Image Processing Reference
In-Depth Information
Let V ( u , v ), U ( u , v ), and F ( u , v ) present the probability densities of v ( i , j ), u ( i , j ), and f ( i , j ), re-
spectively. Equation (5) can be expressed as
Making the approximation that ln u and ln f are uncorrelated random variables, Equation
(6) is found by convolution as follows:
The multiplication corrupts the field and a division can undo the corruption. In the fre-
quency domain, multiplications and divisions convert to convolutions and deconvolutions as
In which V , U , and F are probability densities. After this stage, the uniformity distribution
( F ) is modeled and viewed as blurring intensity distribution U that is the main stage for cor-
recting bias field.
2.4.2 Correction step
An straightforward technique for image bias field correction would be that if the spatial fre-
quencies of u ( i , j ) (the true image) and f ( i , j ) bias field are disjointed, the bias field can be re-
moved by filtering out the spatial frequencies illustrating the bias field. In some cases, use-
ful knowledge in MRI related to higher spatial frequencies than the intensity nonuniform-
ity. Thus, by removing low spatial frequencies, intensity nonuniformity can be suppressed.
The problem is that in most cases, spatial frequency information of the bias field and true im-
age are not perfectly separated, and they have some overlapped components. For example,
in MRI scans, when low spatial frequencies are removed, the spatial image will be consider-
ably changed, implying the existence of useful knowledge at low spatial frequency bands. In
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