Higher-Order Function Networks for Learning Composable 3D Object Representations

Abstract

We present a new approach to 3D object representation where a neural network encodes the geometry of an object directly into the weights and biases of a second 'mapping' network. This mapping network can be used to reconstruct an object by applying its encoded transformation to points randomly sampled from a simple geometric space, such as the unit sphere. We study the effectiveness of our method through various experiments on subsets of the ShapeNet dataset. We find that the proposed approach can reconstruct encoded objects with accuracy equal to or exceeding state-of-the-art methods with orders of magnitude fewer parameters. Our smallest mapping network has only about 7000 parameters and shows reconstruction quality on par with state-of-the-art object decoder architectures with millions of parameters. Further experiments on feature mixing through the composition of learned functions show that the encoding captures a meaningful subspace of objects.

To be published in International Conference on Learning Representations (ICLR 2020) [https://openreview.net/forum?id=HJgfDREKDB]; 19 pages

References in corpus (8)

• Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks
• MeshCNN: A Network with an Edge
• Learning Representations and Generative Models for 3D Point Clouds
• Perspective Transformer Nets: Learning Single-View 3D Object Reconstruction without 3D Supervision
• Learning Efficient Point Cloud Generation for Dense 3D Object Reconstruction
• Learning to Reconstruct Shapes from Unseen Classes
• Deep Level Sets: Implicit Surface Representations for 3D Shape Inference
• GEOMetrics: Exploiting Geometric Structure for Graph-Encoded Objects

Cited by in corpus (4)

• Ladybird: Quasi-Monte Carlo Sampling for Deep Implicit Field Based 3D Reconstruction with Symmetry
• Geodesic-HOF: 3D Reconstruction Without Cutting Corners
• Meta Deformation Network: Meta Functionals for Shape Correspondence
• 3D Meta Point Signature: Learning to Learn 3D Point Signature for 3D Dense Shape Correspondence