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Image Geometry and Geometric Transformation

Image Geometry and Geometric Transformation. Geometric distortion is a form of geometric transformation Image may subject to geometric distortion due to imperfect imaging devices or viewing conditions Assume the original image f ( x,y ) has subject to geometric distortion yielding g ( x’,y’ ).

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Image Geometry and Geometric Transformation

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  1. Image Geometry and Geometric Transformation

  2. Geometric distortion is a form of geometric transformation Image may subject to geometric distortion due to imperfect imaging devices or viewing conditions Assume the original image f(x,y) has subject to geometric distortion yielding g(x’,y’) Coord. transf. func. need 8 or more points to find {ci; 1  i  8} Geometric Distortion (x,y) (x’,y’)

  3. Gray Level Interpolation • Spatial transform establish a correspondence between a point (x’, y’) in the distorted image g(x’,y’) and original image f(x,y). To correct the geometric transformation, one needs to estimate gray values of f(x,y), • If x and y are integers, then • If x and y are fraction numbers, but fall within the border of the original image, then interpolation will be needed to find

  4. Nearest Neighbor Gray Level Interpolation

  5. Estimate the value of (=g(x’,y’)) using four nearest neighbors when x’ and y’ are fractional numbers. Let Substitute g(x1,y1), g(x1,y2), g(x2,y1), g(x2,y2) into above equation and solve for a, b, c, d Bilinear Interpolation (x1,y2) (x2,y2) (x’,y’) (x1,y1) (x2,y1)

  6. Example 5.16 • An image with 25 regularly spaced tiepoints. • Geometric distortion by rearranging the tiepoints • Distorted image, nearest neighbor interpolation • Restored image, NN • Distorted image, bilinear transformation • Restored image, BT

  7. Another Example • Original image • Distorted image using bilinear transform • Difference between a and b • Geometrically restored image using bilinear transform for gray level interpolation

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