© by Yu Hen Hu 1 ECE533 Digital Image Processing Image Geometry and Geometric Transformation

© by Yu Hen Hu 2 ECE533 Digital Image Processing Geometric Distortion l Geometric distortion is a form of geometric transformation l Image may subject to geometric distortion due to imperfect imaging devices or viewing conditions l 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 {c i ; 1  i  8} (x,y) (x’,y’)

© by Yu Hen Hu 3 ECE533 Digital Image Processing Gray Level Interpolation l 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), l If x and y are integers, then l If x and y are fraction numbers, but fall within the border of the original image, then interpolation will be needed to find

© by Yu Hen Hu 4 ECE533 Digital Image Processing Nearest Neighbor Gray Level Interpolation

© by Yu Hen Hu 5 ECE533 Digital Image Processing Bilinear Interpolation l Estimate the value of (=g(x’,y’)) using four nearest neighbors when x’ and y’ are fractional numbers. Let l Substitute g(x 1,y 1 ), g(x 1,y 2 ), g(x 2,y 1 ), g(x 2,y 2 ) into above equation and solve for a, b, c, d (x 1,y 2 ) (x 1,y 1 ) (x 2,y 2 ) (x 2,y 1 ) (x’,y’)

© by Yu Hen Hu 6 ECE533 Digital Image Processing Example 5.16 a.An image with 25 regularly spaced tiepoints. b.Geometric distortion by rearranging the tiepoints c.Distorted image, nearest neighbor interpolation d.Restored image, NN e.Distorted image, bilinear transformation f.Restored image, BT

© by Yu Hen Hu 7 ECE533 Digital Image Processing Another Example a.Original image b.Distorted image using bilinear transform c.Difference between a and b d.Geometrically restored image using bilinear transform for gray level interpolation