BnB-Based Robust PnP Pose Estimation Method for Outliers

The Perspective-n-Point (PnP) problem is a fundamental issue in the field of computer vision. However, the PnP problem is susceptible to the influence of outliers. In this paper, we introduce a robust PnP pose estimation method based on the Branch and Bound (BnB) algorithm. Considering that the computational complexity of the BnB method is related to the dimensionality of the parameter space, we construct a cost function based on the maximization of the consensus set for the parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${R}^{T} t$</tex-math></inline-formula>. This approach reduces the search from a 6D space to a 3D space, thereby decreasing computational complexity and reducing computation time. Subsequently, we derive the upper and lower bounds for the BnB algorithm and perform pruning until convergence to obtain the global optimal solution for this parameter. After identifying corresponding point pairs that meet the inlier threshold, we employ Singular Value Decomposition (SVD) to solve for the translation and rotation parameters from this parameter. Finally, extensive comparative studies across synthetic and real datasets reveal that our method delivers accurate pose estimation and demonstrates robustness against noise and outliers, offering a viable solution for PnP issues in practical applications.