:10.1137/20m1381848

Cited by 2 publications

(3 citation statements)

References 6 publications

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“…Namely, as the images under the blow up morphisms, of the final pair of lines in the unique Schläfli double six on S determined by the lines { xi } 5 i=1 and { yj } 5 j=1 . This was also noted in [17].…”

Section: K =supporting

confidence: 63%

“…Proof. The proof of the incidence relations follows from dimension counting and can be found in [17,Lemma 6.1]. The two sets of lines are part of a unique Schläfli double six on S since each double six is already uniquely defined by three of its line pairs, and we have 5 line pairs here with the correct incidences (see Lemma A.1 (3)).…”

Section: K =mentioning

confidence: 99%

“…The existence of, and constructions for, this 6th point were noted in both [17] and [22], but not the rational formula. The rational formula shows that if (x i , y i ) 5…”

Section: K =mentioning

confidence: 99%

See 2 more Smart Citations

The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products

Connelly¹,

Agarwal²,

Ergur³

et al. 2023

Preprint

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Given k ≤ 6 points (x i , y i ) ∈ P 2 × P 2 , we characterize rank deficiency of the k × 9 matrix Z k with rows x i ⊗ y i in terms of the geometry of the point configurations {x i } and {y i }. While this question comes from computer vision the answer relies on tools from classical algebraic geometry: For k ≤ 5, the geometry of the rank-drop locus is characterized by cross-ratios and basic (projective) geometry of point configurations. For the case k = 6 the rank-drop locus is captured by the classical theory of cubic surfaces.

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Section: K =supporting

confidence: 63%

Section: K =mentioning

confidence: 99%