Nonparametric Regression for 3D Point Cloud Learning.

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Journal of Machine Learning Research Pub Date : 2024-01-01
Xinyi Li, Shan Yu, Yueying Wang, Guannan Wang, Li Wang, Ming-Jun Lai
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Abstract

In recent years, there has been an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient smoothing tool based on multivariate splines over the triangulation to extract the underlying signal and build up a 3D solid model from the point cloud. The proposed method can denoise or deblur the point cloud effectively, provide a multi-resolution reconstruction of the actual signal, and handle sparse and irregularly distributed point clouds to recover the underlying trajectory. In addition, our method provides a natural way of numerosity data reduction. We establish the theoretical guarantees of the proposed method, including the convergence rate and asymptotic normality of the estimator, and show that the convergence rate achieves optimal nonparametric convergence. We also introduce a bootstrap method to quantify the uncertainty of the estimators. Through extensive simulation studies and a real data example, we demonstrate the superiority of the proposed method over traditional smoothing methods in terms of estimation accuracy and efficiency of data reduction.

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用于 3D 点云学习的非参数回归。
近年来,在各个领域收集到的不规则形状的点云数量呈指数级增长。鉴于实体模型对点云的重要性,我们开发了一种基于三角剖分的多元样条的新型高效平滑工具,以提取底层信号并从点云中建立三维实体模型。所提出的方法能有效地对点云进行去噪或去模糊处理,提供实际信号的多分辨率重建,并能处理稀疏和不规则分布的点云,从而恢复底层轨迹。此外,我们的方法还提供了一种减少数值数据的自然方法。我们建立了所提方法的理论保证,包括估计器的收敛速率和渐近正态性,并证明收敛速率达到了最佳非参数收敛。我们还引入了一种自举方法来量化估计器的不确定性。通过大量的模拟研究和真实数据实例,我们证明了所提出的方法在估计精度和数据缩减效率方面优于传统的平滑方法。
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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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