41-Issue 5
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Browsing 41-Issue 5 by Author "Ju, Tao"
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Item Topological Simplification of Nested Shapes(The Eurographics Association and John Wiley & Sons Ltd., 2022) Zeng, Dan; Chambers, Erin; Letscher, David; Ju, Tao; Campen, Marcel; Spagnuolo, MichelaWe 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.