# A Branch-and-Bound Algorithm for Checkerboard Extraction in Camera-Laser Calibration

## TL;DR

This paper introduces a deterministic branch-and-bound algorithm for accurately extracting checkerboards in camera-laser calibration, improving robustness and applicability over heuristic methods.

## Contribution

It presents a novel, globally optimal, non-heuristic algorithm for checkerboard extraction that does not rely on background constraints or measurement discontinuities.

## Key findings

- The method achieves accurate checkerboard extraction in simulations and experiments.
- It is applicable to both 2D and 3D laser scanners with multiple checkerboards.
- The approach outperforms heuristic methods in robustness and generality.

## Abstract

We address the problem of camera-to-laser-scanner calibration using a checkerboard and multiple image-laser scan pairs. Distinguishing which laser points measure the checkerboard and which lie on the background is essential to any such system. We formulate the checkerboard extraction as a combinatorial optimization problem with a clear cut objective function. We propose a branch-and-bound technique that deterministically and globally optimizes the objective. Unlike what is available in the literature, the proposed method is not heuristic and does not require assumptions such as constraints on the background or relying on discontinuity of the range measurements to partition the data into line segments. The proposed approach is generic and can be applied to both 3D or 2D laser scanners as well as the cases where multiple checkerboards are present. We demonstrate the effectiveness of the proposed approach by providing numerical simulations as well as experimental results.