A robust similarity measure for volumetric image registration with outliers *

• Investigation of robust alignment methods for volumetric medical images
• Proposal of two novel similarity measures based on the cosine of normalised 3D volumetric gradients
• The measures are shown to be robust to occlusions and bias field corruption.
• The first review of robust 3D Lucas–Kanade methods for affine image alignment
• The proposed methods show good performance for non-rigid alignment.

Image registration under challenging realistic conditions is a very important area of research. In this paper, we focus on algorithms that seek to densely align two volumetric images according to a global similarity measure. Despite intensive research in this area, there is still a need for similarity measures that are robust to outliers common to many different types of images. For example, medical image data is often corrupted by intensity inhomogeneities and may contain outliers in the form of pathologies. In this paper we propose a global similarity measure that is robust to both intensity inhomogeneities and outliers without requiring prior knowledge of the type of outliers. We combine the normalised gradients of images with the cosine function and show that it is theoretically robust against a very general class of outliers. Experimentally, we verify the robustness of our measures within two distinct algorithms. Firstly, we embed our similarity measures within a proof-of-concept extension of the Lucas–Kanade algorithm for volumetric data. Finally, we embed our measures within a popular non-rigid alignment framework based on free-form deformations and show it to be robust against both simulated tumours and intensity inhomogeneities.