# Smooth Mesh Estimation from Depth Data using Non-Smooth Convex Optimization

arXiv: https://arxiv.org/abs/2108.02957 · HTML: https://mlsanity.com/paper/2108.02957/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 6 Aug 2021.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Kimera: an Open-Source Library for Real-Time Metric-Semantic Localization and Mapping](https://mlsanity.com/paper/1910.02490/) (2019)
- [3D Dynamic Scene Graphs: Actionable Spatial Perception with Places, Objects, and Humans](https://mlsanity.com/paper/2002.06289/) (2020)
- [Kimera: from SLAM to Spatial Perception with 3D Dynamic Scene Graphs](https://mlsanity.com/paper/2101.06894/) (2021)
- [On-Manifold Preintegration for Real-Time Visual-Inertial Odometry](https://mlsanity.com/paper/1512.02363/) (2015)
- [Primal-Dual Mesh Convolutional Neural Networks](https://mlsanity.com/paper/2010.12455/) (2020)
- [Visual-Inertial Monocular SLAM with Map Reuse](https://mlsanity.com/paper/1610.05949/) (2016)
- [SurfelMeshing: Online Surfel-Based Mesh Reconstruction](https://mlsanity.com/paper/1810.00729/) (2018)
- [Incremental Visual-Inertial 3D Mesh Generation with Structural Regularities](https://mlsanity.com/paper/1903.01067/) (2019)
- [VITAMIN-E: VIsual Tracking And MappINg with Extremely Dense Feature Points](https://mlsanity.com/paper/1904.10324/) (2019)
- [OVPC Mesh: 3D Free-space Representation for Local Ground Vehicle Navigation](https://mlsanity.com/paper/1811.10266/) (2018)
- [High-Performance and Tunable Stereo Reconstruction](https://mlsanity.com/paper/1511.00758/) (2015)
- [Mesh Reconstruction from Aerial Images for Outdoor Terrain Mapping Using Joint 2D-3D Learning](https://mlsanity.com/paper/2101.01844/) (2021)

## Built on by (most cited first, 1 of 1)

- [TerrainMesh: Metric-Semantic Terrain Reconstruction from Aerial Images Using Joint 2D-3D Learning](https://mlsanity.com/paper/2204.10993/) (2022)

## Abstract (arXiv)

Meshes are commonly used as 3D maps since they encode the topology of the scene while being lightweight. Unfortunately, 3D meshes are mathematically difficult to handle directly because of their combinatorial and discrete nature. Therefore, most approaches generate 3D meshes of a scene after fusing depth data using volumetric or other representations. Nevertheless, volumetric fusion remains computationally expensive both in terms of speed and memory. In this paper, we leapfrog these intermediate representations and build a 3D mesh directly from a depth map and the sparse landmarks triangulated with visual odometry. To this end, we formulate a non-smooth convex optimization problem that we solve using a primal-dual method. Our approach generates a smooth and accurate 3D mesh that substantially improves the state-of-the-art on direct mesh reconstruction while running in real-time.