Medical Image Processing - Digital Signal Processing for Medical Imaging Using Matlab - page 73

Fig. 4.3 Original MRI image
subjected to linear filtering

4.2.4 Linear Filterering and the Hankel Transformation

Gradual change in the pixel value gives the low frequency content of the image.
The sudden change in the pixel values give the high frequency content of the
image. Based on the requirement, we can view the image by using linear filtering as
demonstrated below.

1. Consider the MRI image as shown in the Fig. 4.3 .
2. The magnitude spectrum of the MRI image and its logirthmic view (with origin
in the middle) is shown in the Fig. 4.4 .
3. The logirthmic spectrum of the image after passing through the filter and its
corresponding spatial domain images are shown in the Fig. 4.5 .
4. It is observed that the Fig. 4.5 b consists of low frequency content of the image
(overall information, gradual change) and Fig. 4.5 d consists of high frequency
content of the image (detail information).

4.2.4.1 Hankel Transformation

The typical magnitude response (spectrum) of the ideal low pass filter is as shown in
the Fig. 4.6 . It is observed that the filter is circularly symmetric (we get the identical
spectrum even after rotating the spectrum image with an angle

). This property is
exploited to obtain the hankel transformation and are used to design any circularly
symmetric filter as described below.

θ

1. As the spectrum is circularly symmetric, we consider the values along the
y-axis from 0 to ∞ and are represented as F ( q ) . The hankel transformation