Surface normal estimation of black specular objects from multiview polarization images

Abstract

Abstract. Polarization is a phenomenon that cannot be observed by the human eye, but it provides rich information regarding scenes. The proposed method estimates the surface normal of black specular objects through polarization analysis of reflected light. A unique surface normal cannot be determined from a polarization image observed from a single viewpoint; thus, we observe the object from multiple viewpoints. To analyze the polarization state of the reflected light at the corresponding points when observed from multiple viewpoints, the abstract shape is predetermined using a space carving technique. Unlike a conventional photometric stereo or multiview stereo, which cannot estimate the shape of a black specular object, the proposed method estimates the surface normal and three-dimensional coordinates of black specular objects via polarization analysis and space carving.

Height-from-Polarisation with Unknown Lighting or Albedo

“…However, this approach requires a polarised light source. Coarse geometry obtained by multi-view space carving [24], [25] has been used to resolve polarisation ambiguities. Kadambi et al [5], [26] combined a single polarisation image with a depth map obtained by an RGBD camera.…”

“…We can now combine the height-from-polarisation cost (20) 482 with the cost functions associated with the two priors (21), (25) 483 to form a single system of equations in linear least squares form (see Fig. 3).…”

Depth From a Polarisation + RGB Stereo Pair

“…However, this approach requires a polarised light source. Coarse geometry obtained by multiview space carving [20,21] has been used to resolve polarisation ambiguities. Kadambi et al [15,16] combine a single polarisation image with a depth map obtained by an RGBD camera.…”

“…Consider an image with N foreground pixels whose unknown depth values are vectorised in Z ∈ R N . The surface normal direction (unnormalised) can be computed for all pixels with: (21) and (22) leads to equations that are linear in depth. We now combine these equations into a large linear system of equations for the whole image.…”

“…A has 4N +N D rows, 3N columns and is sparse. Each row evaluates one equation of the form of (18), (21) and (22). λ > 0 is a weight which trades off the influence of the guide depth values against satisfaction of the polarisation constraints.…”