Depth for Multi-Modal Contour Ensembles
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
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, a variant used for handling ensembles with contours with multiple intersections. 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, illustrate the use case of progressive depth computation and enable non-parametric multimodal analysis. To promote research and adoption, we offer the contour-depth Python package.
Description
CCS Concepts: Human-centered computing → Scientific visualization; Mathematics of computing → Nonparametric statistics; Statistical graphics; Cluster analysis
@article{10.1111:cgf.15083,
journal = {Computer Graphics Forum},
title = {{Depth for Multi-Modal Contour Ensembles}},
author = {Chaves-de-Plaza, Nicolas F. and Molenaar, Mathijs and Mody, Prerak and Staring, Marius and Egmond, René van and Eisemann, Elmar and Vilanova, Anna and Hildebrandt, Klaus},
year = {2024},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.15083}
}