Mutuallnformation:A Similarity Measure for Intensity Based Image Registration
0.335 ,---~,---~---~-------,
0.33
e!
~
13 0.325
E
~ 0.32
.!!!
:~ 0.315
0.31
0.305 L-.-_~
-21.56
-21.06
-20.56
Rotation angle
-20.06
-19.56
9S
Fig. 3.5. MI registration function obtained using the same pair of images as shown in Fig. 3.3
but employing 2D implementation of the PVI algorithm
splits the cell (fiI> fi2, fi3, fi4) into four sub-cells having areas WI> W2, W3, and
W4 with the constraint Li wi(Ta(.x)) = 1. The joint histogram is then obtained
by updating four entries defined by (F(x), R(fii)), i = 1, ... ,4, as follows:
Vi : ha (F(x), R(fid) = ha (F(x), R(fii)) + Wi .
(3.14)
The method results in a very smooth MI registration function, and does not
introduce any extra intensity values. That is, the indices of all the non-zero
entries in the estimated joint histogram are completely defined by the set of
intensity values in the floating image and the set of intensity values in the
reference image (see (3.9), where each element is specified by its 2D index
[0 ~ M - 1, 0 ~ N - 1]). In the two-step procedure described previously,
new intensity values, which are not in the original set of intensity values in
the reference image, may be introduced because of interpolation. In addition,
in the two-step procedure, if a more sophisticated interpolation method like
cubic convolution interpolation or cubic B-spline interpolation is employed,
the interpolated values may go beyond the range of the intensity values used
(e. g. 0 ~ 2SS in general). In this case, extra effort may be required to obtain
a meaningful estimate of the joint histogram by keeping the interpolated values
between 0 and 2SS. Fig. 3.S shows the registration function using the same
image data as shown in Fig. 3.3 but the 2D implementation ofPVI is employed.
Clearly, in this case, the MI registration function is much smoother.
3.4
Interpolation Induced Artifacts
Very often, when a new similarity measure is adopted for image registration,
it is a common practice to use a pair of identical images to test its efficacy.
0.335 ,---~,---~---~-------,
0.33
e!
~
13 0.325
E
~ 0.32
.!!!
:~ 0.315
0.31
0.305 L-.-_~
-21.56
-21.06
-20.56
Rotation angle
-20.06
-19.56
9S
Fig. 3.5. MI registration function obtained using the same pair of images as shown in Fig. 3.3
but employing 2D implementation of the PVI algorithm
splits the cell (fiI> fi2, fi3, fi4) into four sub-cells having areas WI> W2, W3, and
W4 with the constraint Li wi(Ta(.x)) = 1. The joint histogram is then obtained
by updating four entries defined by (F(x), R(fii)), i = 1, ... ,4, as follows:
Vi : ha (F(x), R(fid) = ha (F(x), R(fii)) + Wi .
(3.14)
The method results in a very smooth MI registration function, and does not
introduce any extra intensity values. That is, the indices of all the non-zero
entries in the estimated joint histogram are completely defined by the set of
intensity values in the floating image and the set of intensity values in the
reference image (see (3.9), where each element is specified by its 2D index
[0 ~ M - 1, 0 ~ N - 1]). In the two-step procedure described previously,
new intensity values, which are not in the original set of intensity values in
the reference image, may be introduced because of interpolation. In addition,
in the two-step procedure, if a more sophisticated interpolation method like
cubic convolution interpolation or cubic B-spline interpolation is employed,
the interpolated values may go beyond the range of the intensity values used
(e. g. 0 ~ 2SS in general). In this case, extra effort may be required to obtain
a meaningful estimate of the joint histogram by keeping the interpolated values
between 0 and 2SS. Fig. 3.S shows the registration function using the same
image data as shown in Fig. 3.3 but the 2D implementation ofPVI is employed.
Clearly, in this case, the MI registration function is much smoother.
3.4
Interpolation Induced Artifacts
Very often, when a new similarity measure is adopted for image registration,
it is a common practice to use a pair of identical images to test its efficacy.