Robust Huber similarity measure for image registration in the presence of spatially-varying intensity distortion

• Image registration is considered in the presence of non-stationary distortion.
• Spatially varying intensity distortion is modeled using sparse representation.
• A robust measure based on proposed model is proposed via ML view and Huber norm.
• Image registration is statistically analyzed via non-linear regression problem.
• Registration accuracy is decreased in the presence of non-stationary distortions.

Similarity measure is an important part of image registration. The main challenge of similarity measure is lack of robustness to different distortions. A well-known distortion is spatially-varying intensity distortion. Its main characteristic is correlation among pixels. Most traditional intensity based similarity measures (e.g., SSD, MI) assume stationary image and pixel to pixel independence. Hence, these similarity measures are not robust against spatially-varying intensity distortion. Here, we suppose that non-stationary intensity distortion has a sparse representation in transform domain, i.e. its distribution has high peak at origin and a long tail. We use two viewpoints of Maximum Likelihood (ML) and Robust M-estimator. First, using the ML view, we propose robust Huber similarity measure (RHSM) in spatial transform domain as a new similarity measure in a mono-modal setting. In fact, RHSM is a combination of ℓ2 and ℓ1 norms. To demonstrate robustness of the proposed similarity measure, image registration is treated as a non-linear regression problem. In this view, covariance matrix of estimated parameters is obtained based on the one-step M-estimator. Then with minimizing Fisher information function, robust similarity measure of RHSM is introduced. This measure produces accurate registration results on both artificial as well as real-world problems that we have examined.