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ReSDF: Redistancing implicit surfaces using neural networks
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DOI：10.1016/j.jcp.2024.112803.png)
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摘要
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This paper proposes a deep -learning -based method for recovering a signed distance function (SDF) of a given hypersurface represented by an implicit level set function. Using the flexibility of constructing a neural network, we use an augmented network by defining an auxiliary output to represent the gradient of the SDF. There are three advantages of the augmented network; (i) the target interface is accurately captured, (ii) the gradient has a unit norm, and (iii) two outputs are approximated by a single network. Moreover, unlike a conventional loss term which uses a residual of the eikonal equation, a novel training objective consisting of three loss terms is designed. The first loss function enforces a pointwise matching between two outputs of the augmented network. The second loss function leveraged by a geometric characteristic of the SDF imposes the shortest path obtained by the gradient. The third loss function regularizes a singularity of the SDF caused by discontinuities of the gradient. Numerical results across a wide range of complex and irregular interfaces in two and three-dimensional domains confirm the effectiveness and accuracy of the proposed method. We also compare the results of the proposed method with physics -informed neural networks approaches and the fast marching method.
Keyword:
Signed distance function
Level set function
Reinitialization
Deep learning
Eikonal equation
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期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
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