Geometry-Conditioned Pix2Pix: Leveraging Explicit Conditioning on SAR Projected Local Incidence Angle for SAR-to-EO Translation Quality Improvement

Abstract. Electro-optical (EO) imagery is intuitive but highly dependent on weather and illumination, whereas synthetic aperture radar (SAR) imagery provides reliable all-weather observations yet offers limited spectral information. To complement these modalities, recent studies have applied conditional generative adversarial network (cGAN)-based image-to-image translation to SAR-to-EO translation. However, side-looking SAR introduces spatial distortions such as foreshortening and layover that cause relative misalignment with EO imagery, undermining pixel-wise supervision and yielding structural discrepancies between translated outputs and reference EO imagery. In this study, we propose Geometry-Conditioned Pix2Pix (GC-Pix2Pix), which explicitly incorporates on the projected local incidence angle (PLIA) information derived from SAR imagery to better preserve structure and alignment in translated EO imagery. The method is based on Pix2Pix and comprises a two-branch generator and a PatchGAN discriminator. The generator consists of a main network that processes SAR polarimetric channels (VV, VH) and a conditioning subnetwork that extracts PLIA features. The subnetwork uses multi-layer convolutional blocks to capture local PLIA patterns, and the extracted features are then fused with features from the main branch and emphasized via a spatial attention module. For training and evaluation, we assembled a dataset over South Korea that combines Sentinel-1A/1C GRD VV/VH with PLIA and Sentinel-2B Level-2A RGB imagery. We compared GC-Pix2Pix against representative baselines. Across multiple image quality assessment metrics and complementary qualitative analyses, the proposed approach consistently improved SAR-to-EO translation performance. This study establishes a foundational framework for enhancing SAR data utility by synthesizing high-quality EO imagery as an alternative for continuous Earth observation.