Matches in SemOpenAlex for { <https://semopenalex.org/work/W2013276990> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W2013276990 endingPage "392" @default.
- W2013276990 startingPage "366" @default.
- W2013276990 abstract "Our goal is to interpret computer vision in terms of the vanishing or non-vanishing of certain sets of polynomials. To this end, we establish the algebraic geometric foundations of computer vision using transformation groups. Let α be a three-dimensional object in whose structure m points and n lines play an important role. Let β be a possible two-dimensional image in whose structure are m points and n lines which may be an image of those chosen in α . We show that there is a set of polynomials F i ( α , β ) which must vanish when β is a true image of α . The F i are the maximal subdeterminants of a ( 3 m + 2 n ) × ( 12 + m ) matrix and their vanishing says that the rank of this matrix is at most 11 + m . Let Z = { ( α , β ) : F i ( α , β ) = 0 for all i } and let Γ = { ( α , β ) : β is a true image of α } . We show that the Zariski-closure of Γ is an irreducible component of Z and give a precise description of the other components. We construct a set U ′ , defined by the non-vanishing of certain polynomials, so that U ′ ∩ Γ = U ′ ∩ Z . We conclude with two applications to object recovery: when ( m , n ) = ( 3 , 3 ) , we show that different objects have the same image sets; for any ( m , n ), we show that objects cannot be distinguished by any polynomial function on their image sets." @default.
- W2013276990 created "2016-06-24" @default.
- W2013276990 creator A5013218598 @default.
- W2013276990 date "2005-02-01" @default.
- W2013276990 modified "2023-09-26" @default.
- W2013276990 title "On the equations relating a three-dimensional object and its two-dimensional images" @default.
- W2013276990 cites W1483009832 @default.
- W2013276990 cites W148764929 @default.
- W2013276990 cites W1515679419 @default.
- W2013276990 cites W1530454533 @default.
- W2013276990 cites W175035292 @default.
- W2013276990 cites W1965338002 @default.
- W2013276990 cites W1976595761 @default.
- W2013276990 cites W1981680502 @default.
- W2013276990 cites W2033819227 @default.
- W2013276990 cites W2045963804 @default.
- W2013276990 cites W2080132708 @default.
- W2013276990 cites W2319418017 @default.
- W2013276990 cites W2481344083 @default.
- W2013276990 cites W2041534512 @default.
- W2013276990 doi "https://doi.org/10.1016/j.aam.2004.07.005" @default.
- W2013276990 hasPublicationYear "2005" @default.
- W2013276990 type Work @default.
- W2013276990 sameAs 2013276990 @default.
- W2013276990 citedByCount "3" @default.
- W2013276990 countsByYear W20132769902012 @default.
- W2013276990 countsByYear W20132769902013 @default.
- W2013276990 crossrefType "journal-article" @default.
- W2013276990 hasAuthorship W2013276990A5013218598 @default.
- W2013276990 hasBestOaLocation W20132769901 @default.
- W2013276990 hasConcept C154945302 @default.
- W2013276990 hasConcept C2777686260 @default.
- W2013276990 hasConcept C2781238097 @default.
- W2013276990 hasConcept C29694066 @default.
- W2013276990 hasConcept C33923547 @default.
- W2013276990 hasConcept C41008148 @default.
- W2013276990 hasConcept C71924100 @default.
- W2013276990 hasConceptScore W2013276990C154945302 @default.
- W2013276990 hasConceptScore W2013276990C2777686260 @default.
- W2013276990 hasConceptScore W2013276990C2781238097 @default.
- W2013276990 hasConceptScore W2013276990C29694066 @default.
- W2013276990 hasConceptScore W2013276990C33923547 @default.
- W2013276990 hasConceptScore W2013276990C41008148 @default.
- W2013276990 hasConceptScore W2013276990C71924100 @default.
- W2013276990 hasIssue "2" @default.
- W2013276990 hasLocation W20132769901 @default.
- W2013276990 hasOpenAccess W2013276990 @default.
- W2013276990 hasPrimaryLocation W20132769901 @default.
- W2013276990 hasRelatedWork W1974891317 @default.
- W2013276990 hasRelatedWork W1979597421 @default.
- W2013276990 hasRelatedWork W2007980826 @default.
- W2013276990 hasRelatedWork W2063488590 @default.
- W2013276990 hasRelatedWork W2352927548 @default.
- W2013276990 hasRelatedWork W4230623537 @default.
- W2013276990 hasRelatedWork W4230638242 @default.
- W2013276990 hasRelatedWork W4245490552 @default.
- W2013276990 hasRelatedWork W4246661265 @default.
- W2013276990 hasRelatedWork W4250879966 @default.
- W2013276990 hasVolume "34" @default.
- W2013276990 isParatext "false" @default.
- W2013276990 isRetracted "false" @default.
- W2013276990 magId "2013276990" @default.
- W2013276990 workType "article" @default.