Shape from specular flow

Yair Adato, Yuriy Vasilyev, T. Zickler, Ohad Ben-Shahar

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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 fieldor specular flowin 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.

Original languageEnglish
Article number5499479
Pages (from-to)2054-2070
Number of pages17
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number11
StatePublished - 24 Aug 2010


  • Gaussian curvature
  • Specular objects
  • environment motion field
  • parabolic points
  • shape reconstruction
  • specular curvature
  • specular flow


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