Simplifying geometric camera calibration with minimal requirements on calibration objects or angular directions

Kurzfassung

Geometric camera calibration is a fundamental step in computer vision, as it provides the intrinsic parameters that define the camera projection model. Classical calibration methods, such as Zhang's technique, achieve high accuracy but require multiple images of a known calibration pattern and careful data acquisition, which limits their usability in constrained or low-effort scenarios. This thesis explores camera calibration under minimal data requirements, with the aim of simplifying the calibration process while preserving geometric reliability. Two approaches are investigated. First, a one-shot calibration method based on Zhang's formulation is studied, reducing calibration to a single image of a planar object with the minimum number of features. The influence of camera-pattern pose on parameter observability is analyzed, leading to practical guidelines for selecting configurations that provide sufficient perspective and radial distortion evidence. Second, a zero-shot calibration method is introduced, which eliminates the need for calibration images and patterns. By modeling the camera as an angular measurement device, intrinsic parameters are estimated from angular constraints between viewing rays, including explicit radial distortion modeling. Theoretical and numerical analyses are used to characterize parameter coupling and identify well-conditioned measurement configurations. The results show that meaningful camera calibration is possible with significantly reduced data, provided that sufficient geometric information is available. This work contributes to a better understanding of intrinsic parameter observability and supports the development of simpler and more accessible calibration procedures.