论文标题
深层的先验
Deep Manifold Prior
论文作者
论文摘要
我们提出了歧管结构化数据的先验，例如3D形状的表面，其中采用了深层神经网络来使用从随机初始化开始的梯度下降来重建目标形状。我们表明，以这种方式生成的表面是平滑的，其限制行为以高斯过程为特征，并且我们在数学上得出了完全连接和卷积网络的此类属性。我们在各种歧管重建应用中演示了我们的方法，例如点云降解和插值，在不需要培训数据的同时，对竞争基线取得了更好的结果。我们还表明，当训练数据可用时，我们的方法允许在Atlasnet框架下开发表面的替代参数化，从而导致紧凑的网络体系结构，并在标准图像上更好地重建结果，以形成重建基准。
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.
