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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