Information Technology Reference
In-Depth Information
resulting 3D blurring causes overlapping between regions. Because of the finite
spatial resolution, the image of a small source is a larger but dimmer source. Part
of the signal from the source spills out and hence is seen outside the actual source.
Mathematically speaking, the finite resolution effect is described by a 3D convolu-
tion operation.
The second phenomenon causing PVE is image sampling. In PET, the radiotracer
distribution is sampled on a voxel grid. Obviously, the contours of the voxels do not
match the actual contours of the tracer distribution. Most voxels therefore include
different types of tissues. This phenomenon is often called the tissue fraction ef-
fect. The signal intensity in each voxel is the mean of the signal intensities of the
underlying tissues included in that voxel. Note that even if the imaging system had
perfect spatial resolution, there would still be some PVE because of image sam-
pling. This phenomenon is why PVE not only is an issue in PET, which has poor
spatial resolution compared with other imaging modalities, but also is of concern in
high-resolution imaging, such as MRI or CT.
12.4
Fuzzy Set Theory for Medical Image Segmentation
The variety of medical imagining techniques, with each own advantages and disad-
vantage, would make a global processing very inefficient. That is, it is not possible
to develop an optimal algorithm to deal with all kind of images at the same time.
However, when considering medical images as fuzzy images, we can use fuzzy
techniques for image processing developed in last decades.
In this section we show a short review of fuzzy techniques most commonly used
for medical image segmentation. Finally we study in depth an algorithm of image
segmentation based on uncertainty measures using ignorance functions.
12.4.1
Fuzzy Cluster Means
One of the most used algorithms for medical image segmentation in the last decades
is fuzzy cluster means (FCM). As we have explained in the previous section, the
uncertainty present in images does not allow to know the correct intensity of each
pixel. In this sense, FCM has been used to assign a membership degree of each pixel
to every area (object) of the image. Besides, this is a non supervised method, so it
is very useful for being used by medical staff non specialized in medical imaging.
FCM has been used for the majority of medical images and for multiple applica-
tions. A typical example is [18] where fuzzy c-means is used for segmenting breast
cancer on MRI. Also it has been used in single-photon emission tomography SPET
images [1] to detect dynamic neuroreceptors. Moreover it has been adapted to typi-
cal noisy and low resolution oncological PET images [6]. From retinal images [35]
it has been used for the extraction of blood vessels. Among the applications, in [28]
FCM has been used for automated detection of white matter changes of the brain in
an elderly population or in [20] has been devoted to identify breast tissue regions
judged abnormal .
