  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 paper, 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
data set and showing flexible adaptation to a particular shape instance.
