Linear Depth Estimation from an Uncalibrated, Monocular Polarisation Image
We present a method for estimating surface height directly from a single polarisation image simply by solving a large, sparse system of linear equations. To do so, we show how to express polarisation constraints as equations that are linear in the unknown depth. The ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to objects with uniform albedo exhibiting diffuse and specular reflectance. We extend it to an uncalibrated scenario by demonstrating that the illumination (point source or first/second order spherical harmonics) can be estimated from the polarisation image, up to a binary convex/concave ambiguity. We believe that our method is the first monocular, passive shape-from-x technique that enables well-posed depth estimation with only a single, uncalibrated illumination condition. We present results on glossy objects, including in uncontrolled, outdoor illumination.
KeywordsPolarisation Shape-from-x Bas-relief ambiguity
This work was undertaken while W. Smith was a visiting scholar at UCSD, supported by EPSRC Overseas Travel Grant EP/N028481/1. S. Tozza was supported by Gruppo Nazionale per il Calcolo Scientifico (GNCS-INdAM). This work was supported in part by ONR grant N00014-15-1-2013 and the UC San Diego Center for Visual Computing. We thank Zak Murez for assistance with data collection.
- 2.Miyazaki, D., Tan, R.T., Hara, K., Ikeuchi, K.: Polarization-based inverse rendering from a single view. In: Proceedings of ICCV, pp. 982–987 (2003)Google Scholar
- 3.Kadambi, A., Taamazyan, V., Shi, B., Raskar, R.: Polarized 3D: high-quality depth sensing with polarization cues. In: Proceedings of ICCV (2015)Google Scholar
- 5.Schechner, Y.Y.: Self-calibrating imaging polarimetry. In: Proceedings of ICCP (2015)Google Scholar
- 8.Morel, O., Meriaudeau, F., Stolz, C., Gorria, P.: Polarization imaging applied to 3D reconstruction of specular metallic surfaces. In: Proceedings of EI 2005, pp. 178–186 (2005)Google Scholar
- 9.Huynh, C.P., Robles-Kelly, A., Hancock, E.: Shape and refractive index recovery from single-view polarisation images. In: Proceedings of CVPR, pp. 1229–1236 (2010)Google Scholar
- 10.Mahmoud, A.H., El-Melegy, M.T., Farag, A.A.: Direct method for shape recovery from polarization and shading. In: Proceedings of ICIP, pp. 1769–1772 (2012)Google Scholar
- 11.Rahmann, S., Canterakis, N.: Reconstruction of specular surfaces using polarization imaging. In: Proceedings of CVPR (2001)Google Scholar
- 15.Drbohlav, O., Šára, R.: Unambiguous determination of shape from photometric stereo with unknown light sources. In: Proceedings of ICCV, pp. 581–586 (2001)Google Scholar
- 16.Ngo, T.T., Nagahara, H., Taniguchi, R.: Shape and light directions from shading and polarization. In: Proceedings of CVPR, pp. 2310–2318 (2015)Google Scholar