Question
Show that relation between any image point (xim, yim)T of a plane (in the form of (x1,x2,x3)T in projective space ) and its corresponding point
Show that relation between any image point (xim, yim)T of a plane (in the form of (x1,x2,x3)T in projective space ) and its corresponding point (Xw, Yw, Zw)T on the plane in 3D space can be represented by a 3x3 matrix. You should start from the general form of the camera model (x1,x2,x3)T = MintMext (Xw, Yw, Zw, 1)T, where the image center (ox, oy), the focal length f, the scaling factors( sx and sy), the rotation matrix R and the translation vector T are all unknown. Note that in the course slides and the lecture notes, I used a simplified model of the perspective project by assuming ox and oy are known and sx = sy =1, and only discussed the special cases of planes.. So you cannot directly copy those equations I used. Instead you should use the general form of the projective matrix, and the general form of a plane nx Xw + ny Yw + nzZw = d.
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