This chapter presents a methodology for an image enhancement process of computed tomography perfusion images by means of partition generated with appropriately defined fuzzy relation. The proposed image processing is used to improve the radiological analysis of the brain perfusion. Colour image segmentation is a process of dividing the pixels of an image in several homogenously- coloured and topologically connected groups, called regions. As the concept of homogeneity in a colour space is imprecise, a measure of dependency between the elements of such a space is introduced. The proposed measure is based on a pixel metric defined in the HSV colour space. By this measure a fuzzy similarity relation is defined, which next is used to introduce a clustering method that generates a partition, and so a segmentation. The achieved segmentation results are used to enhance the considered computed tomography perfusion images with the purpose of improving the corresponding radiological recognition.
Data clustering is a popular technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the classification of a set of objects into different groups, or more precisely, the partitioning of a data set into subsets (clusters), so that the data in each subset share some common trait – often proximity, according to some defined distance measure.
The computed tomography perfusion imaging is a new technique, which appears to provide early diagnosis of major vessel occlusions in the brain. Computed Tomography perfusion (CT-perfusion) imaging also provides valuable information about the hemodynamic status of ischemic brain tissue (Tekşam, Çakır & Coşkun, 2005), e.g. CT perfusion imaging for childhood moyamoya disease before and after surgical revascularization (Sakamoto et al., 2006). The concept of developing Perfusion CT primarily as a procedure for functional imaging has proved especially advantageous for its practical clinical application. By using harmonised contrast medium and scan protocols and by implementing a series of postprocessing steps within the framework of image calculation (König, Klotz & Heuser, 2000).
In this chapter fuzzy data partitional clustering method based on fuzzy relations is proposed to develop an image enhancement algorithm dedicated to CT-perfusion images. As a field of application, medical imagery was chosen. Medical imaging techniques such as X-ray, CT, Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET), Ultrasound (USG), etc., are indispensable for the precise analysis of various medical pathologies. Computer power and medical scanner data alone are not enough; we need the art to extract the necessary boundaries, surfaces, and segmented volumes of these organs in the spatial and temporal domains. This art of organ extraction is segmentation. Image segmentation is essentially a process of pixel classification, wherein the image pixels are segmented into subsets by assigning the individual pixels to classes. These segmented organs and their boundaries are very critical in the quantification process for physicians and medical surgeons in any branch of medicine which deals with imaging (Suri et al., 2002).
Colour image segmentation, viewed as the process of dividing the image into regions characterized by colour homogeneity, is one of the most widely used tools in image processing (Chamorro-Martinez et al., 2003). Many types of segmentation techniques have been proposed in the literature, for example those based on histogram analysis (Gillet, Macaire, Bone-Lococq & Pastaire, 2001), clustering (Zhong & Yan, 2000), split and merge (Barges & Aldon, 2000), region growing (Moghaddamzadeh & Bourbakis, 1997), edge based algorithms (Shiji & Hamada, 1999), etc. Most of the proposals that fall in the aforementioned categories provide a crisp segmentation of images, where each pixel has to belong to a unique region. However, the separation between regions is usually imprecise in natural images, so crisp techniques are not often appropriate. To solve this problem, some approaches propose the definition of region as a fuzzy subset of pixels, in such a way that every pixel of the image has a membership degree to that region. These regions form a fuzzy partition of the input set of pixels (Bezdek, 1981).
Recently, as it has been illustrated in numerous scientific publications, fuzzy techniques are often applied as complementary to existing techniques and can contribute to the development of better and more robust methods. It seems to be true that applications of fuzzy techniques are very successful in the area of image processing (Kerre & Nachtegael, 2000; Tizhoosh, 1998). Moreover, the field of medicine has become a very attractive domain for the application of fuzzy set theory. This is due to the large role that imprecision and uncertainty play in this field (Mordeson et al., 2000).