Graphics Reference
In-Depth Information
The extraction of features generally serves the recognition process in a number of ways. It can
be considered as a form of data reduction that captures the essential discriminative information
from the full-dimensional data. It also serves as a tool for matching facial surfaces. Often, 3D
face recognition systems achieve invariance to facial pose and expression variations by means
of extracting invariant features.
Many feature extraction approaches have been used in 3D face recognition. They can
be categorized on the basis of the size of the surface area from which they are extracted
(holistic, regional, or point features). Other categorizations include, rigid versus deformable
feature extraction and uni modal (shape only) versus multi modal (e.g., shape and texture).
In this section, the most prominent rigid approaches to feature extraction are discussed.
They are organized according to their surface size. Nonrigid approaches are discussed in
Section 2.5.
2.4.1 Holistic 3D Facial Features
The holistic approaches extract 3D facial features from the whole surface of the face. Most
feature extraction approaches fall in this category.
Iterative Closest Point
The ICP algorithm, proposed by Besl and Mckay (1992) and Chen and Medioni (1991) for
corresponding and registering 3D surfaces, was initially widely used for 3D modeling. Later,
ICP proved to be equally useful for surface matching, providing a high accuracy particularly
for rigid surfaces. On the downside, the computational complexity of ICP is high. Nonetheless,
there are efficient variants, for example, the one by Greenspan and Yurick (2003), which uses a
K-D tree to speed up the search for closest points (the main bottleneck of ICP). The registration
error, expressed as the sum of the Euclidean distances or other distances (e.g., city block) or
their histogram, is used for matching.
Description of ICP:
The ICP algorithm requires an initial coarse registration. Less accurate
registration approaches such as those based on the detection of the fiducial points of the face
(either 3D or 2D in case of textured scans) and/or pose correction can be used to provide an
initial coarse registration. Starting from that coarse registration, ICP iteratively estimates the
rigid transformations (rotations and translations) between the two surface (which minimizes
the registration error) and updates one of the two surfaces accordingly. When the registration
error from one iteration to another diminishes and/or after a pre-specified number of iterations,
the algorithm assume convergence. The convergence of ICP can be influenced by the shape
of the surface. Surfaces that can be slid on each other in one or two geodesic directions can
yield low registration errors but an incorrect registration. Examples of these surfaces include
planar, spherical, and cylindrical (which can be slided bidirectionally). Any 3D surface that
can result from the rotation of a curve (rotational surface) or its translation along a straight
line, will induce the ICP to potentially converge somewhere along the direction of rotation or
translation of the curve. However, facial surfaces as most free-form surfaces exhibit a decent
convergence behavior.
