Hessian-based Similarity Metric for Multimodal Medical Image Registration

One of the fundamental elements of both traditional and certain deep learning medical image registration algorithms is measuring the similarity/dissimilarity between two images. In this work, we propose an analytical solution for measuring similarity between two different medical image modalities based on the Hessian of their intensities. First, assuming a functional dependence between the intensities of two perfectly corresponding patches, we investigate how their Hessians relate to each other. Secondly, we suggest a closed-form expression to quantify the deviation from this relationship, given arbitrary pairs of image patches. We propose a geometrical interpretation of the new similarity metric and an efficient implementation for registration. We demonstrate the robustness of the metric to intensity nonuniformities using synthetic bias fields. By integrating the new metric in an affine registration framework, we evaluate its performance for MRI and ultrasound registration in the context of image-guided neurosurgery using target registration error and computation time.