Neural Geometry Image-Based Representations with Optimal Transport (OT)

• URL: http://arxiv.org/abs/2511.18679v1
• Date: Mon, 24 Nov 2025 01:43:19 GMT
• Title: Neural Geometry Image-Based Representations with Optimal Transport (OT)
• Authors: Xiang Gao, Yuanpeng Liu, Xinmu Wang, Jiazhi Li, Minghao Guo, Yu Guo, Xiyun Song, Heather Yu, Zhiqiang Lao, Xianfeng David Gu,
• Abstract summary: We introduce our neural geometry image-based representation, which is decoder-free, storage-efficient, and naturally suited for neural processing.<n> Experimental results demonstrate state-of-the-art storage efficiency and restoration accuracy, measured by compression ratio (CR), Chamfer distance (CD), and Hausdorff distance (HD)
• Score: 18.327691985523476
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural representations for 3D meshes are emerging as an effective solution for compact storage and efficient processing. Existing methods often rely on neural overfitting, where a coarse mesh is stored and progressively refined through multiple decoder networks. While this can restore high-quality surfaces, it is computationally expensive due to successive decoding passes and the irregular structure of mesh data. In contrast, images have a regular structure that enables powerful super-resolution and restoration frameworks, but applying these advantages to meshes is difficult because their irregular connectivity demands complex encoder-decoder architectures. Our key insight is that a geometry image-based representation transforms irregular meshes into a regular image grid, making efficient image-based neural processing directly applicable. Building on this idea, we introduce our neural geometry image-based representation, which is decoder-free, storage-efficient, and naturally suited for neural processing. It stores a low-resolution geometry-image mipmap of the surface, from which high-quality meshes are restored in a single forward pass. To construct geometry images, we leverage Optimal Transport (OT), which resolves oversampling in flat regions and undersampling in feature-rich regions, and enables continuous levels of detail (LoD) through geometry-image mipmapping. Experimental results demonstrate state-of-the-art storage efficiency and restoration accuracy, measured by compression ratio (CR), Chamfer distance (CD), and Hausdorff distance (HD).

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