MMSSD: Image Registration via Multiplicative Model based SSD

Image registration, is the process of aligning multiple images, and the presence of complex and spatially varying intensity distortions (SVID), significantly complicates the alignment process. Variations in pixel intensities across different regions of an image cause spatially varying intensity distortion. As proposed in previous studies, similarity metrics have had a critical role in addressing this issue. Since traditional similarity metrics like sum-of-squared differences (SSD) use the assumption of pixel-to-pixel independence, they can not be a robust measure of similarity when the intensity varies. Different models such as multiplicative can be used to define a robust similarity measure (SM). This paper proposes a robust similarity measure that considers spatially varying intensity distortion as a multiplicative model and it is effectively represented by a small number of coefficients in the transformed space. This similarity measure is called multiplicative model based SSD (MMSSD). This paper modifies and regularizes the SSD measure by the multiplicative model and sparse representation (SR). The Half-Quadratic Splitting (HQS) algorithm optimizes the proposed similarity measure. This approach breaks down the optimization problem into three sub-problems. The HQS helps to solve the optimization problem by iteratively solving these sub-problems. The main step of this process is the estimation of this distortion. In fact, the proposed approach estimates the intensity variations and geometrical transform simultaneously. Validated the effectiveness of the proposed similarity metric by achieving high accuracy in registering images from simulated and clinically acquired datasets.