发表机构
University of Milano-Bicocca; Politecnico di Milano; University of Bonn; Pegaso University（米兰比可卡大学; 米兰理工大学; 波恩大学; 佩加索大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种几何感知的基元分解框架，通过图割优化的内点精化步骤整合法线一致性等几何先验，提升超二次曲面分解的精度与鲁棒性，在合成和真实数据上优于基于RANSAC的方法。
AI 中文摘要
将三维点云分解为可解释的几何基元，一直是计算机视觉和计算机图形学中的一个长期挑战。在现有的表示方法中，超二次曲面提供了一种紧凑且富有表现力的模型，能够捕捉多种形状。然而，其估计本身具有挑战性，因为这需要求解一个非线性优化问题，并且对噪声、离群点和重叠结构特别敏感。尽管诸如RANSAC及其变体等鲁棒估计方法取得了强劲性能，但它们主要依赖于空间邻近性和基于残差的标准，这常常导致在相邻或复杂排列的基元之间产生错误的内点分配。在本工作中，我们引入了一个几何感知的基元分解框架，该框架明确地将局部表面属性纳入拟合过程。具体来说，我们提出了一个内点精化步骤，将其表述为一个能量最小化问题，并通过图割优化求解。我们的公式整合了几何先验，如法线一致性，从而能够实现比纯粹基于残差的标准更可靠的内点选择。该方法自然适用于单模型估计和多模型分解。通过利用点级残差之外的几何信息，我们的方法减少了错误内点的传播，并稳定了参数估计。在合成和真实数据集上的实验表明，与最先进的基于RANSAC的方法相比，我们在几何精度、对噪声和离群点的鲁棒性以及收敛效率方面均取得了一致的改进。
英文摘要
The decomposition of 3D point clouds into interpretable geometric primitives remains a longstanding challenge in Computer Vision and Computer Graphics. Among the available representations, superquadrics offer a compact and expressive model capable of capturing a wide range of shapes. However, their estimation is inherently challenging, as it requires solving a non-linear optimization problem and is particularly sensitive to noise, outliers, and overlapping structures. While robust estimation methods such as RANSAC and its variants achieve strong performance, they rely primarily on spatial proximity and residual-based criteria, often leading to incorrect inlier assignments across adjacent or complex arrangements of primitives. In this work, we introduce a geometric-aware framework for primitive decomposition that explicitly incorporates local surface properties into the fitting process. Specifically, we propose an inlier refinement step formulated as an energy minimization problem and solved via graph-cut optimization. Our formulation integrates geometric priors, such as normal consistency, enabling more reliable inlier selection beyond purely residual-based criteria. The approach naturally applies to both single-model estimation and multi-model decomposition. By leveraging geometric information beyond point-wise residuals, our method reduces erroneous inlier propagation and stabilizes parameter estimation. Experiments on synthetic and real datasets show consistent improvements in geometric accuracy, robustness to noise and outliers, and convergence efficiency compared to state-of-the-art RANSAC-based methods.
Comments19 pages, 11 figures, under review
