Topological Simplification of Nested Shapes
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We 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.
Description
CCS Concepts: Computing methodologies --> Shape analysis; Volumetric models
@article{10.1111:cgf.14611,
journal = {Computer Graphics Forum},
title = {{Topological Simplification of Nested Shapes}},
author = {Zeng, Dan and Chambers, Erin and Letscher, David and Ju, Tao},
year = {2022},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14611}
}