LinearPolar/LogPolar transformation distoring an iris

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I'm currently running the following Python (OpenCV 3):

out = cv2.linearPolar(self.roi, center, self.iris_radius, cv2.WARP_FILL_OUTLIERS)

Input image: / Result:

The problem I'm having is that this creates something distorted; what I expected was the output to be tall and thin, to reduce the amount of data thrown away & interpolation.

What can I do to improve the result, and produce a nice, beautiful, detailed iris strip?