Adaptive B-Spline-Based Distortion Modeling and Calibration for Cameras with Freeform Lenses

Freeform lenses introduce spatially varying and asymmetric distortions that cannot be reliably modeled by conventional calibration frameworks. This work presents a calibration approach that represents the distortion field using a bicubic B-spline surface and integrates it directly into parameter estimation. To address instability caused by uneven sampling, an adaptive knot placement strategy guided by distortion-aware density estimation is introduced, together with a regularized control-point formulation. These components enable stable optimization under non-uniform and sparse observations. Experiments on synthetic and real datasets show that the proposed method consistently achieves sub-pixel reprojection accuracy (0.39–0.80 pixels on synthetic data and 0.24 pixels on real data) and improves geometric rectification quality compared with representative parametric and non-parametric approaches. The results indicate that continuous distortion modeling with adaptive spatial parameterization provides a reliable solution for calibrating complex lens systems.