Type of Publication

Others

Date:

11 /

2022

Status

Published

DOI:

10.1016/j.cag.2022.09.003

Exploring differential geometry in neural implicits

Featured in:

Computers & Graphics

Authors:

Tiago Novello, Guilherme Schardong, Luiz Schirmer, Vinícius da Silva, Hélio Lopes and Luiz Velho

Abstract

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions.To train a neural implicit function, we propose a loss functional that approximates a signed distance function, and allows terms with high-order derivatives, such as the alignment between the principal directions of curvature, to learn more geometric details. During training, we consider a non-uniform sampling strategy based on the curvatures of the point-sampled surface to prioritize points with more geometric details. This sampling implies faster learning while preserving geometric accuracy when compared with previous approaches.We also use the analytical derivatives of a neural implicit function to estimate the differential measures of the underlying point-sampled surface.

Citation
Tiago Novello, Guilherme Schardong, Luiz Schirmer, Vinícius da Silva, Hélio Lopes and Luiz Velho (2022). Exploring differential geometry in neural implicits. Computers & Graphics, 108, 49-60.

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