Biomedical Engineering Reference
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Figure 5.3: Tsai-Shah's linear SFS algorithm applied to the synthetic vase im-
age. (a) is the input image with light source ( x = 1, y = 0, z = 1). (b), (c), and
(d) are the reconstructed surface from three different directions.
the data available for shape reconstruction is not the complete intensity func-
tion, but rather its sampled version—a discrete data set. In addition, the re-
flectance map is usually determined experimentally as well. Usually people
believe that the problem has at least one solution, but it is clear that the
uniqueness of the solution is difficult to get. The optimization approach is
one of the earliest approaches that has been proposed and researched for
several decades. The original work can be traced back to the Ph.D. thesis of
Horn [26]. Different constraint functions (see Section 5.2.3.2) can be used to
minimize the energy function. First, we consider a general way to construct
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