Biomedical Engineering Reference
In-Depth Information
Figure 9.
Structure of the 3D feature descriptor. Only eight samples of neighboring cells
and six histogram bins are shown in the Figure for illustration purposes. See attached CD
for color version.
the zero-axes of the coordinate system, as calculated above. The final descriptor
is built as shown in Figure 9. This vector is normalized to reduce the effect of
linear intensity changes [74]. In this work, we use neighborhoods of 8
×
8
×
8 for
both canonical gradient orientation and descriptor's entries, and cells of 4
×
4
×
4,
which means that eight cells are used for building the entries of the descriptor.
For each cell, we use eight and four histogram bins for
φ
and
θ
, respectively. So,
the descriptor is of size 8
×
8
×
4 = 256, and after adding the overhead of the
original location, pyramid level, and the canonical orientation, the total descriptor
size becomes 256 + 6 = 262.
Finally, given a descriptor feature
F
1
in the first image, its match,
F
2
, in the
second image is found when the following condition is satisfied:
D
(
F
1
,F
2
)
min(
D
(
F
1
,F
2
))
F
2
=
F
1
,
and
F
2
=
F
2
,
< Threshold <
1
,
∀
(6)
where
D
(
·
·
) is the Euclidean distance. Other distances may be used as well.
,
3.4.3. Global and Local Motion Modeling
To model the global motion between the two images
I
t
(
·
) and
I
s
(
·
), we build
the 3D feature descriptor as described in Section 3.4.1, and then we match the
features of the reference image to those of the transformed image. The matched
pairs are used to estimate a 3D global transformation through the gradient descent
minimization of the mean squared positional error between the corresponding
points. In this work, a 9 DOF affine transformation model is adopted.
