GM-R^2：面向无监督几何表征与配准的生成式匹配学习
GM-R^2: Generative Matching Learning for Unsupervised Geometric Representation and Registration
把描述子学习重构成以深度图为条件的跨视角生成任务，用视图合成的代理监督隐式约束对应点特征一致性；其去噪无关的耦合 ControlNet 与可缩放等距柱状投影（无需内参的点云转深度）可直接用于无监督 3D 配准与点云到深度图的稠密投影。
原文依据 reformulating descriptor learning as geometry-conditioned cross-view image generation
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论本文提出 GM-R^2，一种用于无监督几何描述子学习与对应匹配的新型生成式匹配学习框架。通过将描述子学习重构为以几何为条件的跨视角图像生成，GM-R^2 利用结构对齐的视图合成所提供的代理监督信号，隐式地强制对应关系上的特征一致性，从而实现稳健的三维匹配。为具体实现 GM-R^2，我们引入以深度图为条件的去噪无关耦合 ControlNet，作为所需的几何条件跨视角生成器。它通过耦合深度图输入设计，有效地将朴素 ControlNet 的单视角生成扩展到跨视角，并进一步去除对潜变量噪声的依赖，以支持仅依赖几何的推理（这正是三维匹配所期望的）。此外，我们提出可缩放等距柱状投影，用于无需内参的点云到深度映射，该投影自适应地缩放到窄视场输入所占据的角度区域，以获取稠密距离图。在 3DMatch 和 ScanNet 数据集上的大量实验验证了 GM-R^2 的优越精度，甚至超越了有监督方法。
英文原文摘要 1165 字符
This paper proposes GM-R^2, a novel Generative Matching Learning framework for unsupervised geometric descriptor learning and correspondence matching. By reformulating descriptor learning as geometry-conditioned cross-view image generation, GM-R^2 leverages the proxy supervisory signal from structurally aligned view synthesis to implicitly enforce feature consistency across correspondence, enabling robust 3D matching. To instantiate GM-R^2, we introduce Denoising-Agnostic Coupled ControlNet conditioned on depth maps as the required geometry-conditioned cross-view generator. It effectively extends the single-view generation of naive ControlNet to the cross-view via coupled depth-map input design and further remove the latent noise dependency to support geometry-only inference (expected by 3D matching). Moreover, we present Zoomable Equirectangular Projection for intrinsics-free point cloud-to-depth mapping that adaptively zooms into the angular region occupies by the narrow-FOV input for dense range-map acquisition. Extensive experiments on 3DMatch and ScanNet datasets verify the superior precision of our GM-R^2, even surpassing supervised methods.