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I am seeking a mathematical method to perform non-rigid transformations of quadrilaterals as demonstrated below.enter image description here

Here you can imagine the four coordinates of a rectangular figure where the data interior to the coordinates has been extracted but is known to be incorrect due to the distortion in the original figure. The goal is to determine the transformation which corrects the figure coordinates to known points and to apply that transformation to the figure data; thereby reducing data extraction errors.

One could always use image processing tools to alter the image perspective prior to data extraction, but I would like to learn a clean way to do this using math. Any suggestions?

jborb3663
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  • affine transformations? – user619894 Jul 19 '21 at 19:15
  • Not necessarily affine transformations. I am using webplotdigitizer to extract data and have found that my data points are often incorrect due to inadequate image correction.

    Generally, is there a way to take any four cartesian coordinates that bound a quadrilateral and apply a single transformation to correct them to known values?

     – jborb3663 Jul 19 '21 at 19:23
  • OK, then how about a projective transformation? – user619894 Jul 20 '21 at 12:25
  • @user619894 Thank you, this looks promising. – jborb3663 Jul 20 '21 at 14:51
  • @user619894 Projective transformations did the trick! Thank you so much, an elegant solution. Seems like knowing the terminology is half the battle. – jborb3663 Jul 20 '21 at 15:38

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This can be done with projective transformations. Many thanks to user619894 for pointing me in the right direction.

jborb3663
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  • basically the projective matrix has 8 free parameters and the quadrilateral yields 8 equations to satisfied. – user619894 Jul 20 '21 at 17:11