Knowledge-Guided Symbolic Regression for Interpretable Camera Calibration

Calibrating cameras accurately requires the identification of projection and distortion models that effectively account for lens-specific deviations. Conventional formulations, like the pinhole model or radial-tangential corrections, often struggle to represent the asymmetric and nonlinear distortions encountered in complex environments such as autonomous navigation, robotics, and immersive imaging. Although neural methods offer greater adaptability, they demand extensive training data, are computationally intensive, and often lack transparency. This work introduces a symbolic model discovery framework guided by physical knowledge, where symbolic regression and genetic programming (GP) are used in tandem to identify calibration models tailored to specific optical behaviors. The approach incorporates a broad class of known distortion models, including Brown-Conrady, Mei-Rives, Kannala-Brandt, and double-sphere, as modular components, while remaining extensible to any predefined or domain-specific formulation. Embedding these models directly into the symbolic search process constrains the solution space, enabling efficient parameter fitting and robust model selection without overfitting. Through empirical evaluation across a variety of lens types, including fisheye, omnidirectional, catadioptric, and traditional cameras, we show that our method produces results on par with or surpassing those of established calibration techniques. The outcome is a flexible, interpretable, and resource-efficient alternative suitable for deployment scenarios where calibration data are scarce or computational resources are constrained.