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Geometric Transformations: Warping, Registration, MorphingMorphing Yao Wang Polytechnic University, Brooklyn, NY 11201 With contribution from Zhu Liu, Onur Guleryuz, and Partly based on AA. KK. JJainain, FFundamentalsundamentals ooff DigitalDigital ImageImage ProcessingProcessing Lecture Outline Introduction ImageImage deformationdeformation modelmodel Image warping Image registration ImageImage morphingmorphing Geometric Transformation EL512 Image Processing 2 What is Geometric Transformation? So far, the image processing operations wewe havehave discusseddiscussed mmodifyodify tthehe colorcolor valuesvalues of pixels in a given image WithWith geometricgeometric ttransformation,ransformation, wewe modifymodify the positions of pixels in a image, but keep their colors unchanged –To create special effects –To register two images taken of the same scene at different times –To morph one image to another Geometric Transformation EL512 Image Processing 3 How to define a geometric transformation? Let (u, v) represent the image coordinate in an original image, and (x, y) in a deformed (or warped) image. We useuse aa functionfunction pairpair toto relaterelate correspondingcorresponding ppixelsixels iinn tthehe two images: – Forward mapping: xx(u,v), or xx(u) yy yy((uu,vv)) – Inverse mapping: u u(x,y) , or uu(x) vv((x,, yy)) Let f(u, v) or f(u) denote the original image and g(x, y) or g(g(xx)) tthehe deformeddeformed iimage.mage. ThenThen theythey areare rrelatedelated by:by: g(x,y) f(u(x,y),v(x,y)), or g(x) f(u(x)) f (u,v) g(x(u,v), y(u,v)) f(u) g(x(u)) Geometric Transformation EL512 Image Processing 4
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