Single-image estimation of Brown-Conrady distortion in Fringe Projection Profilometry

Osman Ali, Dalia Elobaid, Xiangjun Kong, Tibebe Yalew, Waiel Elmadih, Samanta Piano

Abstract. Accurate modelling of lens distortion is essential for reliable geometric reconstruction in computer vision and optical metrology systems. Conventional characterisation approaches estimate distortion parameters from multiple images by leveraging repeated observations of a three-dimensional (3D) target under different viewpoints. However, practical constraints may limit data acquisition to a single usable image, motivating the investigation of reduced-data alternatives. This work investigates the estimation of Brown–Conrady distortion coefficients directly from a single distorted checkerboard image. The problem is formulated as a supervised regression task, in which a convolutional neural network predicts radial and tangential distortion parameters. A synthetic dataset is generated to provide controlled variations in distortion and corresponding ground-truth labels. The results demonstrate that the model is able to extract distortion-related information from image geometry and produce physically plausible parameter estimates. Although the numerical accuracy of the predicted coefficients remains limited, the resulting geometric transformations are consistent and preserve the global distortion structure, with minor local deviations. This behaviour reflects an inherent ambiguity in the estimation problem, where multiple parameter combinations can produce similar image deformations when only a single view is available. Overall, the proposed approach shows that single-image distortion estimation can yield geometrically meaningful predictions, while highlighting the fundamental limitations associated with recovering a unique set of distortion parameters from limited geometric information.