# Discrete-Continuous Smoothing and Mapping

arXiv: https://arxiv.org/abs/2204.11936 · HTML: https://mlsanity.com/paper/2204.11936/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 56 references that are in the map.
- First posted on arXiv 25 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [Modeling Perceptual Aliasing in SLAM via Discrete-Continuous Graphical Models](https://mlsanity.com/paper/1810.11692/) (2018)
- [Probabilistic Data Association via Mixture Models for Robust Semantic SLAM](https://mlsanity.com/paper/1909.11213/) (2019)
- [Advances in Inference and Representation for Simultaneous Localization and Mapping](https://mlsanity.com/paper/2103.05041/) (2021)
- [Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees](https://mlsanity.com/paper/1903.11683/) (2019)
- [Discrete graphical models -- an optimization perspective](https://mlsanity.com/paper/2001.09017/) (2020)
- [Advancing Mixture Models for Least Squares Optimization](https://mlsanity.com/paper/2103.02472/) (2021)
- [NF-iSAM: Incremental Smoothing and Mapping via Normalizing Flows](https://mlsanity.com/paper/2105.05045/) (2021)
- [Consensus-Informed Optimization Over Mixtures for Ambiguity-Aware Object SLAM](https://mlsanity.com/paper/2107.09265/) (2021)
- [iMHS: An Incremental Multi-Hypothesis Smoother](https://mlsanity.com/paper/2103.13178/) (2021)

## Built on by (most cited first, 3 of 3)

- [Zero-shot Object-Centric Instruction Following: Integrating Foundation Models with Traditional Navigation](https://mlsanity.com/paper/2411.07848/) (2024)
- [LOSS-SLAM: Lightweight Open-Set Semantic Simultaneous Localization and Mapping](https://mlsanity.com/paper/2404.04377/) (2024)
- [Semantic Semi-Incremental Data-Association-Free Object SLAM](https://mlsanity.com/paper/2607.23384/) (2026)

## Abstract (arXiv)

We describe a general approach for maximum a posteriori (MAP) inference in a class of discrete-continuous factor graphs commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use interfaces for specifying and solving inference problems formulated in terms of either discrete or continuous graphical models, at present, no similarly general tools exist enabling the same functionality for hybrid discrete-continuous problems. We aim to address this problem. In particular, we provide a library, DC-SAM, extending existing tools for inference problems defined in terms of factor graphs to the setting of discrete-continuous models. A key contribution of our work is a novel solver for efficiently recovering approximate solutions to discrete-continuous inference problems. The key insight to our approach is that while joint inference over continuous and discrete state spaces is often hard, many commonly encountered discrete-continuous problems can naturally be split into a "discrete part" and a "continuous part" that can individually be solved easily. Leveraging this structure, we optimize discrete and continuous variables in an alternating fashion. In consequence, our proposed work enables straightforward representation of and approximate inference in discrete-continuous graphical models. We also provide a method to approximate the uncertainty in estimates of both discrete and continuous variables. We demonstrate the versatility of our approach through its application to distinct robot perception applications, including robust pose graph optimization, and object-based mapping and localization.