# Learning Embedding of 3D models with Quadric Loss

arXiv: https://arxiv.org/abs/1907.10250 · HTML: https://mlsanity.com/paper/1907.10250/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 4 of 4)

- [PvDeConv: Point-Voxel Deconvolution for Autoencoding CAD Construction in 3D](https://mlsanity.com/paper/2101.04493/) (2021)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [Im2Mesh GAN: Accurate 3D Hand Mesh Recovery from a Single RGB Image](https://mlsanity.com/paper/2101.11239/) (2021)
- [Automatic Reverse Engineering: Creating computer-aided design (CAD) models from multi-view images](https://mlsanity.com/paper/2309.13281/) (2023)

## Abstract (arXiv)

Sharp features such as edges and corners play an important role in the perception of 3D models. In order to capture them better, we propose quadric loss, a point-surface loss function, which minimizes the quadric error between the reconstructed points and the input surface. Computation of Quadric loss is easy, efficient since the quadric matrices can be computed apriori, and is fully differentiable, making quadric loss suitable for training point and mesh based architectures. Through extensive experiments we show the merits and demerits of quadric loss. When combined with Chamfer loss, quadric loss achieves better reconstruction results as compared to any one of them or other point-surface loss functions.