hw2_2005 - SIMG-782 Introduction to Digital Image...

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SIMG-782 Introduction to Digital Image Processing Homework 2 – Due September 15, 2005 1. Let u = [ u 1 , u 2 , 1] T and v = [ v 1 , v 2 , 1] T denote the homogeneous coordinates of points in planes P and Q , respectively. Matching point pairs are related by a projection matrix H as v i = Hu i , i = 1 , 2 , . . . , n (a) A transform from P to Q in the form of a translation by ( x 0 , x 1 ) then a rotation by θ then a scaling by ( s 0 , s 1 ) is described by the matrix H = 0 . 951623 0 . 443749 - 6 . 97686 - 0 . 401487 0 . 860992 - 2 . 29753 0 0 1 Determine the values of ( x 0 , x 1 , s 0 , s 1 , θ ). (b) A transform from P to Q in the form of a translation by ( x 0 , x 1 ) then a scaling by ( s 0 , s 1 ) then a rotation by θ is described by the matrix H = 0 . 951623 0 . 401487 - 6 . 76555 - 0 . 443749 0 . 860992 - 2 . 08622 0 0 1 Determine the values of ( x 0 , x 1 , s 0 , s 1 , θ ) for this order transformations. 2. Matching pairs of points from
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