Instability of the eikonal equation and shape from shading

Ian Barnes; Kewei Zhang

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 1, page 127-138
  • ISSN: 0764-583X

Abstract

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In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in ℝ 2 . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms.

How to cite

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Barnes, Ian, and Zhang, Kewei. "Instability of the eikonal equation and shape from shading." ESAIM: Mathematical Modelling and Numerical Analysis 34.1 (2010): 127-138. <http://eudml.org/doc/197553>.

@article{Barnes2010,
abstract = { In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in $\mathbb\{R\}^2$. Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. },
author = {Barnes, Ian, Zhang, Kewei},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Eikonal equation; shape from shading; instability; numerical analysis.; numerical analysis; computer image analysis},
language = {eng},
month = {3},
number = {1},
pages = {127-138},
publisher = {EDP Sciences},
title = {Instability of the eikonal equation and shape from shading},
url = {http://eudml.org/doc/197553},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Barnes, Ian
AU - Zhang, Kewei
TI - Instability of the eikonal equation and shape from shading
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 1
SP - 127
EP - 138
AB - In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in $\mathbb{R}^2$. Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms.
LA - eng
KW - Eikonal equation; shape from shading; instability; numerical analysis.; numerical analysis; computer image analysis
UR - http://eudml.org/doc/197553
ER -

References

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