Shape from Polarization of
Thermal Emission and Reflection

Shape estimation for transparent objects is challenging due to their complex light transport. To circumvent these difficulties, we leverage the Shape from Polarization (SfP) technique in the Long-Wave Infrared (LWIR) spectrum, where most materials are opaque and emissive. While a few prior studies have explored LWIR SfP, these attempts suffered from significant errors due to inadequate polarimetric modeling, particularly the neglect of reflection. Addressing this gap, we formulated a polarization model that explicitly accounts for the combined effects of emission and reflection. Based on this model, we estimated surface normals using not only a direct model-based method but also a learning-based approach employing a neural network trained on a physically-grounded synthetic dataset. Furthermore, we modeled the LWIR polarimetric imaging process, accounting for inherent systematic errors to ensure accurate polarimetry. We implemented a prototype system and created ThermoPol, the first real-world benchmark dataset for LWIR SfP. Through comprehensive experiments, we demonstrated the high accuracy and broad applicability of our method across various materials, including those transparent in the visible spectrum.