FlexPara: Flexible Neural Surface Parameterization

TL;DR

FlexPara presents an unsupervised neural framework for global free-boundary and multi-chart surface parameterization. It unifies bi-directional cycle mappings with deforming, wrapping, cutting, and unwrapping sub-networks to learn both optimal seams and 2D UV layouts without ground-truth UV maps, while enforcing distortion control via differential and triangle-based losses. Extending to multi-chart parameterization, it introduces a differentiable chart-assignment module and per-chart cycle mappings with chart-weighted losses to achieve low distortion with a controllable number of charts. The approach delivers state-of-the-art results on challenging, high-genus models and real-world scans, supports scalable texture mapping, and offers practical benefits for downstream geometry processing tasks and 3D asset pipelines.

Abstract

Surface parameterization is a fundamental geometry processing task, laying the foundations for the visual presentation of 3D assets and numerous downstream shape analysis scenarios. Conventional parameterization approaches demand high-quality mesh triangulation and are restricted to certain simple topologies unless additional surface cutting and decomposition are provided. In practice, the optimal configurations (e.g., type of parameterization domains, distribution of cutting seams, number of mapping charts) may vary drastically with different surface structures and task characteristics, thus requiring more flexible and controllable processing pipelines. To this end, this paper introduces FlexPara, an unsupervised neural optimization framework to achieve both global and multi-chart surface parameterizations by establishing point-wise mappings between 3D surface points and adaptively-deformed 2D UV coordinates. We ingeniously design and combine a series of geometrically-interpretable sub-networks, with specific functionalities of cutting, deforming, unwrapping, and wrapping, to construct a bi-directional cycle mapping framework for global parameterization without the need for manually specified cutting seams. Furthermore, we construct a multi-chart parameterization framework with adaptively-learned chart assignment. Extensive experiments demonstrate the universality, superiority, and inspiring potential of our neural surface parameterization paradigm. The code will be publicly available at https://github.com/AidenZhao/FlexPara

Figures (17)

• Figure 1: Examples of global and multi-chart parameterizations achieved by our methods using grid-checkerboard texture mapping to visualize parametric distortion. We illustrate global parameterization on the Stanford Bunny, Bear and a twisted knot model. For multi-chart parameterization, we present results on a polycube model with sharp features, a bird model exhibiting symmetry and thin structures, and a spherical gyroid model with high genus. Note that our multi-chart parameterization effectively preserves sharp features and global symmetry, and robustly handles models with intricate topologies. The grid-checkerboard texture highlights low angular and area distortions achieved by both our global and multi-chart parameterization algorithms.
• Figure 2: Illustration of bi-directional cycle mapping for global neural surface parameterization, composed of (a) 2D$\rightarrow$3D$\rightarrow$2D cycle mapping branch, and (b) 3D$\rightarrow$2D$\rightarrow$3D cycle mapping branch. Modules with the same color share network parameters. (c) shows the learned cutting seams. (d) shows the grid-checkboard image texture mapping.
• Figure 3: Illustration of multi-chart neural surface parameterization framework, composed of fusion module, chart-assignment module, and multi single directional cycle mapping branches (Unwrap-Net and Wrap-Net). The lower left shows the grid-checkerboard image texture mapping. The right shows an example of a chart assignment result and UV mappings.
• Figure 4: A gallery for our global parameterization results, utilizing a grid-checkboard image to illustrate the parameterization deformation. Standard models (with the red-blue gradient grid-checkerboard image) and complex topology models (with the blue grid-checkerboard image) are demonstrated.
• Figure 5: A gallery for our multi-chart parameterization results. It shows segmentation results for configurations utilizing 2, 4, and 8 charts (from left to right).