Quantifying the Resolution of a Template after Image Registration

Abstract

In many image processing applications (e.g. computational anatomy) a groupwise registration is performed on a sample of images and a template image is simultaneously generated. From the template alone it is in general unclear to which extent the registered images are still spatially misaligned. The local spatial variation left after registration may be seen as the resolution of the resulting template. In this sense we develop the first template resolution measure (TRM) quantifying the misalignment at each location of the template. The TRM is based on the key insight that the size of such misalignments can be determined as the amount of smoothing required to bring the registered images in agreement. This relationship is mathematically derived from characteristic examples in one dimension. This way, the TRM quantifies the remaining spatial variation in the template's units of length. Furthermore we propose to enhance the template by an effective visualization of its resolution measure. Finally we demonstrate the TRM's applicability and validate its interpretability for example datasets in two and three dimensions. The corresponding code is publicly available on GitHub.