Ray-LLM: Suppressing Runge’s Phenomenon in Data-SparseFisheye Calibration via Neuro-Symbolic Synthetic Anchoring

Standard fisheye calibration pipelines, utilizing the Kannala-Brandt model, rely on minimizing the Root-Mean-Square (RMS) reprojection error. While RMS is the statistically optimal estimator under Gaussian noise assumptions, its effectiveness is strictly conditional on the spatial distribution of observations. In practice, acquiring dense feature points at the lens periphery is notoriously labor-intensive, leading to unavoidable data sparsity. We demonstrate that applying the standard RMS objective to such sparse datasets induces a critical failure mode: the solver minimizes global error by overfitting the central region, resulting in unconstrained polynomial oscillations (Runge’s phenomenon) at the edges. To bridge this Data-Solver Gap, we propose Ray-LLM, a physics-informed active calibration framework. Crucially, we maintain the standard RMS optimization pipeline without modifying the solver. Instead, our method employs a Neuro-Symbolic Agent that diagnoses parameter instability and autonomously injects 'Physically-Anchored' synthetic data into sparse zones. This approach effectively acts as a dynamic geometric regularizer, constraining the polynomial coefficients to adhere to physical laws. Experimental results confirm that Ray-LLM enables the unmodified RMS solver to achieve superior geometric rectilinearity and stability in data-starved regimes, offering a labor-free alternative to exhaustive manual data collection.