Projective geometry for Computer Vision
Projective geometry for Computer Vision
Projective geometry for Computer Vision
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<strong>Projective</strong> mappings of conics<br />
◮ Note that a conic is represented (homogeneously) as<br />
x T Cx = 0<br />
◮ Under a point trans<strong>for</strong>mation x ′ = Hx the conic becomes<br />
x T Cx = x ′ T [H −1 ] T CH −1 x ′ = x ′ T H −T CH −1 x ′ = 0<br />
◮ This is the quadratic <strong>for</strong>m of x ′T C ′ x ′ with C ′ = H −T CH −1 .<br />
This gives the trans<strong>for</strong>mation rule <strong>for</strong> a conic.<br />
Subhashis Banerjee<br />
<strong>Projective</strong> <strong>geometry</strong> <strong>for</strong> <strong>Computer</strong> <strong>Vision</strong>