Biomedical Engineering Reference
In-Depth Information
implement. However, the reconstruction accuracy of this kind of methods is
limited. The assumption of simple linear models is not quite satisfactory for the
actual objects (see Section 5.2.3.2). Therefore, more advanced methods, such
as multiscale methods, are introduced to overcome the disadvantage of these
linear approaches. As an example, we will introduce a wavelet-based method in
the following section.
To end this section, we would like to acknowledge the website http://
www.cs.ucf.edu/˜vision/source.html; all the source codes used in this section
can be found in this site.
Finally, we will iterate the importance of the direction of the light source. We
recall that the brightness of an object depends on the following three factors:
(1) microstructure of the surface,
(2) distribution of the incident light,
(3) orientation of the surface with respect to the view and light source.
It is notable that if we change the direction of the light source, the irradiance
map will be changed coordinately. This will have an impact on the convergence
properties for certain numerical methods (see Section 5.3 and [64]).
5.4 Wavelet-Based Methods
Wavelet theory has been enthusiastically adopted by people in the area of signal
and image processing. It has been proved to be a useful tool in many applications.
A wavelet-based shape from shading method was introduced in [31]. Unlike
methods introduced in Section 5.3, the objective function in the constrained
optimization problem is replaced by its projection to the wavelet subspaces. To
understand this approach, we first recall some elements in wavelet theory.
5.4.1 Background of Wavelets Analysis
5.4.1.1 1D Wavelets
To begin with, we present here a few elements of one-dimensional orthogonal
wavelet theory, in which an orthonormal basis
{
ψ
mn
}
of
L
2
(
R
) is constructed
