### abstract

- An image of a purely specular object is just a distortion of its surrounding illumination environment. Therefore, when only little (or nothing) about the illumination environment is known, inferring the geometrical structure of specular objects is a very challenging task. Nevertheless, recent studies have addressed this problem by exploiting relative motion between the observed object, the camera and the environment (e.g.,[1, 4]). In the image plane such motion induces a specular flow – the optical flow of observed specular reflections – which has been shown to be independent of environment content and therefore to facilitate shape reconstruction. The shape-from-specular-flow (SFSF) approach follows the intuitive hierarchical thinking: First, estimate the relevant (specular) flow in the image plane. Next, exploit it for (specular) shape recovery by solving the SFSF equation ([1]). The SFSF equation expresses the relationship between the specular flow, the shape of the specular object, and its motion relative to the environment. A linear form for the SFSF equation have been formulated in [4] assuming that the unknown specular object is represented via the field of its reflection vectors, r∈ S2. In this case the SFSF equation becomes ∂r(x) ∂x u(x) = ω× r(x), (1)