A Generalized Differentiable Evaluation Plug-in for Loop Subdivision in Surface Reconstruction Pipelines

Tianhao Xie, Brian A. Barsky, Sudhir Mudur and Tiberiu Popa

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2024-180
August 15, 2024

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2024/EECS-2024-180.pdf

Continuity in surface representations is extremely important for many design, analysis, simulation and visualization tasks in aero, hydro, automotive and graphics industries. While piecewise continuous NURBS have been ubiquitous, handling topologically complex surfaces can be cumbersome. Hence, linear piecewise polygonal/triangular meshes have been increasingly dominant. Today, these are reconstructed by suitably trained deep learning networks usually from multi-view images or point clouds, however, these meshes are not smooth along the edges and at vertices. In this paper, we present a powerful differentiable surface fitting method which can be integrated into surface reconstruction pipelines. We use the Loop subdivision surface, which in the limit yields the smooth surface underlying the point cloud, and can also handle complex surface topology. The principal idea is to stage the Loop subdivision scheme such that it enables generalized analytical evaluation on any triangulation, i.e., without any constraints on vertex valences. Importantly, this in turn enables us to formulate the subdivision process as an unconstrained minimization problem of a differentiable function which can be solved with standard numerical solvers. The other contribution is the use of the Implicit Moving Least Squares (IMLS) surface fitting as an energy loss to add shape-awareness to the commonly used Chamfer loss for improving output quality. We demonstrate our plug-in in multiple contexts such as smooth surface reconstruction from the point cloud using classical Poisson reconstruction, or in an end-to-end deep neural network pipeline such as deep marching tetrahedra. We further apply our method to spatial-temporal reconstruction through a differentiable renderer. We have both a CPU as well as a fast GPU implementation of our technique that can be easily plugged into any deep-learning pipeline for point clouds or meshes. The code will be made publicly available.

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BibTeX citation:

@techreport{Xie:EECS-2024-180,
    Author = {Xie, Tianhao and Barsky, Brian A. and Mudur, Sudhir and Popa, Tiberiu},
    Title = {A Generalized Differentiable Evaluation Plug-in for Loop Subdivision in Surface Reconstruction Pipelines},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2024},
    Month = {Aug},
    URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2024/EECS-2024-180.html},
    Number = {UCB/EECS-2024-180},
    Abstract = {Continuity in surface representations is extremely important for many design, analysis, simulation and visualization tasks in aero, hydro, automotive and graphics industries. While piecewise continuous NURBS have been ubiquitous, handling topologically complex surfaces can be cumbersome. Hence, linear piecewise polygonal/triangular meshes have been increasingly dominant. Today, these are reconstructed by suitably trained deep learning networks usually from multi-view images or point clouds, however, these meshes are not smooth along the edges and at vertices. In this paper, we present a powerful differentiable surface fitting method which can be integrated into surface reconstruction pipelines. We use the Loop subdivision surface, which in the limit yields the smooth surface underlying the point cloud, and can also handle complex surface topology. The principal idea is to stage the Loop subdivision scheme such that it enables generalized analytical evaluation on any triangulation, i.e., without any constraints on vertex valences. Importantly, this in turn enables us to formulate the subdivision process as an unconstrained minimization problem of a differentiable function which can be solved with standard numerical solvers. The other contribution is the use of the Implicit Moving Least Squares (IMLS) surface fitting as an energy loss to add shape-awareness to the commonly used Chamfer loss for improving output quality. We demonstrate our plug-in in multiple contexts such as smooth surface reconstruction from the point cloud using classical Poisson reconstruction, or in an end-to-end deep neural network pipeline such as deep marching tetrahedra. We further apply our method to spatial-temporal reconstruction through a differentiable renderer. We have both a CPU as well as a fast GPU implementation of our technique that can be easily plugged into any deep-learning pipeline for point clouds or meshes. The code will be made publicly available.}
}

EndNote citation:

%0 Report
%A Xie, Tianhao
%A Barsky, Brian A.
%A Mudur, Sudhir
%A Popa, Tiberiu
%T A Generalized Differentiable Evaluation Plug-in for Loop Subdivision in Surface Reconstruction Pipelines
%I EECS Department, University of California, Berkeley
%D 2024
%8 August 15
%@ UCB/EECS-2024-180
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2024/EECS-2024-180.html
%F Xie:EECS-2024-180