Dynamic Refraction Stereo

In this paper we consider the problem of reconstructing the 3D position and surface normal of points on an unknown, arbitrarily-shaped refractive surface. We show that two viewpoints are sufficient to solve this problem in the general case, even if the refractive index is unknown. The key requiremen...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2011-08, Vol.33 (8), p.1518-1531
Main Authors: Morris, N. J. W., Kutulakos, K. N.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial intelligence
Computer science
control theory
systems
Dynamics
Exact sciences and technology
Image reconstruction
Intelligence
Liquids
Mirrors
Optical surface waves
Pattern analysis
Pattern recognition. Digital image processing. Computational geometry
Reconstruction
refractive index estimation
Sea surface
Shape
shape-from-X
Stereo
Studies
Surface reconstruction
Three dimensional
Three dimensional displays
time-varying imagery
transparency
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Summary:In this paper we consider the problem of reconstructing the 3D position and surface normal of points on an unknown, arbitrarily-shaped refractive surface. We show that two viewpoints are sufficient to solve this problem in the general case, even if the refractive index is unknown. The key requirements are 1) knowledge of a function that maps each point on the two image planes to a known 3D point that refracts to it, and 2) light is refracted only once. We apply this result to the problem of reconstructing the time-varying surface of a liquid from patterns placed below it. To do this, we introduce a novel "stereo matching" criterion called refractive disparity, appropriate for refractive scenes, and develop an optimization-based algorithm for individually reconstructing the position and normal of each point projecting to a pixel in the input views. Results on reconstructing a variety of complex, deforming liquid surfaces suggest that our technique can yield detailed reconstructions that capture the dynamic behavior of free-flowing liquids.
ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2011.24