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Unformatted text preview: Ch2 – Basic Operations • Overview • Point Operations • Algebraic Operations • Geometric Operations – Translation, rotation, scale, shear – Combined operations • Distance Operations • Conclusion Geometric Operations • Geometric operations are used to change the position, orientation, size, or shape of images • Generate an output image by selecting appropriate pixels from the input image – Output[y][x] = Input[ My(x,y) ][ Mx(x,y) ] – My and Mx define the geometric operation • We can use nearest neighbor or bilinear interpolation to sample the input image Geometric Operations • Must implement coordinate range checking to handle image boundaries properly • Common solutions: – Wrap around – use modulo arithmetic – Reflection – go backwards into image – Nearest boundary – select point on boundary – Zero pad – pixels outside image are zero Geometric Operations • What is value of f(7,1) for image below? – Wrap around: f(1,1) – Reflection: f(4,1) – Nearest boundary: f(5,1) – Zero pad: 0 0 1 2 3 4 5 0 1 W R N Z 2 3 4 Geometric Operations • What is value of f(3,5) for image below? – Wrap around: f(3,0) – Reflection: f(3,4) – Nearest boundary: f(3,4) – Zero pad: 0 0 1 2 3 4 5 0 W 1 2 3 4 RN Z Geometric Operations • Translation: – Mx(x,y) = xTx – My(x,y) = yTy – Output[y][x] = Input[My(x,y)][Mx(x,y)] • This will move image right Tx and down Ty • Useful to keep object of interest in middle • Can be used for video transition effects (wipes) Geometric Operations Input image Translated image with Tx=15, Ty=30 using zero pad Geometric Operations Input image Translated image with Tx=15, Ty=30 using wrap around Geometric Operations • Scaling: – Mx(x,y) = x/Sx – My(x,y) = y/Sy – Output[y][x] = Input[My(x,y)][Mx(x,y)] • This will stretch an image by Sx and Sy • Useful to zoom in on object of interest without changing size of output image Geometric Operations Input image Scaled image with Sx=1.1, Sy=0.9 using zero pad Geometric Operations Input image Scaled image with Sx=1.1, Sy=0.9 using wrap around Geometric Operations • Rotation: – Mx(x,y) = x*cos(A) – y*sin(A) – My(x,y) = x*sin(A) + y*cos(A) – Output[y][x] = Input[My(x,y)][Mx(x,y)] • Rotates image clockwise by A degrees • Used to correct for camera tilt and/or orient object of interest in the image • Rotation:...
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This note was uploaded on 12/01/2011 for the course CSCE 5013 taught by Professor Staff during the Fall '08 term at Arkansas.
 Fall '08
 STAFF

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