Topological Simplification of Nested Shapes

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dc.contributor.authorZeng, Danen_US
dc.contributor.authorChambers, Erinen_US
dc.contributor.authorLetscher, Daviden_US
dc.contributor.authorJu, Taoen_US
dc.contributor.editorCampen, Marcelen_US
dc.contributor.editorSpagnuolo, Michelaen_US
dc.date.accessioned2022-06-27T16:19:55Z
dc.date.available2022-06-27T16:19:55Z
dc.date.issued2022
dc.description.abstractWe present a method for removing unwanted topological features (e.g., islands, handles, cavities) from a sequence of shapes where each shape is nested in the next. Such sequences can be found in nature, such as a multi-layered material or a growing plant root. Existing topology simplification methods are designed for single shapes, and applying them independently to shapes in a sequence may lose the nesting property. We formulate the nesting-constrained simplification task as an optimal labelling problem on a set of candidate shape deletions (''cuts'') and additions (''fills''). We explored several optimization strategies, including a greedy heuristic that sequentially propagates labels, a state-space search algorithm that is provably optimal, and a beam-search variant with controllable complexity. Evaluation on synthetic and real-world data shows that our method is as effective as single-shape simplification methods in reducing topological complexity and minimizing geometric changes, and it additionally ensures nesting. Also, the beam-search strategy is found to strike the best balance between optimality and efficiency.en_US
dc.description.number5
dc.description.sectionheadersTiling and Nesting
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume41
dc.identifier.doi10.1111/cgf.14611
dc.identifier.issn1467-8659
dc.identifier.pages161-173
dc.identifier.pages13 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14611
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14611
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectCCS Concepts: Computing methodologies --> Shape analysis; Volumetric models
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.subjectVolumetric models
dc.titleTopological Simplification of Nested Shapesen_US
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