Physics-guided image synthesis for crack localization using flying-spot thermography

In non-destructive testing, ‘Flying-spot’ thermography is a method for detecting defects, such as cracks, based on the infrared scanning of samples using a localized laser heat source. To automate this detection, recent studies have proposed the use of deep learning approaches, which offer superior detection performance but require large training datasets. Some of these studies have employed a particular class of generative models, known as diffusion models, to generate additional data to train the defect detection model. However, in low-data regimes, common in NDT, diffusion models tend to merely replicate the limited training samples, resulting in a generator with poor diversity, which undermines the objective of generative augmentation. Additionally, there is no physical meaning enforced to the images the model generates, leading to synthetic images that may exhibit temperature fields inconsistent with the heat equation, or even contain clear physical inaccuracies. In a previous work, we introduced a physics-guided diffusion model for the generation of synthetic thermal images of crack-free samples with physical consistency. Whereas the literature typically integrates physical information through partial differential equations (PDEs), our method directly incorporated the analytical solution of the heat equation for semi-infinite homogeneous solids, corresponding to defect-free samples. We build upon this work and generalize the approach to images containing cracks, enabling its application to realistic scenarios of physics-guided data augmentation for crack detection in laser thermography. On top of that, we propose the use of a refined boundary-aware analytical solution that explicitly accounts for edge effects, removing the need of the semi-infinity assumption. The effectiveness of the proposed approach is assessed using multiple metrics, including a physics-based error metric, the Fréchet Inception Distance, and, most importantly, performance on a downstream crack localization task (through F1-score and Mean Average Precision), the primary application of the proposed physics-based image synthesis approach. Finally, we show that the benefits of the physics-guided diffusion model are most significant in low and very low data regimes, through an evaluation of the downstream task under these conditions.