Statistical atlas construction via weighted functional boxplots

[Display omitted] •A weighted functional boxplot is proposed to build spatio-temporal atlases.•We demonstrate the applicability of our method to functions, shapes, and images.•We elaborate how an atlas can be robustly augmented with statistical data.•Changes of pediatric airway and corpus callosum over time are captured.•We report quantitative assessment in subglottic stenosis of pediatric airways. Atlas-building from population data is widely used in medical imaging. However, the emphasis of atlas-building approaches is typically to estimate a spatial alignment 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. We also define a score system based on the pediatric airway atlas to quantitatively measure the severity of subglottic stenosis (SGS) in the airway. This scoring allows the classification of pre- and post-surgery SGS subjects and radiographically normal controls. Experimental results show the utility of atlas information to assess the effect of airway surgery in children.