Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns the noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised fashion. We use the IMLS to regularize the distance values reported by the MLP while using the MLP to regularize the normals of the data points for running the IMLS. We also prove that at the convergence, our neural network, benefiting from the mutual learning mechanism between the MLP and the IMLS, produces a faithful SDF whose zero-level set approximates the underlying surface. We conducted extensive experiments on various benchmarks, including synthetic scans and real scans. The experimental results show that {\em Neural-IMLS} can reconstruct faithful shapes on various benchmarks with noise and missing parts. The source code can be found at~\url{https://github.com/bearprin/Neural-IMLS}.

翻译：曲面重建在输入点云（尤其是真实扫描数据）存在噪声且缺乏法向信息时极具挑战性。针对多层感知器（MLP）与隐式移动最小二乘函数（IMLS）能够提供底层曲面对偶表示这一特性，我们提出Neural-IMLS——一种新型自监督方法，可直接从无定向原始点云中学习抗噪声的有符号距离函数（SDF）。该方法利用IMLS约束MLP输出的距离值，同时借助MLP规范化数据点法向量以支持IMLS运算。我们进一步证明，在收敛状态下，基于MLP与IMLS相互学习机制的神经网络能够生成可靠的SDF，其零水平集可精确逼近底层曲面。我们在包含合成扫描与真实扫描数据的多个基准测试上开展了广泛实验。结果表明，Neural-IMLS在含噪声及缺失部分的各类基准数据上均能重建出精确的曲面形状。源代码详见~\url{https://github.com/bearprin/Neural-IMLS}。