Neural Implicit Surface Evolution

• URL: http://arxiv.org/abs/2201.09636v4
• Date: Mon, 21 Aug 2023 02:55:53 GMT
• Title: Neural Implicit Surface Evolution
• Authors: Tiago Novello, Vinicius da Silva, Guilherme Schardong, Luiz Schirmer, Helio Lopes, Luiz Velho
• Abstract summary: This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE) It extends the representation of implicit surfaces to the space-time $mathbbR3times mathbbR$, which opens up mechanisms for continuous transformations.
• Score: 0.8505099974703285
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time $\mathbb{R}^3\times \mathbb{R}$, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually $\mathbb{R}^3 \times \{0\}$. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

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