Camera Pose Revisited

2026-01-18

AI Summary

This work proposes PnP-ProCay78, a novel algorithm addressing the accuracy and efficiency challenges in initial pose estimation for the planar Perspective-n-Point (PnP) problem. The method introduces a geometrically transparent and computationally efficient hybrid cost function that innovatively combines projection error minimization with a proxy term for translation reconstruction error derived via analytical elimination. Rotation is parameterized using the Cayley representation, and deterministic initialization coupled with least-squares optimization eliminates the need for costly search procedures. Theoretical analysis reveals convergence properties of the optimization trajectory within Cayley space. Experimental results demonstrate that the algorithm achieves projection accuracy comparable to SQPnP and slightly superior to IPPE on both RGB and low-resolution thermal imaging data, while maintaining a more streamlined structure.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Estimating the position and orientation of a camera with respect to an observed scene is one of the central problems in computer vision, particularly in the context of camera calibration and multi-sensor systems. This paper addresses the planar Perspective--$n$--Point problem, with special emphasis on the initial estimation of the pose of a calibration object. As a solution, we propose the \texttt{PnP-ProCay78} algorithm, which combines the classical quadratic formulation of the reconstruction error with a Cayley parameterization of rotations and least-squares optimization. The key component of the method is a deterministic selection of starting points based on an analysis of the reconstruction error for two canonical vectors, allowing costly solution-space search procedures to be avoided. Experimental validation is performed using data acquired also from high-resolution RGB cameras and very low-resolution thermal cameras in an integrated RGB--IR setup. The results demonstrate that the proposed algorithm achieves practically the same projection accuracy as optimal \texttt{SQPnP} and slightly higher than \texttt{IPPE}, both prominent \texttt{PnP-OpenCV} procedures. However, \texttt{PnP-ProCay78} maintains a significantly simpler algorithmic structure. Moreover, the analysis of optimization trajectories in Cayley space provides an intuitive insight into the convergence process, making the method attractive also from a didactic perspective. Unlike existing PnP solvers, the proposed \texttt{PnP-ProCay78} algorithm combines projection error minimization with an analytically eliminated reconstruction-error surrogate for translation, yielding a hybrid cost formulation that is both geometrically transparent and computationally efficient.

Problem

• Camera Pose
• Perspective-n-Point
• PnP
• Calibration
• Planar PnP

Innovation

• PnP-ProCay78
• Cayley parameterization
• deterministic initialization
• hybrid cost formulation
• planar Perspective-n-Point