Biomedical Engineering Reference
In-Depth Information
Similarly, to use a bilinear interpolation, the rendering hints can be specified
as
RenderingHints rh=new RenderingHints (
RenderingHints.KEY
-
INTERPOLATION,
RenderingHints.VALUE
-
INTERPOLATION
-
BILINEAR);
Both interpolation methods were used. If a nearest neighbor interpolation is
used, the optimization process tends to be quicker, but the success rate of regis-
tration tends to be lower. Thus, all results reported in this chapter are obtained
using bilinear interpolation.
4.2.4
Estimation of Joint and Marginal Distributions
To calculate the mutual information, one has to have the marginal and joint pdfs.
Since they are unknown, they have to be estimated from the data under study.
We estimate these pdfs from their corresponding histograms.
To compute the histograms, the pixel pairs at the same grid are binned.
Assume the bin size is
B
r
·
B
f
, where
B
r
and
B
f
are the bin size for the pixels in
reference image and floating image, respectively.
A fixed bin size (32) is used. We will not discuss bin size effect since our
preliminary results indicate that there are no apparent effects on the registration
performance. For the byte image as the retinal GIF files normally are, there are
256 values in each color channel. However, when images are digitized and then
translated from color to grayscale, there is some error. The image does not have
very bright and very dark regions. Moreover, the lossy JPEG image compression
is frequently used. These facts lead to a sparsely filled histogram if a 256
×
256 bin
is used. Therefore, before we bin the pixel pairs their values are processed and
then binned.
Assume the maximum pixel value is
I
max
and the minimum pixel value
is
I
min
. Since we only have B bins, each bin needs to accommodate step
=
(
I
max
−
I
min
)
/
B
different pixel values. Given a pixel value
v
, obviously it will
be binned to bin (
v
−
I
min
)/step. Notice that we did not distinguish reference and
floating images. The formula and schemes are applicable to both images. Also
notice that interpolation never increases or decreases the max and min pixel
values (except it may introduce zero-valued pixels due to transformation). This
assertion is clear for the nearest neighbor interpolation. It is also true for the
