An automatic method of segmenting a magnetic resonance image (MRI) [14] into tissue regions would be a very useful aid to physicians. It has been shown that fuzzy clustering is effective in segmenting MRI's of the normal human brain [3,11] and it can be used in conjunction with domain knowledge to segment brain tumors [4,2].
A typical MR image consists of > 65,000 pixels in a slice from 1mm to 5mm thick. A brain volume is covered by a set of from 150 to 30 slices depending upon the slice thickness and head volume. Fuzzy clustering of each slice in a brain image will be very time consuming. For example, it takes from 4 to 20 minutes to form cluster partitions of a 5mm thick MR image of the brain into 10 classes on a SUN Ultrasparc workstation. The time depends upon how precise the stopping criteria is.
Each MR slice of the human brain comes from a spatial location in which structure is expected. Hence, one might build a set of fuzzy rules to attempt to segment an image into tissue types. Since, the structures are deformable and must be located this approach is not as straightforward as it might seem [8]. In this paper we show a set of adaptive fuzzy rules can be used to identify voxels based upon their feature space characteristics. Essentially, relative intensities are used.
Our approach is applied to MR images in the axial plane, Figure 1. The features used are the intensities of each voxel in a T1 weighted, T2 weighted and proton density (PD) weighted image of a 5mm thick slab Figure 2. The feature images are acquired in one session and no head movement is allowed.
A set of fuzzy rules is adapted to an image by creating the antecedent fuzzy sets from identifiable points on the histograms of the three feature images. The histogram of a feature may be translated into a fuzzy set because each tissue has a set of intensity levels and the tissues lie next to one another in feature space. Due to partial volume effects, the voxels may contain mixed tissue types, the tissues overlap in feature space. This overlap naturally suggests fuzzy set coverage, if the intensity values that mark the change from one tissue type to another can be identified.
The rules classify an image into six classes; white matter, gray matter, cerebro-spinal fluid (csf), pathology, skull tissues and background (air). The system has been tested on 105 slices from 15 subjects. In the next section, the fuzzy rules and the adaptation process are described. This is followed by a description of the experiments and an analysis of experimental results when compared with clustering using the fuzzy c-means algorithm. A summary discusses the utility of this kind of approach to image segmentation.
