Determining a rotation of a tetrahedron from a projection

Richard J. Gardner; Paolo Gronchi; Thorsten Theobald

Determining a rotation of a tetrahedron from a projection

Metric Geometry 2012-07-10 v2 Computational Geometry Computer Vision and Pattern Recognition

Authors: Richard J. Gardner , Paolo Gronchi , Thorsten Theobald

Abstract

The following problem, arising from medical imaging, is addressed: Suppose that $T$ is a known tetrahedron in $\R^3$ with centroid at the origin. Also known is the orthogonal projection $U$ of the vertices of the image $\phi T$ of $T$ under an unknown rotation $\phi$ about the origin. Under what circumstances can $\phi$ be determined from $T$ and $U$ ?

Keywords

tetrahedron rotation determination orthogonal projection medical imaging centroid unknown rotation

Cite

@article{arxiv.1111.7100,
  title  = {Determining a rotation of a tetrahedron from a projection},
  author = {Richard J. Gardner and Paolo Gronchi and Thorsten Theobald},
  journal= {arXiv preprint arXiv:1111.7100},
  year   = {2012}
}

Comments

16 pages, 3 figures; minor revision based on reviewers' comments

Determining a rotation of a tetrahedron from a projection

Abstract

Keywords

Cite

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