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Generalized Warping Technique
I wrote a generalized 8-parameter image warping transform, that is, a transform in 2-D homogeneous coordinates by a general 3x3 matrix. Technique used was to sample the output space, apply the inverse transform, and use a simple bilinear filter (weighting the four nearest pixels). I got surprisingly good results, with less aliasing than I expected, so a more sophisticated filter seems unnecessary. Most of the transformations I will need in this research will be translations, rotations, and scaling, but I also tried some challenging examples (see the last picture). Here are some fun examples:
Mandrill (512x512)
Before:
After Translation: Note the subtly different colors.
After Rotation and shrinking:
After Singular Transform:
High-Frequency Checkerboard (512x512)
Before:
After Singular Transform: Note the singularity in the off-center, the ringing around that region, the rough edges, and the low resolution at the upper-right.
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