We present a novel approach for completing and reconstructing 3D shapes from incomplete scanned data by using deep neural networks. Rather than being trained on supervised completion tasks and applied on a testing shape, the network is optimized from scratch on the single testing shape to fully adapt to the shape and complete the missing data using contextual guidance from the known regions. The ability to complete missing data by an untrained neural network is usually referred to as the deep prior . In this article, we interpret the deep prior from a neural tangent kernel (NTK) perspective and show that the completed shape patches by the trained CNN are naturally similar to existing patches, as they are proximate in the kernel feature space induced by NTK. The interpretation allows us to design more efficient network structures and learning mechanisms for the shape completion and reconstruction task. Being more aware of structural regularities than both traditional and other unsupervised learning-based reconstruction methods, our approach completes large missing regions with plausible shapes and complements supervised learning-based methods that use database priors by requiring no extra training dataset and showing flexible adaptation to a particular shape instance.

中文翻译：

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神经切线内核透视中通过深度先验的无监督形状完成

我们提出了一种使用深度神经网络从不完整的扫描数据中完成和重建 3D 形状的新方法。网络不是在监督完成任务上进行训练并应用于测试形状，而是在单个测试形状上从头开始优化，以完全适应形状并使用来自已知区域的上下文指导来完成缺失的数据。通过未经训练的神经网络完成缺失数据的能力通常被称为深度先验. 在本文中，我们从神经切线核 (NTK) 的角度解释了深度先验，并表明经过训练的 CNN 完成的形状补丁自然类似于现有的补丁，因为它们接近由 NTK 诱导的内核特征空间。这种解释使我们能够为形状完成和重建任务设计更有效的网络结构和学习机制。与传统的和其他基于无监督学习的重建方法相比，我们的方法更了解结构规律，以合理的形状完成大的缺失区域，并通过不需要额外的训练数据集并显示灵活适应于使用数据库先验的基于监督学习的方法来补充特定的形状实例。