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# lecture10 - 1 CSE 471 Media Processing and Multimedia Image...

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Unformatted text preview: 1 CSE 471 Media Processing and Multimedia Image Warping Often we want to change the size or shape of an image What types of changes? Image Warping Mapping an image onto another image, where the new image may be larger, smaller, or a different shape as the first image. 2 CSE 471 Media Processing and Multimedia Some types of image warps Arbitrary Each pixel specifies where it comes from Matched features We will make points go from one feature point to another and interpolate in-between Affine Operations can consist of scaling, skew, rotation, and translation • 6 parameter operation • Very common! 3 CSE 471 Media Processing and Multimedia Affine transformations General formulation x’ = ax + by + c y’ = dx + ey + f (x,y) in one image, (x’,y’) in the other… We can think of this as: Source to destination -or- Destination to source 4 CSE 471 Media Processing and Multimedia Direction Source to destination Destination to source W h i c h o n e d o w e n e e d ? 5 CSE 471 Media Processing and Multimedia Examples Source to destination: x’=0.707x - 0.707y + 5 y’=0.707x + 0.707y + 10 Destination to source: x’ = 0.706x + 0.706y – 10.59 y’ = -0.706x + 0.706y – 3.53 x y x' y' x'' y'' 5 10 1 1 5 11.414 0.998284 0.998284 10 10 5 24.14 9.98284 9.98284 100 100 5 151.4 99.8284 99.8284 100 75.7 80.7 99.8284-5.8E-15 6 CSE 471 Media Processing and Multimedia Affine operations Translation y’ = y + f x’ = x + c Scaling x’ = ax y’ = dy Rotation (CCW about 0,0) x’ = xcos θ- ysin θ y’ = xsin θ + ycos θ Skew (or Shear) x’ = x + by y’ = y x’ = ax + by + c y’ = dx + ey + f 7 CSE 471 Media Processing and Multimedia Matrix and Vector Operations We would like to express our operations using matrices and vectors = ⇔ = = y x d a y x dy y ax x ' ' ' ' - = ⇔ + =- = y x y x y x y y x x θ θ θ θ θ θ θ θ cos sin sin cos ' ' cos sin ' sin cos ' Scaling: Rotation: Translation: = ⇔ + = + = y x y x f y y c x x ? ?...
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lecture10 - 1 CSE 471 Media Processing and Multimedia Image...

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