Depth for Multi-Modal Contour Ensembles

The contour depth methodology enables non-parametric summarization of contour ensembles by extracting their representatives, confidence bands, and outliers for visualization (via contour boxplots) and robust downstream procedures.We address two shortcomings of these methods. Firstly, we significantly expedite the computation and recomputation of Inclusion Depth (ID), introducing a linear-time algorithm for epsilon ID, the more commonly used variant handling ensembles with contours that tend to intersect frequently. We also present the inclusion matrix, which contains the pairwise inclusion relationships between contours, and leverage it to accelerate the recomputation of ID. Secondly, extending beyond the single distribution assumption, we present the Relative Depth (ReD), a generalization of contour depth for ensembles with multiple modes. Building upon the linear-time eID, we introduce CDclust, a clustering algorithm that untangles ensemble modes of variation by optimizing ReD. Synthetic and real datasets from medical image segmentation and meteorological forecasting showcase the speed advantages, illustrating the progressive depth computation use case and enabling non-parametric multi-modal analysis. To promote research and adoption, we offer the contour-depth Python library.

@Article { CMMSEEVH24,
  author       = "Chaves de Plaza, Nicolas and Molenaar, Mathijs and Mody, Prerak P. and Staring, Marius and Egmond, Ren\'e van
                  and Eisemann, Elmar and Vilanova, Anna and Hildebrandt, Klaus",
  title        = "Depth for Multi-Modal Contour Ensembles",
  journal      = "Computer Graphics Forum (Proc. of EuroVis)",
  year         = "2024",
  url          = "http://graphics.tudelft.nl/Publications-new/2024/CMMSEEVH24"
}