Accurate multi-dimensional alignment

We present an algorithm for aligning rotated and translated volumes, which operates in the frequency domain. The Fourier domain allows us to compute the rotation and translation parameters separately, thus reducing a problem with six degrees of freedom to two problems of three degrees of freedom each. We propose a three-step procedure. The first step estimates the rotation axis, the second computes the planar rotation relative to the rotation axis, and the third recovers the translational displacement by using the phase correlation technique. By using the 3-D pseudo-polar FFT, the estimation of the rotation axis is shown to be algebraically accurate. Experimental results show that the algorithm is accurate and robust to noise.