algorithm - Procrustes analysis / Finding the Angle Between two images represented by two sets of 2d points -


if have 2 sets of points can rotate 1 around procrustes analysis align 1 other.

but suppose these 2 sets of points each attached images , rotate images well. there way can rotate image, instead of rotating points? tutorial there uses dot product rotation (solve u, s, v = svd(p1', p2) , p2 . v . u', p' transposed p)

however doesn't tell me angle between images is.

the page on wikipedia calculates angle between each pair of points think.

maybe i'm asking impossible? if rotate first set of points align first, can't rotate respective images angle well? point being, angle that?

i noticed v . u' gives me 2 x 2 matrix seems rotation matrix (there's wikipedia page can't link there due posting priviledges). got sin , cos of third , first elements , used arctan2, results i'm getting kind of weird. know have transformed radians i'm not convinced i'm doing right. trying rotation gives me on gimp makes seem it's not want, i'll test more.

it seems approach correct. 2 things come mind:

1) paper linked (procrustes analysis) involves translation , scaling in addition rotation. depending on whether or not operations performed on images, may end strange results don't appear match.

2) think may overcomplicating angle calculation. v * u' appears correct rotation matrix, believe correct angle requires 1 of matrix entries in 2x2 matrix. instance, use acos() of first matrix entry. you've noticed, (depending on program) give answer in radians you'll have convert degrees if want try out rotation in gimp, etc.

hope helps!


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