title: Surface boxplots.
abstract: In this paper, we introduce a surface boxplot as a tool for visualization and exploratory analysis of samples of images. First, we use the notion of volume depth to order the images viewed as surfaces. In particular, we define the median image. We use an exact and fast algorithm for the ranking of the images. This allows us to detect potential outlying images that often contain interesting features not present in most of the images. Second, we build a graphical tool to visualize the surface boxplot and its various characteristics. A graph and histogram of the volume depth values allow us to identify images of interest. The code is available in the supporting information of this paper. We apply our surface boxplot to a sample of brain images and to a sample of climate model outputs.
authors.affiliation: CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia.
authors.forename: Marc G
authors.initials: MG
authors.lastname: Genton
authors.affiliation: Scientific Computing and Imaging Institute, Salt Lake City, UT 84112, USA.
authors.forename: Christopher
authors.initials: C
authors.lastname: Johnson
authors.affiliation: Department of Computer and Information Science, University of Oregon, Eugene, OR 97403, USA.
authors.forename: Kristin
authors.initials: K
authors.lastname: Potter
authors.affiliation: CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia.
authors.forename: Georgiy
authors.initials: G
authors.lastname: Stenchikov
authors.affiliation: Department of Statistics, Ohio State University, Columbus, OH 43210, USA.
authors.forename: Ying
authors.initials: Y
authors.lastname: Sun
keywords: band depth; fast algorithm; functional boxplot; image data; large dataset; ranking; visualization; volume depth