Metric Multiview Geometry – a Catalogue in Low Dimensions
arxiv(2024)
摘要
We systematically compile an exhaustive catalogue of multiview varieties and
anchored multiview varieties arising from projections of points and lines in 1,
2, and 3-dimensional projective space. We say that two such varieties are
ED-equivalent if there is a linear isomorphism between that that preserve
ED-critical points. This gives rise to fourteen equivalence classes, and we
determine various properties - dimension, set-theoretic equations, and
multidegrees - for all varieties featured in our catalogue. In the case of
points, we also present a complementary study of resectioning varieties and
their singular loci. Finally, we propose conjectures for the Euclidean distance
degrees of all varieties appearing in our comprehensive compilation.
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