Camera Pose Revisited

Estimating the position and orientation of a camera with respect to an observed scene remains a fundamental problem in computer vision, particularly in calibration procedures and multi-sensor vision systems. This paper revisits the planar Perspective–n–Point (PnP) problem with emphasis on rotation representation, initialization strategy, and optimization behavior. We propose the PnP-ProCay78 algorithm, which combines analytical elimination of translation via quadratic reconstruction error with nonlinear least-squares minimization of projection residuals in Cayley parameter space. A deterministic initialization scheme based on canonical directions of the reconstruction matrix eliminates the need for spectral search over the full solution space. Experimental evaluation on heterogeneous datasets acquired from high-resolution RGB cameras and low-resolution thermal cameras demonstrates that the proposed method achieves reprojection accuracy comparable to state-of-the-art OpenCV implementations such as SQPnP and IPPE. Convergence analysis in Cayley space reveals stable and rapidly contracting optimization trajectories, with consistent behavior across sensors of significantly different resolution and noise characteristics. The results indicate that a carefully chosen rotation parameterization combined with a transparent optimization framework can yield competitive numerical performance while maintaining geometric interpretability and structural simplicity.