Orgorbitsgalleryhtml hierarchy of 2d transformations

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Unformatted text preview: ྏ a2 a4 0 0⎤ྏ ⎡ྎ1 0 b1 ⎤ྏ ⎡ྎ a1 0⎥ྏ ⎢ྎ0 1 b2 ⎥ྏ = ⎢ྎa3 ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ 1⎥ྏ ⎢ྎ0 0 1 ⎥ྏ ⎢ྎ 0 ⎦ྏ ⎣ྏ ⎦ྏ ⎣ྏ a2 a4 0 a1b1 + a2b2 ⎤ྏ a3b1 + a4b2 ⎥ྏ ⎥ྏ ⎥ྏ 1 ⎦ྏ Projective Group (Homography) •  3 x 3 transform defined in Homogeneous coordinates •  Simulates out of plane rotations •  Preserves straight lines •  Physical Interpretation: Plane + Camera Examples of Projective Transformations http://wearcam.org/orbits/gallery.html Hierarchy of 2D Transformations Length Ratios Length Ratios Length Cross-Ratios Pseudo Perspective Model •  Linear approximation of projective model •  Small motion approximation of full homography •  Does not preserve straight lines •  Obtained through Taylor Expansion Bilinear Model •  Linear approximation of projective model •  8 parameters, so perfectly maps four points •  Does not preserve straight lines •  Preserves relative distances (nonchirping model •  Obtained through Taylor Expansion Displacement Models Ref: Steve Mann & Rosalind W. Picard, “Video Orbits of the Projective Group: A simple approach to featureless estimation of parameters”, IEEE Trans. on Image Processing, Vol. 6, No. 9, Septembe...
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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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