Noise Filtering Methods in MRI - Advance Image Processing in Magnetic Resonance Imaging - page 174

Subsequently, the standard anisotropic diffusion method was extended by
Yang [20], who, instead of using local gradients to control the filter anisotropy,
introduced a filter whose shape is pointwise adapted to the local structure of the
image within a neighborhood, using both a local intensity orientation and an
anisotropic measure of level contours. Yang demonstrated that the noise filtering
efficacy of the algorithm is good both in simulated and real images, although the
computational efficiency needs improvement.
These anisotropic filters applied to magnitude MR data introduce a bias in the
image, because they do not account for the Rician nature of the data, which is more
effective in low SNR. In order to reduce this bias, Sijbers [24] proposed a modified
version of the Yang filter that introduces the Rice distribution into the maximum
likelihood estimation of the filter parameters. Results obtained with simulated
images and experimental magnitude MR data confirm that the differences between
Gaussian- and Rician-based filters are visible in regions with low SNR.

6.6 APPLICATION OF ANISOTROPIC

DIFFUSION FILTERING

The filter proposed by Perona et al. [12] is able to produce object edge enhance-
ment if the proper choice of the diffusion constant K is made. In this section, we
exploit this property to improve myocardial contours of cardiac images for a
subsequent automatic segmentation operation.
In MR images of myocardium, gradient strength at the endocardium is usually
different from that at the epicardium. Moreover, MRI of the myocardium is
strongly influenced by gray-scale inhomogeneities that are responsible for local
changes in tissue mean and variance. To account for such drawbacks, the proper
diffusion parameter was determined by a simulation procedure.
We first exploited the relation between the K parameter and image gradient

∇ I, using a 1-D simulation study. The error function, sampled with 16 data

points, was used as an ideal model of a blurred step edge to simulate a gray-
level discontinuity in the image. The sampling frequency was determined by
considering that a typical MR image of 256 256 data points requires approx-

imately 16 pixels to realize a gray-level transition at the myocardium interfaces.
On the gradient profile, the slope measured at the inflection point multiplied
by a constant term was used for simulation purposes. The relationship between
the slope increment

×

∆ S and K was computed as a function of the iteration step

N ( Figure 6.3 ). It demonstrates that the slope is a function of K and exhibits

band-pass behavior.
Starting from the K value where

∆ S is maximum, the relationship between

K and I ranged from 0 to 30

to include gray-level excursion at the endocardium and epicardium interfaces
(typically ranging from 10 to 25). A linear relationship between K and

∇ I was derived by simulation. In the simulation, ∇

∇ I was

found ( Figure 6.4 ), where ∇ I = 2.85K. It means that to obtain a maximum slope

I in the image, the K value should be adapted according to the data
of Figure 6.4. In our implementation, we assessed the best compromise value for

∆ S at any ∇