RISM: Single-Modal Image Registration via Rank-Induced Similarity Measure

Similarity measure is an important block in image registration. Most traditional intensity-based similarity measures (e.g., sum-of-squared-difference, correlation coefficient, and mutual information) assume a stationary image and pixel-by-pixel independence. These similarity measures ignore the correlation between pixel intensities; hence, perfect image registration cannot be achieved, especially in the presence of spatially varying intensity distortions. Here, we assume that spatially varying intensity distortion (such as bias field) is a low-rank matrix. Based on this assumption, we formulate the image registration problem as a nonlinear and low-rank matrix decomposition (NLLRMD). Therefore, image registration and correction of spatially varying intensity distortion are simultaneously achieved. We illustrate the uniqueness of NLLRMD, and therefore, we propose the rank of difference image as a robust similarity in the presence of spatially varying intensity distortion. Finally, by incorporating the Gaussian noise, we introduce rank-induced similarity measure based on the singular values of the difference image. This measure produces clinically acceptable registration results on both simulated and real-world problems examined in this paper, and outperforms other state-of-the-art measures such as the residual complexity approach.