Image stack surface area minimization for groupwise and multimodal affine registration

Considering the graph of a feature function as an embedded surface in three dimensions is a standard device in computer vision. When multiple feature functions (eg. multiple images) are available, the natural extension of the above concept is to a higher-dimensional embedded surface. This has received surprisingly little attention. In this paper, we advocate for this view by showing the utility of surface area for estimating spatial transformations between images for the purposes of registration. In contrast to the entropy of the stack of images (when represented as continuous and differentiable functions) being zero, the surface area turns out to be useful measure for image registration. We show that during the progression of standard registration algorithms like Congealing, the area of the stack of images being registered decreases. Our own algorithm for affine registration based on image stack surface area (ISSA) minimization has several advantages compared with Congealing and Mutual Information (MI) registration. Finally, we highlight the generality of our framework by also showcasing experiments on affine point-set registration.