4.5 Article

Exploring differential geometry in neural implicits

Journal

COMPUTERS & GRAPHICS-UK
Volume 108, Issue -, Pages 49-60

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.cag.2022.09.003

Keywords

Implicit surfaces; Neural Implicits; Neural Networks; Curvatures

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This paper introduces a method that utilizes neural networks and discrete geometry of point-sampled surfaces to approximate surfaces. By training neural implicit functions, more geometric details can be learned, and a non-uniform sampling strategy is used for faster learning.
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. (C) 2022 Elsevier Ltd. All rights reserved.

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