# Deterministic consensus maximization with biconvex programming

arXiv: https://arxiv.org/abs/1807.09436 · HTML: https://mlsanity.com/paper/1807.09436/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2018.

## Built on by (most cited first, 8 of 8)

- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Robust Fitting on a Gate Quantum Computer](https://mlsanity.com/paper/2409.02006/) (2024)
- [Unsupervised Learning for Robust Fitting:A Reinforcement Learning Approach](https://mlsanity.com/paper/2103.03501/) (2021)
- [Consensus Maximisation Using Influences of Monotone Boolean Functions](https://mlsanity.com/paper/2103.04200/) (2021)
- [DS-SAC: Density Search for Sample Consensus](https://mlsanity.com/paper/2607.03972/) (2026)
- [Cross-View Feature Matching: Survey, Benchmarking, and Foundation-Model Perspectives](https://mlsanity.com/paper/2608.11093/) (2026)

## Abstract (arXiv)

Consensus maximization is one of the most widely used robust fitting paradigms in computer vision, and the development of algorithms for consensus maximization is an active research topic. In this paper, we propose an efficient deterministic optimization algorithm for consensus maximization. Given an initial solution, our method conducts a deterministic search that forcibly increases the consensus of the initial solution. We show how each iteration of the update can be formulated as an instance of biconvex programming, which we solve efficiently using a novel biconvex optimization algorithm. In contrast to our algorithm, previous consensus improvement techniques rely on random sampling or relaxations of the objective function, which reduce their ability to significantly improve the initial consensus. In fact, on challenging instances, the previous techniques may even return a worse off solution. Comprehensive experiments show that our algorithm can consistently and greatly improve the quality of the initial solution, without substantial cost.