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

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2023-14

January 25, 2023

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2023/EECS-2023-14.pdf

In this paper we present a powerful differentiable surface fitting technique to derive a compact surface representation for a given dense point cloud or mesh, with application in the domains of graphics and CAD/CAM. We have chosen the Loop subdivision surface, which in the limit yields the smooth surface underlying the point cloud, and can handle complex surface topology better than other popular compact representations, such as NURBS. The principal idea is to fit the Loop subdivision surface not directly to the point cloud, but to the IMLS (implicit moving least squares) surface defined over the point cloud. As both Loop subdivision and IMLS have analytical expressions, we are able to formulate the problem as an unconstrained minimization problem of a completely differentiable function that can be solved with standard numerical solvers. Differentiability enables us to integrate the subdivision surface into any deep learning method for point clouds or meshes. We demonstrate the versatility and potential of this approach by using it in conjunction with a differentiable renderer to robustly reconstruct compact surface representations of spatial-temporal sequences of dense meshes.

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BibTeX citation:

@techreport{Xie:EECS-2023-14,
    Author= {Xie, Tianhao and Barsky, Brian A. and Mudur, Sudhir and Popa, Tiberiu},
    Title= {Differentiable Subdivision Surface Fitting},
    Year= {2023},
    Month= {Jan},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2023/EECS-2023-14.html},
    Number= {UCB/EECS-2023-14},
    Abstract= {In this paper we present a powerful differentiable surface fitting technique
to derive a compact surface representation for a given dense
point cloud or mesh, with application in the domains of graphics and
CAD/CAM. We have chosen the Loop subdivision surface, which
in the limit yields the smooth surface underlying the point cloud,
and can handle complex surface topology better than other popular
compact representations, such as NURBS. The principal idea is to
fit the Loop subdivision surface not directly to the point cloud, but
to the IMLS (implicit moving least squares) surface defined over the
point cloud. As both Loop subdivision and IMLS have analytical expressions,
we are able to formulate the problem as an unconstrained
minimization problem of a completely differentiable function that
can be solved with standard numerical solvers. Differentiability
enables us to integrate the subdivision surface into any deep learning
method for point clouds or meshes. We demonstrate the versatility
and potential of this approach by using it in conjunction with
a differentiable renderer to robustly reconstruct compact surface
representations of spatial-temporal sequences of dense meshes.},
}

EndNote citation:

%0 Report
%A Xie, Tianhao 
%A Barsky, Brian A. 
%A Mudur, Sudhir 
%A Popa, Tiberiu 
%T Differentiable Subdivision Surface Fitting
%I EECS Department, University of California, Berkeley
%D 2023
%8 January 25
%@ UCB/EECS-2023-14
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2023/EECS-2023-14.html
%F Xie:EECS-2023-14