Projective Geometry - Institute for Computer Graphics and Vision
Projective Geometry - Institute for Computer Graphics and Vision
Projective Geometry - Institute for Computer Graphics and Vision
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Institut für Elektrische Meßtechnik und Meßsignalverarbeitung<br />
<strong>Projective</strong> Trans<strong>for</strong>mations in P n<br />
• “projective trans<strong>for</strong>mation” = “collineation” =<br />
“projectivity” = “homography” H<br />
• Invertible mapping P n → P<br />
<br />
n<br />
<br />
• x1, x2,<br />
x3<br />
lie on a line Hx1<br />
, Hx2<br />
, Hx3<br />
lie on a line<br />
„geradentreue“ Abbildung<br />
• (n+1) x (n+1) matrix<br />
• In P 2 : x1<br />
' h11<br />
h12<br />
h13<br />
x1<br />
<br />
<br />
x'<br />
<br />
<br />
<br />
<br />
<br />
x<br />
x<br />
2<br />
3<br />
<br />
' Hx<br />
<br />
' <br />
<br />
<br />
<br />
x<br />
<br />
<br />
x<br />
• H has (n+1) 2 -1 DoF, H is non-singular<br />
<br />
<br />
<br />
<br />
h<br />
h<br />
21<br />
31<br />
h<br />
h<br />
22<br />
32<br />
h<br />
h<br />
23<br />
33<br />
2<br />
3<br />
<br />
<br />
<br />
<br />
Professor Augmented Horst Reality Cerjak, VU 19.12.20051 <strong>Projective</strong> <strong>Geometry</strong> Axel Pinz<br />
7.3.2011<br />
20