Graphics Reference
In-Depth Information
the subject. Furthermore, let
Y
be a continuous random variable representing a sample curve.
Given an observation
Y
y
, the uncertainty of
X
once
y
is observed can be measured through
the
Shannon
entropy of the posterior distribution, that is defined as
=
H
(
X
|
Y
=
y
)
=−
P
(
X
=
x
i
|
y
)log
P
(
X
=
x
i
|
y
)
.
(5.3)
x
i
y
) are high for facial curves
y
that are observed in the faces of many
subjects and low for facial curves
y
that are observed in the faces of just a few subjects. The
lower the value of
H
(
X
Values of
H
(
X
|
Y
=
y
), the more the observation of the facial curve
y
on a face scan
tells about the identity of the subject.
Operatively, since in a real application context only the gallery scan is available for each
subject, estimation of
P
(
X
|
Y
=
(
y
) of the facial
curve
y
can be approximated with a measure of the frequency of observing a curve similar to
y
(up to a threshold
=
x
i
|
Y
=
y
) is prevented. Therefore, the saliency
S
N
N
g
, being
N
the number of occurrences
of
y
in the scans of the gallery and
N
g
the number of gallery scans.
e
−
τ
) in the gallery scans
S
(
y
)
=
Face Matching Using Keypoints and Facial Curves
Face comparison is performed by jointly matching the keypoints and the facial curves of
two faces. First, SIFT descriptors of the keypoints detected in the probe and the gallery are
compared so that for each keypoint in the probe, a candidate corresponding keypoint in the
gallery is identified. In particular, a keypoint
k
p
in the probe is assigned to a keypoint
k
g
in
the gallery if they match each other among all keypoints, that is, if
k
p
is closer to
k
g
than
to any other keypoint in the gallery and
k
g
is closer to
k
p
than to any other keypoint in the
probe. For this purpose, proximity of keypoints is measured through the Euclidean distance
between 128-dimensional SIFT descriptors associated with the keypoints. This analysis of the
proximity of keypoint descriptors results in the identification of a candidate set of keypoint
correspondences. Identification of the actual set of keypoint correspondences must pass a
final constraint targeting the consistent spatial arrangement of corresponding keypoints on the
probe and the gallery. The RANSAC algorithm is used to identify outliers in the candidate
set of keypoint correspondences. This involves generating transformation hypotheses using
a minimal number of correspondences and then evaluating each hypothesis on the basis of
the number of inliers among all features under that hypothesis. In this way, corresponding
keypoints whose spatial arrangement is an outlier are removed from the match.
Correspondences between inliers pairs of keypoints of two face scans are used to measure
the distance between the two facial scans. Given a probe and a gallery, the correspondences
identified by the spatial consistency can be formalized in terms of a function
ξ
:
ℵ →ℵ
that
(
p
)
i
(
g
)
ξ
(
i
)
associates with a facial curve
C
in the probe, its corresponding facial curve
C
in the
(
p
)
i
gallery. For each matched facial curve in the probe
C
, the distance to the corresponding
(
g
)
ξ
(
i
)
in the gallery is evaluated by weighting the result of Equation 5.2 by the
saliency
of the gallery scan
facial curve
C
ξ
(
i
)
ξ
(
i
)
(
p
)
i
(
g
)
(
g
)
d
i
=
D
C
, C
S
C
.
(5.4)
