GSO-Net: Grid Surface Optimization via Learning Geometric Constraints

Abstract

In the context of surface representations, we find a natural structural similarity between grid surface and image data. Motivated by this inspiration, we propose a novel approach: encoding grid surfaces as geometric images and using image processing methods to address surface optimization-related problems. As a result, we have created the first dataset for grid surface optimization and devised a learning-based grid surface optimization network specifically tailored to geometric images, addressing the surface optimization problem through a data-driven learning of geometric constraints paradigm. We conduct extensive experiments on developable surface optimization, surface flattening, and surface denoising tasks using the designed network and datasets. The results demonstrate that our proposed method not only addresses the surface optimization problem better than traditional numerical optimization methods, especially for complex surfaces, but also boosts the optimization speed by multiple orders of magnitude. This pioneering study successfully applies deep learning methods to the field of surface optimization and provides a new solution paradigm for similar tasks, which will provide inspiration and guidance for future developments in the field of discrete surface optimization.

Dataset

We construct Bessel surfaces of various shapes by using different number and arrangement of 3D control points and different degrees of Bessel curves, and define different surface features to ensure the rich diversity of surface dataset. Here are some examples of surfaces in the dataset:

Loss function

The expected geometric properties of the surface are transformed into the loss function. We found that deep learning methods allow us to use more straightforward and complex loss functions than traditional numerical optimization methods, for example, we can directly use Gaussian curvature as the loss. While constant convolution kernels are employed to calculate the edges formed by vertices.

Result

Developable Surface Optimization

In the task of developable surface optimization, where (a) is the input model, b is the optimization result of the traditional algorithm, and (c)(d)(e) is the optimization result of the method adopted in this paper. Under the condition of developability, the model corresponding to the method proposed in this paper has smaller deformation and the corresponding heat map color is lighter.

Surface Flatten

In the task of surface flattening, where (a) is the input model, (b) is the initialization result, (c) is the traditional method of comparison, and (d) and (e) are the methods proposed in this paper. As can be seen from the figure, the lighter color of the heatmap of the method proposed in this paper means less error.

Surface Denoise

In the surface denoising task, where (a) is a fairing surface, (a) is the noise surface obtained by adding noise of different intensity to (A), and (B) is the result of denoising (a) by using the method proposed in this paper. It can be seen that our method can filter noise of different intensity well.

BibTeX

@inproceedings{wang2024gso, title={GSO-Net: Grid Surface Optimization via Learning Geometric Constraints}, author={Wang, Chaoyun and Xin, Jingmin and Zheng, Nanning and Jiang, Caigui}, booktitle={Proceedings of the AAAI Conference on Artificial Intelligence}, volume={38}, number={8}, pages={8163--8171}, year={2024} }