  With systems for acquiring 3D surface data being evermore commonplace, it has
become important to reliably extract specific shapes from the acquired data. In
the presence of noise and occlusions, this can be done through the use of
statistical shape models, which are learned from databases of clean examples of
the shape in question. In this paper, we review, analyze and compare different
statistical models: from those that analyze the variation in geometry globally
to those that analyze the variation in geometry locally. We first review how
different types of models have been used in the literature, then proceed to
define the models and analyze them theoretically, in terms of both their
statistical and computational aspects. We then perform extensive experimental
comparison on the task of model fitting, and give intuition about which type of
model is better for a few applications. Due to the wide availability of
databases of high-quality data, we use the human face as the specific shape we
wish to extract from corrupted data.
