# RANSIC: Fast and Highly Robust Estimation for Rotation Search and Point Cloud Registration using Invariant Compatibility

arXiv: https://arxiv.org/abs/2104.09133 · HTML: https://mlsanity.com/paper/2104.09133/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 9 of 9)

- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates](https://mlsanity.com/paper/1903.08588/) (2019)
- [ROBIN: a Graph-Theoretic Approach to Reject Outliers in Robust Estimation using Invariants](https://mlsanity.com/paper/2011.03659/) (2020)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications](https://mlsanity.com/paper/2007.15109/) (2020)
- [IRON: Invariant-based Highly Robust Point Cloud Registration](https://mlsanity.com/paper/2103.04357/) (2021)

## Built on by (most cited first, 16 of 16)

- [A Single Correspondence Is Enough: Robust Global Registration to Avoid Degeneracy in Urban Environments](https://mlsanity.com/paper/2203.06612/) (2022)
- [FastMAC: Stochastic Spectral Sampling of Correspondence Graph](https://mlsanity.com/paper/2403.08770/) (2024)
- [KISS-Matcher: Fast and Robust Point Cloud Registration Revisited](https://mlsanity.com/paper/2409.15615/) (2024)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [TriVoC: Efficient Voting-based Consensus Maximization for Robust Point Cloud Registration with Extreme Outlier Ratios](https://mlsanity.com/paper/2111.00657/) (2021)
- [DANIEL: A Fast and Robust Consensus Maximization Method for Point Cloud Registration with High Outlier Ratios](https://mlsanity.com/paper/2110.05075/) (2021)
- [Efficient and Deterministic Search Strategy Based on Residual Projections for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/2305.11716/) (2023)
- [Robust Self-Tuning Data Association for Geo-Referencing Using Lane Markings](https://mlsanity.com/paper/2207.14042/) (2022)
- [PCR-99: A Practical Method for Point Cloud Registration with 99 Percent Outliers](https://mlsanity.com/paper/2402.16598/) (2024)
- [Fast globally optimal Truncated Least Squares point cloud registration with fixed rotation axis](https://mlsanity.com/paper/2508.15613/) (2025)
- [Correspondence-Free Fast and Robust Spherical Point Pattern Registration](https://mlsanity.com/paper/2508.02339/) (2025)
- [ICOS: Efficient and Highly Robust Rotation Search and Point Cloud Registration with Correspondences](https://mlsanity.com/paper/2104.14763/) (2021)
- [Outlier-Robust Geometric Perception: A Novel Thresholding-Based Estimator with Intra-Class Variance Maximization](https://mlsanity.com/paper/2204.01324/) (2022)
- [Point Cloud Registration via Probabilistic Self-Update Local Correspondence and Line Vector Sets](https://mlsanity.com/paper/2604.26318/) (2026)
- [DiffSAC: Diffusion-guided Sampling for Consensus-based Robust Estimation](https://mlsanity.com/paper/2608.30603/) (2026)
- [PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration](https://mlsanity.com/paper/2609.25375/) (2026)

## Abstract (arXiv)

Correspondence-based rotation search and point cloud registration are two fundamental problems in robotics and computer vision. However, the presence of outliers, sometimes even occupying the great majority of the putative correspondences, can make many existing algorithms either fail or have very high computational cost. In this paper, we present RANSIC (RANdom Sampling with Invariant Compatibility), a fast and highly robust method applicable to both problems based on a new paradigm combining random sampling with invariance and compatibility. Generally, RANSIC starts with randomly selecting small subsets from the correspondence set, then seeks potential inliers as graph vertices from the random subsets through the compatibility tests of invariants established in each problem, and eventually returns the eligible inliers when there exists at least one K-degree vertex (K is automatically updated depending on the problem) and the residual errors satisfy a certain termination condition at the same time. In multiple synthetic and real experiments, we demonstrate that RANSIC is fast for use, robust against over 95% outliers, and also able to recall approximately 100% inliers, outperforming other state-of-the-art solvers for both the rotation search and the point cloud registration problems.