# Instability of the eikonal equation and shape from shading

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topBarnes, 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 -

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