Deep Manifold Prior
This provides a novel prior for manifold reconstruction tasks, benefiting fields like computer graphics and 3D vision, though it builds on existing frameworks like AtlasNet.
The paper tackles the problem of reconstructing manifold-structured data like 3D shapes by using deep neural networks as a prior, starting from random initialization without training data, and achieves considerably better results in applications such as point cloud denoising and interpolation compared to competitive baselines.
We present a prior for manifold structured data, such as surfaces of 3D shapes, where deep neural networks are adopted to reconstruct a target shape using gradient descent starting from a random initialization. We show that surfaces generated this way are smooth, with limiting behavior characterized by Gaussian processes, and we mathematically derive such properties for fully-connected as well as convolutional networks. We demonstrate our method in a variety of manifold reconstruction applications, such as point cloud denoising and interpolation, achieving considerably better results against competitive baselines while requiring no training data. We also show that when training data is available, our method allows developing alternate parametrizations of surfaces under the framework of AtlasNet, leading to a compact network architecture and better reconstruction results on standard image to shape reconstruction benchmarks.