Gradient-based subspace phase correlation for fast and effective image alignment

• To prove the efficacy of subspace phase correlation in estimating 2D image offsets.
• To prove more robust results yielded from subspace approach under zero-mean noise.
• To prove our method robust to non-zero-mean noise caused by non-overlapped regions.
• To prove higher peaks yielded by our method for robustness with reduced complexity.
• To validate the effectiveness with various synthetic data and noisy MRI images.

Phase correlation is a well-established frequency domain method to estimate rigid 2-D translational motion between pairs of images. However, it suffers from interference terms such as noise and non-overlapped regions. In this paper, a novel variant of the phase correlation approach is proposed, in which 2-D translation is estimated by projection-based subspace phase correlation (SPC). Conventional wisdom has suggested that such an approach can only amount to a compromise solution between accuracy and efficiency. In this work, however, we prove that the original SPC and the further introduced gradient-based SPC can provide robust solution to zero-mean and non-zero-mean noise, and the latter is also used to model the interference term of non-overlapped regions. Comprehensive results from synthetic data and MRI images have fully validated our methodology. Due to its substantially lower computational complexity, the proposed method offers additional advantages in terms of efficiency and can lend itself to very fast implementations for a wide range of applications where speed is at a premium.