Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks

Jiabao Lei, Kui Jia
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5789-5798, 2020.

Abstract

This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from the learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and faces that are associated with zero-level isosurface of the implicit function, and characterize the conditions under which the identified faces are guaranteed to connect and form a closed, piecewise planar surface. We propose a naturally parallelizable algorithm of analytic marching to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-lei20a, title = {Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks}, author = {Lei, Jiabao and Jia, Kui}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5789--5798}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/lei20a/lei20a.pdf}, url = {https://proceedings.mlr.press/v119/lei20a.html}, abstract = {This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from the learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and faces that are associated with zero-level isosurface of the implicit function, and characterize the conditions under which the identified faces are guaranteed to connect and form a closed, piecewise planar surface. We propose a naturally parallelizable algorithm of analytic marching to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones.} }
Endnote
%0 Conference Paper %T Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks %A Jiabao Lei %A Kui Jia %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-lei20a %I PMLR %P 5789--5798 %U https://proceedings.mlr.press/v119/lei20a.html %V 119 %X This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from the learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and faces that are associated with zero-level isosurface of the implicit function, and characterize the conditions under which the identified faces are guaranteed to connect and form a closed, piecewise planar surface. We propose a naturally parallelizable algorithm of analytic marching to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones.
APA
Lei, J. & Jia, K.. (2020). Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5789-5798 Available from https://proceedings.mlr.press/v119/lei20a.html.

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