Developability Approximation for Neural Implicits through Rank
Minimization
- URL: http://arxiv.org/abs/2308.03900v3
- Date: Thu, 2 Nov 2023 07:04:17 GMT
- Title: Developability Approximation for Neural Implicits through Rank
Minimization
- Authors: Pratheba Selvaraju
- Abstract summary: This paper introduces a method for reconstructing an approximate developable surface from a neural implicit surface.
The central idea of our method involves incorporating a regularization term that operates on the second-order derivatives of the neural implicits.
We draw inspiration from the properties of surface curvature and employ rank minimization techniques derived from compressed sensing.
- Score: 0.5439020425819
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Developability refers to the process of creating a surface without any
tearing or shearing from a two-dimensional plane. It finds practical
applications in the fabrication industry. An essential characteristic of a
developable 3D surface is its zero Gaussian curvature, which means that either
one or both of the principal curvatures are zero. This paper introduces a
method for reconstructing an approximate developable surface from a neural
implicit surface. The central idea of our method involves incorporating a
regularization term that operates on the second-order derivatives of the neural
implicits, effectively promoting zero Gaussian curvature. Implicit surfaces
offer the advantage of smoother deformation with infinite resolution,
overcoming the high polygonal constraints of state-of-the-art methods using
discrete representations. We draw inspiration from the properties of surface
curvature and employ rank minimization techniques derived from compressed
sensing. Experimental results on both developable and non-developable surfaces,
including those affected by noise, validate the generalizability of our method.
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