Image Processing Reference
In-Depth Information
such situations, using low pass filtering eliminates not only bias field but also useful know-
ledge in the true image, therefore decreasing the quality of the bias field corrected breast im-
age. Another group of bias field correction methods relies on the assumption that anatomical
knowledge in MRI occurs in the higher spatial frequency bands than intensity nonuniformity.
These methods remove the bias field by filtering out highest spatial frequency bands demon-
strating anatomical knowledge. One of the disadvantages of these methods is that the results
depend on anatomy.
In this chapter, we used SFA idea [ 17 ] , which assumes that anatomical information of MRI
occurs in the high spatial frequencies in the image. In this method, after low pass filtering
since useful low spatial frequencies are removed during the filtering process, the filtered ver-
sion of the ideal signal does not look like the original unbiased signal. SFA models recover
the removed low-frequency information via reconstructing spatial information from the rest
of high spatial frequencies.
In general, we applied a model that uses the assumption that bias field does not corrupt
high spatial frequency bands in the image. Consequently, we first removed all low spatial fre-
quencies without recognizing important information. Second, we recreated the spatial image
from the remained higher spatial frequencies. The low spatial frequencies, which are related
to intensity nonuniformity, are thus removed in the recreated image, leading to an intensity
nonuniformity corrected breast image.
2.4.3 Field estimation
Using the distribution of U , we can estimate bias field estimation as follows. For a measure-
at some location x ,
can be estimated using the distributions F and U ( = [log( u )]).
The estimated value of
given a measurement v j is defined as follows:
By using the estimation of , the estimation of f can be found as follows:
is the estimation of f e , based on the single measurement of
at location x .
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