Phase correlation

Question

How can rotation angle be determined by phase correlation(using fft) of 2 images? The algorithm given in http://en.wikipedia.org/wiki/Phase_correlation returns linear shift, not angular. It also mentions images have to be converted to log-polar coordinates to compute rotation. How is this conversion achieved in python? And post conversion do the same steps of the algorithm hold?

Answer 1

log polar transformation is actually rotation and scale invariant.. rotation corresponds to shift in y axis and scaling corresponds to shift in x axis in log polar transformation

so simple steps are as follows

for finding an image x in image y

find lpts of both x and y

find fft of x say F(X)

for each lpt in y whos logP is lesser than equal to logP of x find its fft say F(y)

find phase correlation of ffts of x and each of those corresponding images

using the formula R=(F(x).F*(Y)) divided by Mod(F(x).F*(y))

find the IFFT of R and the peak value of R corresponds to the rotation deviation in the Y Axis and Scaling deviation in the X Axis from the original Image

references:

1. http://etd.lsu.edu/docs/available/etd-07072005-113808/unrestricted/Thunuguntla_thesis.pdf

   and[http://www.nashruddin.com/phase-correlation-function-in-opencv.html]