x1 0 x2 0 x3 0 x 4 0 y1 0 1 0 0 x1 0 y1 y2 0 y3 10 0

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Unformatted text preview: 0 0 0 ⎥ྏ ⎢ྎ a5 ⎥ྏ ⎢ྎ x3 ' ⎥ྏ ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ ⎥ྏ x3 y3 1 ⎥ྏ ⎢ྎa6 ⎥ྏ ⎢ྎ y3 '⎥ྏ ⎦ྏ ⎣ྏ ⎦ྏ ⎣ྏ ⎦ྏ x=A-1B Recovering Best Affine Transformation •  What if we knew four corresponding points? •  We should be able to utilize the additional information ⎡ྎ x1 y1 1 0 0 0⎤ྏ ⎡ྎ x1 ' ⎤ྏ ⎢ྎ 0 0 0 x y 1⎥ྏ a ⎢ྎ ⎥ྏ ⎡ྎ 1 ⎤ྏ ⎢ྎ y1 ' ⎥ྏ 1 1 ⎢ྎ ⎥ྏ ⎢ྎ x2 y2 1 0 0 0⎥ྏ ⎢ྎa2 ⎥ྏ ⎢ྎ x2 '⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ 0 0 0 x2 y2 1⎥ྏ ⎢ྎ a3 ⎥ྏ = ⎢ྎ y2 '⎥ྏ ⎢ྎ x3 y3 1 0 0 0⎥ྏ ⎢ྎa4 ⎥ྏ ⎢ྎ x3 ' ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ 0 0 0 x3 y3 1⎥ྏ ⎢ྎ a5 ⎥ྏ ⎢ྎ y3 '⎥ྏ ⎢ྎ x y 1 0 0 0⎥ྏ ⎢ྎa ⎥ྏ ⎢ྎ x '⎥ྏ ⎢ྎ ⎥ྏ 4 ⎢ྎ 4 ⎥ྏ ⎣ྏ 6 ⎦ྏ ⎢ྎ 4 ⎥ྏ ⎢ྎ 0 0 0 x4 y4 1⎥ྏ ⎢ྎ y4 '⎥ྏ ⎣ྏ ⎦ྏ ⎣ྏ ⎦ྏ Recovering Best...
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This note was uploaded on 03/02/2014 for the course CS 436 taught by Professor Sohaibkhan during the Winter '13 term at Lahore University of Management Sciences.

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