Geodesic
A Hilbert Scheme in Computer Vision
Canadian journal of mathematics, Tome 65 (2013) no. 5, pp. 961-988

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DOI

Multiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Gröbner basis for the multiview ideal of $n$ generic cameras. As the cameras move, the multiview varieties vary in a family of dimension $11n\,-\,15$ . This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme.
DOI : 10.4153/CJM-2012-023-2
Mots-clés : 14N, 14Q, 68, multigraded Hilbert Scheme, computer vision, monomial ideal, Groebner basis, genericinitial ideal 
Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha. A Hilbert Scheme in Computer Vision. Canadian journal of mathematics, Tome 65 (2013) no. 5, pp. 961-988. doi: 10.4153/CJM-2012-023-2
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     title = {A {Hilbert} {Scheme} in {Computer} {Vision}},
     journal = {Canadian journal of mathematics},
     pages = {961--988},
     year = {2013},
     volume = {65},
     number = {5},
     doi = {10.4153/CJM-2012-023-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-023-2/}
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