Weighted Functional Boxplot with Application to Statistical Atlas Construction

Abstract

Atlas-building from population data is widely used in medical imaging. However, the emphasis of atlas-building approaches is typically to compute a mean / median shape or image based on population data. In this work, we focus on the statistical characterization of the population data, once spatial alignment has been achieved. We introduce and propose the use of the weighted functional boxplot. This allows the generalization of concepts such as the median, percentiles, or outliers to spaces where the data objects are functions, shapes, or images, and allows spatio-temporal atlas-building based on kernel regression. In our experiments, we demonstrate the utility of the approach to construct statistical atlases for pediatric upper airways and corpora callosa revealing their growth patterns. Furthermore, we show how such atlas information can be used to assess the effect of airway surgery in children.