Image Stacks as Parametric Surfaces: Application to Image Registration.

We introduce a framework in which a stack of images is considered to be a 2-D parametric surface embedded in a higher dimensional space. This is a simple yet powerful idea, known in the literature but not exploited to its fullest. We discuss the properties of image stacks as parametric surfaces, apply this framework to image registration by presenting the image stack surface relative area (ISSRA) registration measure. We show the power of ISSRA as an effective objective function for image registration. Essentially, it shows good performance across a variety of different categories of registration problems: pairwise, groupwise, affine, and non-rigid. Mutual information (MI)-a classical and effective approach for registration-is widely considered to be a good choice for multimodal and pairwise registration while being difficult to extend to the groupwise setting. We discuss the deficiency of MI in the groupwise case from a theoretical point of view, present its connection to ISSRA in the pairwise case, and then show the ready extensibility of ISSRA to the groupwise setting. Experiments and comparisons are performed on different categories of image registration to showcase ISSRA's wide range of applicability to registration problems in practice.