Effects of Rotation and Translation on Polar Transformation

The major property of a polar image is that it is insensitive to object rotation about its center, but intolerant of object translation in x‑y space. The figure below shows an object and its rotation signature at 0 degrees rotation, at 75 degrees rotation, and with translation in x-y.

The rotation of an object about its center produces a polar image with the same shape but shifted in theta.

The translation of an object produces a polar image which does not resemble the original model. The polar routines are designed to be somewhat tolerant of poor center placement, but at the expense of execution speed. For this reason, the Polar Coordinate Transformation tool is often preceded by a center-finding function, such as blob analysis.

Object, at 0 degrees, rotated 75 degrees, and translated in x-y