Biomedical Engineering Reference
In-Depth Information
of this problem is discussed and implemented to show the basic ideas. However,
a short chapter like this one has to omit many related topics, which are both
important and exciting. In fact, there are many other techniques and advanced
developments in the area. Fortunately, most of them are very well documented
in the literature. For instance, the following two approaches reflect different
flavors:
1.
Statistical learning and neural network
. [2] introduced a statistical
method to solve the SFS model; the principal component analysis (PCA)
was used to derive a low-dimensional parameterization of head shape
space, and an algorithm was presented for solving shape from shading
based on this approach.
2.
Fast matching method
. The schemes are of use in a variety of applications,
including problems of shape from shading. An excellent review about this
method is given by its pioneer [54]. Applications related to vision problems
can be found in [55] and [53].
We conclude this chapter by pointing out that there is, in general, no proof
of the convergence for the numerical methods introduced in Sections 5.3 and
5.4. An interesting example related to this topic can be found in [30].
5.6 Acknowledgements
The authors would like to thank Dr. Gilbert G. Walter for his encouragement
and his valuable suggestions which led to significant improvement of this paper.
The first author was partially supported by Professor Naoki Saito's grant ONR
YIP N00014-00-1-0469 while completing this paper. She also wishes to thank
Dr. Jianbo Gao for introducing her the reference [31].
