A UNet-GAN two-stage network for rapid and accurate prediction of apple optical properties from single multi-frequency images

Spatial frequency domain imaging (SFDI) is a non-invasive optical imaging technique widely used for the quantitative determination of fruit tissue optical properties, specifically absorption coefficient (μ_a) and reduced scattering coefficient (μ_s^’). However, traditional SFDI methods rely on multiple frequency and phase images, limiting real-time imaging capabilities. To address this issue, we present a novel rapid prediction method based on a two-stage deep neural network architecture, termed FSGOP (Frequency-Spatial Attention UNet and GAN-based two-stage network for optical properties prediction). Compared with conventional three-phase demodulation SFDI, this method reduces the acquisition time by approximately 5/6 and requires only 0.21 s for inference. In the first stage, a UNet network enhanced by Frequency-Spatial Attention (FSA) is employed to effectively decouple the multi-frequency components. In the second stage, a Generative Adversarial Network (GAN) is utilized to predict the optical properties, thereby enabling the simultaneous extraction of μ_a and μ_s^’ maps under different frequency conditions from a single multi-frequency mixed fringe image. In experiments on apples, pears, and peaches, the method yielded normalized mean absolute errors of 0.10 (f₁) and 0.09 (f₂) for μ_s^’, and 0.07 and 0.06 for μ_a, respectively. The results revealed significant complementary information in the optical property maps at different frequencies, with lower frequencies being more sensitive to subsurface damage and higher frequencies revealing surface texture features more effectively. This method enhances information utilization and real-time performance in multi-frequency imaging, offering a rapid, accurate, and low-cost solution for optical property extraction and quality inspection of agricultural products.