Image Registration Based on Low Rank Matrix: Rank-Regularized SSD

Similarity measure is a main core of image registration algorithms. Spatially varying intensity distortion is an important challenge, which affects the performance of similarity measures. Correlation among the pixels is the main characteristic of this distortion. Similarity measures such as sum-of-squared-differences (SSD) and mutual information ignore this correlation; hence, perfect registration cannot be achieved in the presence of this distortion. In this paper, we model this correlation with the aid of the low rank matrix theory. Based on this model, we compensate this distortion analytically and introduce rank-regularized SSD (RRSSD). This new similarity measure is a modified SSD based on singular values of difference image in mono-modal imaging. In fact, image registration and distortion correction are performed simultaneously in the proposed model. Based on our experiments, the RRSSD similarity measure achieves clinically acceptable registration results, and outperforms other state-of-the-art similarity measures, such as the well-known method of residual complexity.