Show that Equation XXXXXXXXXXfollows from Equation XXXXXXXXXX. A camera with intrinsic matrix λ and extrinsic parameters Ω = I , τ = 0 takes an image and then rotates to a new position Ω = Ω 1 , τ = 0...

1. 
   

   
   Show that Equation 15.36 follows from Equation 15.35.
   

   
   

1. 
   

   
   A camera with intrinsic matrix
   
   
   λ
   
   
   
   
   
   
   and extrinsic parameters
   
   Ω
   
   
   
   =
   
   I
   
   
   ,
   
   
   
   
   
   τ
   
   
   
   
   
   
   =
   
   0
   
   
   
   takes an image and
   
   <sup>then
   
   
   
   
   rotates
   
   
   
   
   to
   
   
   
   
   a
   
   
   
   
   new
   
   
   
   
   position
   
   
   
   
   
   Ω
   
   
   
   
   
   
   
   =
   
   
   
   
   
   Ω</sup>
   
   
   1
   
   
   <sup>,
   
   
   
   
   
   
   
   
   
   τ
   
   
   
   
   
   
   
   
   
   
   =
   
   
   
   
   
   0
   
   
   
   
   
   
   
   and
   
   
   
   
   takes
   
   
   
   
   a
   
   
   
   
   second
   
   
   
   
   image.
   
   
   
   
   Show
   
   
   
   
   that
   
   
   
   
   the
   
   
   
   
   homography</sup>
   
   
   
   relating these two images is given by
   

   
   

<sup>Φ



=





ΛΩ</sup>


1


<sup>Λ




−



1



.</sup>