Shape from shading with a linear triangular element surface model
Lee, K.M.
Kuo, C.-C.J.
Dept. of Electr. Eng.-Syst., Univ. of Southern California, Los Angeles, CA;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Aug 1993
Volume: 15,
Issue: 8
On page(s): 815-822
ISSN: 0162-8828
References Cited: 31
CODEN: ITPIDJ
INSPEC Accession Number: 4500757
Digital Object Identifier: 10.1109/34.236247
Current Version Published: 2002-08-06
Abstract
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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