Mamba-SfP: Toward open-scene 3D shape from polarization via selective state space models

Shape from polarization (SfP) recovers surface normals by analyzing the polarization state of reflected light, offering a low-cost route to 3D perception. When SfP is extended from air to open-scene conditions such as multi-scattering and underwater imaging, existing methods rely on assumptions about the optical properties of materials and media, which may introduce systematic errors once the imaging medium changes. Moreover, joint modeling of multiple polarization-derived quantities demands both long-range context modeling and computational efficiency. To address these issues, this paper investigates SfP under diverse scene conditions, using datasets from air, scattering media, and underwater environments as representative cases, and proposes a polarization input representation free of optical-property or refractive-index assumptions to improve cross-condition robustness. Building on this representation, the suitability of CNN-, Transformer-, and Mamba-based paradigms for SfP is analyzed, and a selective state space model network termed Mamba-SfP is developed. Experimental results show that Mamba-SfP achieves mean angular errors of 14.07 ∘ and 13.03 ∘ on MuS-Polar3D and DeepSfP, respectively, and 23.32 ∘ in zero-shot testing on a Jerlov-water dataset. On the Jetson Orin edge device, it attains a favorable accuracy–efficiency trade-off with 33.24 M parameters and 13.96 GFLOPs. These results suggest the potential of the proposed representation and network design for open-scene polarimetric 3D reconstruction. Code is available at: https://github.com/WangPuyun/Mamba-SfP .