Ivan De Boi

Accurate lens distortion correction is important for calibration, registration, image stitching, and 3D reconstruction, especially in low-data device-specific settings where disposable or specialised cameras cannot provide large calibration datasets. We address distortion correction for cameras with highly irregular or non-stationary distortion fields, where fixed polynomial models and generic learning-based rectification methods can struggle. We propose a framework based on Deep Gaussian Processes (DGPs) to model the non-linear mapping required for undistortion. The key motivation is that conventional single-layer GPs with stationary kernels must use one global notion of smoothness, whereas DGPs can represent spatially varying behaviour through composed latent mappings while preserving per-pixel predictive uncertainty. This uncertainty can be used to identify or downweight unreliable corrected regions in downstream tasks. We evaluate the method on three real camera datasets with increasing distortion complexity. The full structured acquisitions contain 512 horizontal and 512 vertical line images per camera. These are not thousands of natural calibration images, but they yield up to 29,532, 11,311, and 31,686 detected intersection correspondences for the RPI, Theta, and Pillcam datasets, respectively. This distinction is important for cameras where acquiring many independent images is impractical. The results are assessed using qualitative rectification, uncertainty maps, normalised collinearity errors, and total training time. Polynomial calibration remains strongest for the regular radial RPI distortion, while DGP and DGP2 models show lower normalised collinearity-error distributions than the standard GP and lightweight MLP baselines on the more distorted Theta and Pillcam datasets. For the full datasets, total DGP/DGP2 training times ranged from 2383.50 s to 10092.50 s, reflecting the additional computational cost of probabilistic non-stationary modelling.

Accurate modelling of reflection, transmission, absorption, and emission at material interfaces is essential for infrared imaging, rendering, and the simulation of optical and sensing systems. This need is particularly pronounced across the short-wave to long-wave infrared (SWIR–LWIR) spectrum, where many materials exhibit dispersion- and wavelength-dependent attenuation described by complex refractive indices. In this work, we introduce a unified formulation of the full Fresnel equations that directly incorporates wavelength-dependent complex refractive-index data and provides physically consistent interface behaviour for both dielectrics and conductors. The approach reformulates the classical Fresnel expressions to eliminate sign ambiguities and numerical instabilities, resulting in a stable evaluation across incidence angles and for strongly absorbing materials. We demonstrate the model through spectral-rendering simulations that illustrate realistic reflectance and transmittance behaviour for materials with different infrared optical properties. To assess its suitability for thermal-infrared applications, we also compare the simulated long-wave emission of a heated glass sphere with measurements from a LWIR camera. The agreement between measured and simulated radiometric trends indicates that the proposed formulation offers a practical and physically grounded tool for wavelength-parametric interface modelling in infrared imaging, supporting applications in spectral rendering, synthetic data generation, and infrared system analysis.

Laser-based systems, essential in diverse applications, demand accurate geometric calibration to ensure precise performance. The calibration process of the system requires establishing a reliable relationship between input parameters and the corresponding 3D description of the outgoing laser beams. The quality of the calibration depends on the quality of the dataset of measured laser lines. To address this challenge, we present a stochastic method for measuring the coordinates of these lines, considering both the camera calibration uncertainties and measurement noise inherent in laser dot detection on a detection board. Our approach to composing an accurate dataset of lines utilises a standard webcam and a checkerboard, avoiding the need for specialised hardware. By modelling the uncertainties involved, we provide a probabilistic description of the fitted laser line, enabling quality assessment of the measurement and integration into subsequent algorithms. We also offer insights into the optimal number of board positions and the number of repeated laser dot measurements, which are both the main time-consuming factors in practice. In summary, our proposed method represents a significant advancement in the field of laser-based system calibration, offering a robust and efficient solution.