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Shape from Shading with a Linear Triangular Element Surface Model
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.236247August 1993 (vol. 15 no. 8) pp. 815-822
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K.M. Lee, C.C.J. Kuo, "Shape from Shading with a Linear Triangular Element Surface Model," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 8, pp. 815-822, August, 1993.
 
 
BibTex
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@article{ 10.1109/34.236247,
author = {K.M. Lee and C.C.J. Kuo},
title = {Shape from Shading with a Linear Triangular Element Surface Model},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {15},
number = {8},
issn = {0162-8828},
year = {1993},
pages = {815-822},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.236247},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Shape from Shading with a Linear Triangular Element Surface Model
IS - 8
SN - 0162-8828
SP815
EP822
EPD - 815-822
A1 - K.M. Lee,
A1 - C.C.J. Kuo,
PY - 1993
KW - image processing; optimisation; linear triangular element surface model; linearized reflectance map; shape-from-shading; image brightness; quadratic cost functional; multigrid computational technique; image processing; optimisation
VL - 15
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

The authors propose to combine a triangular element surface model with a linearized reflectance map to formulate the shape-from-shading problem. The main idea is to approximate a smooth surface by the union of triangular surface patches called triangular elements and express the approximating surface as a linear combination of a set of nodal basis functions. Since the surface normal of a triangular element is uniquely determined by the heights of its three vertices (or nodes), image brightness can be directly related to nodal heights using the linearized reflectance map. The surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique. The proposed method does not require any integrability constraint or artificial assumptions on boundary conditions. Simulation results for synthetic and real images are presented to illustrate the performance and efficiency of the method.

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Index Terms:
image processing; optimisation; linear triangular element surface model; linearized reflectance map; shape-from-shading; image brightness; quadratic cost functional; multigrid computational technique; image processing; optimisation
Citation:
K.M. Lee, C.C.J. Kuo, "Shape from Shading with a Linear Triangular Element Surface Model," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 8, pp. 815-822, Aug. 1993, doi:10.1109/34.236247
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