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DTSTAMP:20260817T171535Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241205T134600
DTEND;TZID=Asia/Tokyo:20241205T135800
UID:siggraphasia_SIGGRAPH Asia 2024_sess130_papers_292@linklings.com
SUMMARY:Neural Laplacian Operator for 3D Point Clouds
DESCRIPTION:Bo Pang, Zhongtian Zheng, Yilong Li, Guoping Wang, and Peng-Sh
 uai Wang (Peking University)\n\nThe Laplacian operator holds a crucial rol
 e in 3D geometry processing, yet it is still challenging to define it on p
 oint clouds.\nPrevious works mainly focused on constructing a local triang
 ulation around each point to approximate the underlying manifold for defin
 ing the Laplacian operator, which may not be very robust or accurate.\nIn 
 contrast, we simply use the $K$-nearest neighbors (KNN) graph constructed 
 from the input point cloud and learn the Laplacian operator on the KNN gra
 ph with graph neural networks (GNNs).\nHowever, the ground-truth Laplacian
  operator is defined on a manifold mesh with a different connectivity from
  the KNN graph and thus cannot be directly used for training.\nTo train th
 e GNN, we propose a novel training scheme by imitating the behavior of the
  ground-truth Laplacian operator on a set of probe functions so that the l
 earned Laplacian operator behaves similarly to the ground-truth Laplacian 
 operator.\nWe train our network on a subset of ShapeNet and evaluate it ac
 ross a variety of point clouds.\nCompared with previous methods, our metho
 d reduces the error by \emph{an order of magnitude} and excels in handling
  sparse point clouds with thin structures or sharp features.\nOur method a
 lso demonstrates a strong generalization ability to unseen shapes.\nWith o
 ur learned Laplacian operator, we further apply a series of Laplacian-base
 d geometry processing algorithms directly to point clouds and achieve accu
 rate results, enabling many exciting possibilities for geometry processing
  on point clouds.\n\emph{We will release our code and trained models to en
 sure reproducibility.}\n\nRegistration Category: Full Access, Full Access 
 Supporter\n\nLanguage Format: English Language\n\nSession Chair: Noam Aige
 rman (University of Montreal, Mila)\n\n
URL:https://asia.siggraph.org/2024/program/?id=papers_292&sess=sess130
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