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In-Depth Information
Application for the segmentation of brain structures in MRI and CT images,
based both on atlas and real data are presented in [11]. In [22] it is proposed a
method for segmenting cerebrospinal fluid and cerebral ventricles from MRI im-
ages. This method segments the cerebral ventricles by using a fuzzy If-Then rules
that can implement physicians' knowledge on the ventricles, which can represent
their abstract shape and position.
Another nuclear images as bone scintigraphy have been used as in [36] for the
diagnosis of bone diseases with a small-sized rule base such that the resulting fuzzy
rules can be easily understood by radiologists. Also the visualization of nerve fibers
where investigated in [4] using fuzzy logic methods that allow better comprehension
of the human brain.
Finally, hybrid techniques as a fuzzy-neural system have been developed for clas-
sifying kidney categories [29].
12.4.4
Fuzzy Measures of Uncertainty
The representation of medical images by means of fuzzy images (orfuzzysets)al-
lows to face segmentation problem by minimizing uncertainty measures. In this
way, the result obtained with minimum uncertainty is asociated with the most accu-
rate solution solution. For example, the main idea presented in [5] is to define the
averages of a given fuzzy set by using different definitions of the mean of a random
compact set. In particular, the average distance of Baddeley-Molchanov and the
mean of Vorob'ev have been used. A medical image application of retinal vessel
detection was performed. The Local fuzzy fractal dimension (LFFD) is proposed
to extract Local fractal features of medical images [40]. The definition of LFFD
is an extension of the pixel-covering method by incorporating fuzzy sets. For the
segmentation of breast tumors in mammograms some measures of inhomogeneity
where presented in [15]. They are computed from the pixels present in a suitably
defined fuzzy ribbon and have indicated potential use in classifying the masses and
tumors as benign or malignant .
Based on the idea of measures of uncertainty some authors have used extensions
of fuzzy sets to represent this uncertainty. An intuitionistic fuzzy image was con-
structed using Sugeno type intuitionistic fuzzy generator and then a local threshold-
ing is applied to segment medical images in [10]. Also in [12] intuitionistic fuzzy
sets have been used in the segmentation of infrared images.
Next, we explain in detail how the concept of ignorance function is used as a
measure of uncertainty for the segmentation of ultrasound images [9].
12.4.5
Ignorance Functions in Ultrasound Images
Ultrasound imaging is a widely used technology for prostate biopsy and brachyther-
apy. The accurate detection of the prostate boundaries in ultrasound images is
crucial for clinical applications, such as the accurate placement of the needles
during the biopsy, accurate prostate volume measurement from multiple frames,
