A linear formulation of shape from specular flow

Guillermo D. Canas, Yuriy Vasilyev, Yair Adato, Todd Zickler, Steven Gortler, Ohad Ben-Shahar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

25 Scopus citations


When a curved mirror-like surface moves relative to its environment, it induces a motion field - or specular flow - on the image plane that observes it. This specular flow is related to the mirror's shape through a non-linear partial differential equation, and there is interest in understanding when and how this equation can be solved for surface shape. Existing analyses of this 'shape from specular flow equation' have focused on closed-form solutions, and while they have yielded insight, their critical reliance on externally-provided initial conditions and/or specific motions makes them difficult to apply in practice. This paper resolves these issues. We show that a suitable reparameterization leads to a linear formulation of the shape from specular flow equation. This formulation radically simplifies the reconstruction process and allows, for example, both motion and shape to be recovered from as few as two specular flows even when no externally-provided initial conditions are available. Our analysis moves us closer to a practical method for recovering shape from specular flow that operates under arbitrary, unknown motions in unknown illumination environments and does not require additional shape information from other sources.

Original languageEnglish
Title of host publication2009 IEEE 12th International Conference on Computer Vision, ICCV 2009
Number of pages8
StatePublished - 1 Dec 2009
Event12th International Conference on Computer Vision, ICCV 2009 - Kyoto, Japan
Duration: 29 Sep 20092 Oct 2009

Publication series

NameProceedings of the IEEE International Conference on Computer Vision


Conference12th International Conference on Computer Vision, ICCV 2009

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition


Dive into the research topics of 'A linear formulation of shape from specular flow'. Together they form a unique fingerprint.

Cite this