Issue No. 11 - November (2010 vol. 32)
Ohad Ben-Shahar , Ben-Gurion University of the Negev, Beer-Sheva
Yuriy Vasilyev , Harvard University, Cambridge
Yair Adato , Ben-Gurion University of the Negev, Beer-Sheva
Todd Zickler , Harvard University, Cambridge
An image of a specular (mirror-like) object is nothing but a distorted reflection of its environment. When the environment is unknown, reconstructing shape from such an image can be very difficult. This reconstruction task can be made tractable when, instead of a single image, one observes relative motion between the specular object and its environment, and therefore, a motion field—or specular flow—in the image plane. In this paper, we study the shape from specular flow problem and show that observable specular flow is directly related to surface shape through a nonlinear partial differential equation. This equation has the key property of depending only on the relative motion of the environment while being independent of its content. We take first steps toward understanding and exploiting this PDE, and we examine its qualitative properties in relation to shape geometry. We analyze several cases in which the surface shape can be recovered in closed form, and we show that, under certain conditions, specular shape can be reconstructed when both the relative motion and the content of the environment are unknown. We discuss numerical issues related to the proposed reconstruction algorithms, and we validate our findings using both real and synthetic data.
Specular objects, specular flow, shape reconstruction, environment motion field, Gaussian curvature, parabolic points, specular curvature.
Ohad Ben-Shahar, Yuriy Vasilyev, Yair Adato, Todd Zickler, "Shape from Specular Flow", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 32, no. , pp. 2054-2070, November 2010, doi:10.1109/TPAMI.2010.126