Image Processing Reference
In-Depth Information
11.11 Examples of GST Applications
Example 11.7. In vehicle crash tests, the test event is filmed with a high-speed cam-
era to quantify the impact of various parameters on human safety by tracking mark-
ers. A common marker is the “cross”, which allows, to quantitate the planar position
of an object as well as its planar rotation (Fig. 11.7). Markers have to be tracked
across numerous frames (in the order of hundreds to thousands). The tracking has to
be fast and robust in that the markers should not be lost from frame to frame. The
rotations and translations of the objects are not constant due to the large accelera-
tions/decelerations, while severe light conditions are common between two frames
(e.g., imperfect flash synchronization). A symmetry tracker using hyperbolas, i.e.,
g
(
z
)=
z
2
=
x
2
y
2
+
i
2
xy
n
=2
⇒
−
(11.107)
has been used to model the family of cross markers. Because of this, the cross-
markers were detected and simultaneously their rotation angles were quantitated
automatically. The image at the bottom, left shows the original superimposed tra-
jectory of thehead, whereas theimage on the rightshows theidentified crosses [23].
Alternatively,thecandidatecrossmarkerscouldhavebeendetectedbylackoflinear
symmetry in Cartesian coordinates, but then the rotation angles of the crosses would
have to be identified separately. This is because a lack of a symmetry in any coordi-
nate system does not provide the angle informationa since only the presence of an
explicitly modeled curve family has a well-defined direction whereas the lack of a
modeled curve family cannot provide the direction information, e.g. [97].
Example 11.8. In biometric authentication, alignment of two fingerprints without
extraction of minutiae
9
has gained increased interest, e.g., [108], since this im-
proves the subsequent person authentication (minutiae-based or not) performance
substantially. Besides improved accuracy, this helps to reduce the costly combina-
torial match of fingerprint minutiae. Recently, silicon-based imaging sensors have
become cheaply available. However, because sensor surfaces are decreasing, in or-
der to accommodate them to portable devices, e.g., mobile phones, the delivered
images of the fingerprints are also small. In turn this results in fewer minutiae points
that are available to consumer applications, which is an additional reason for why
nonminutiae-basedalignmenttechniquesinbiometricauthenticationhavegainedin-
terest. A high automation level of accurate fingerprint alignment is desirable inde-
pendent of which matching technique is utilized. For robustness and precision, an
automatical identification of two standard landmark types: core and delta (Fig. 11.8)
has been proposed [169]. These can be modeled and detected by symmetry deriva-
tive filters in a scheme based on lemma 11.6. Naturally, the used coordinate trans-
formations are different than the one modeling the cross markers. Furthermore, the
detection isperformed withinaGaussian pyramid scheme toimprove theSNR. The
real and imaginary parts of the analytic functions, i.e.,
9
Typically a minutia point is the end of a line or the bifurcation point of two lines.
