# A Novel Method for the Absolute Pose Problem with Pairwise Constraints

## TL;DR

This paper introduces a globally optimal, pairwise-constraint-based method for absolute pose estimation that achieves linear complexity relative to the number of correspondences, improving efficiency in outlier-rich scenarios.

## Contribution

It presents a novel approach that decouples rotation and translation using pairwise constraints, enabling a linear-time globally optimal solution for absolute pose estimation.

## Key findings

- Achieves linear complexity in the number of correspondences.
- Demonstrates robustness and efficiency on synthetic and real-world data.
- Outperforms traditional methods in outlier scenarios.

## Abstract

Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed dimensionality d and the number of measurements N, a robust estimation problem cannot be solved faster than O(N^d). Furthermore, it is almost impossible to remove d from the exponent of the runtime of a globally optimal algorithm. However, absolute pose estimation is a geometric parameter estimation problem, and thus has special constraints. In this paper, we consider pairwise constraints and propose a globally optimal algorithm for solving the absolute pose estimation problem. The proposed algorithm has a linear complexity in the number of correspondences at a given outlier ratio. Concretely, we first decouple the rotation and the translation subproblems by utilizing the pairwise constraints, and then we solve the rotation subproblem using the branch-and-bound algorithm. Lastly, we estimate the translation based on the known rotation by using another branch-and-bound algorithm. The advantages of our method are demonstrated via thorough testing on both synthetic and real-world data