# OperatorNet: Recovering 3D Shapes From Difference Operators

arXiv: https://arxiv.org/abs/1904.10754 · HTML: https://mlsanity.com/paper/1904.10754/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 5 of 5)

- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Training or Architecture? How to Incorporate Invariance in Neural Networks](https://mlsanity.com/paper/2106.10044/) (2021)
- [Disentangling Geometric Deformation Spaces in Generative Latent Shape Models](https://mlsanity.com/paper/2103.00142/) (2021)
- [A Simple Strategy to Provable Invariance via Orbit Mapping](https://mlsanity.com/paper/2209.11916/) (2022)
- [DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domain](https://mlsanity.com/paper/2406.03017/) (2024)

## Abstract (arXiv)

This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input a set of linear operators representing a shape and produces its 3D embedding. We demonstrate that this approach significantly outperforms previous purely geometric methods for the same problem. Furthermore, we introduce a novel functional operator, which encodes the extrinsic or pose-dependent shape information, and thus complements purely intrinsic pose-oblivious operators, such as the classical Laplacian. Coupled with this novel operator, our reconstruction network achieves very high reconstruction accuracy, even in the presence of incomplete information about a shape, given a soft or functional map expressed in a reduced basis. Finally, we demonstrate that the multiplicative functional algebra enjoyed by these operators can be used to synthesize entirely new unseen shapes, in the context of shape interpolation and shape analogy applications.