Depth for Multi-Modal Contour Ensembles

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dc.contributor.authorChaves-de-Plaza, Nicolas F.en_US
dc.contributor.authorMolenaar, Mathijsen_US
dc.contributor.authorMody, Preraken_US
dc.contributor.authorStaring, Mariusen_US
dc.contributor.authorEgmond, René vanen_US
dc.contributor.authorEisemann, Elmaren_US
dc.contributor.authorVilanova, Annaen_US
dc.contributor.authorHildebrandt, Klausen_US
dc.contributor.editorAigner, Wolfgangen_US
dc.contributor.editorArchambault, Danielen_US
dc.contributor.editorBujack, Roxanaen_US
dc.date.accessioned2024-05-21T08:17:53Z
dc.date.available2024-05-21T08:17:53Z
dc.date.issued2024
dc.description.abstractThe 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.en_US
dc.description.number3
dc.description.sectionheadersScalars, Vectors, and Topology
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15083
dc.identifier.issn1467-8659
dc.identifier.pages12 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15083
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15083
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/
dc.subjectCCS Concepts: Human-centered computing → Scientific visualization; Mathematics of computing → Nonparametric statistics; Statistical graphics; Cluster analysis
dc.subjectHuman centered computing → Scientific visualization
dc.subjectMathematics of computing → Nonparametric statistics
dc.subjectStatistical graphics
dc.subjectCluster analysis
dc.titleDepth for Multi-Modal Contour Ensemblesen_US
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