A subspace identification extension to the phase correlation method

Abstract

The phase correlation method (PCM) is known to provide straightforward estimation of rigid translational motion between two images. It is often claimed that the original method is best suited to identify integer pixel displacements, which has prompted the development of numerous subpixel displacement identification methods. However, the fact that the phase correlation matrix is rank one for a noise-free rigid translation model is often overlooked. This property leads to the low complexity subspace identification technique presented here. The combination of non-integer pixel displacement identification without interpolation, robustness to noise, and limited computational complexity make this approach a very attractive extension of the PCM. In addition, this approach is shown to be complementary with other subpixel phase correlation based techniques.

Subpixel Alignment of MRI Data Under Cartesian and Log-Polar Sampling

“…We applied our technique to a set of MRI data, used also by Hoge in his experimentation [3]. Figure 3 shows a pair of MRI images from this data set, and their phase difference matrix.…”

“…Table 1 summarizes the shift parameters obtained by our approach compared to those obtained by physical calibration, Stone et al and Hoge. Similar to [3], we compared the different algorithms using the relative error. Results are shown in Fig.…”

“…We then applied the method to estimate rotation and scaling in a log-polar sampling scheme, assuming known rotation center 3 . In log-polar sampling rotation and scaling reduce to simple translations, which can then be accurately estimated directly from the phase difference matrix as before.…”

“…However, for MRI, which provides directly the Fourier spectrum of the field of view, it would be interesting from both practical and computational points of view to estimate the shifts directly in the Fourier domain. A practical solution for this problem was first proposed by Hoge [3]. His method requires a subspace approximation by Singular Value Decomposition (SVD), and unwrapping of the dominant left and right eigenvectors.…”

Detection and Estimation Satellite Attitude Jitter Using Remote Sensing Imagery

“…Next, the point with the highest correlation is obtained at a subpixel level by parabola fitting to the neighboring correlation values and determining the vertex value. Phase correlation (PC) is also used as a similarity measure (Hoge, 2003;Leprince et al, 2007;Morgan et al, 2010). Consider two N 1 X N 2 images s(n 1 , n 2 ) and s'(n 1 , n 2 )= s(n 1 -δ 1 , n 2 -δ 2 ) that differ by the displacement (δ 1 , δ 2 ).…”