96	D.P. Costello and P.A. Kenny

Yang et al. [35] proposed the use of overlapping mosaics to segment fat in MR images affected by intensity inhomogeneities. This segmentation technique is an example of adaptive thresholding and is discussed further in Sect. 5.4.6.

5.4 Overview of Segmentation Techniques Used to Isolate Fat

Most of the segmentation algorithms discussed in this section are ‘hard segmentation algorithms’, i.e. a definite label is assigned to every voxel in the image (e.g. fat or non-fat). Some consideration will be given to soft segmentation algorithms and their usefulness in dealing with the PVE. These algorithms take into consideration the proportion of each tissue type in every voxel.

Once an image has been segmented, the volume of fat (VF) contained within an image is calculated using:

VFat = NFat Voxels ×Vvoxel.

(5.3)

where NFat Voxels is the number of voxels classified as fat in the image and Vvoxel is the volume of a single voxel. The total fat in kilograms can be calculated by multiplying this value by the density of fat [15].

5.4.1 Thresholding

Thresholding is the simplest forms of image segmentation. It is a real-time segmentation technique that is both fast and computationally inexpensive. Thresholding transforms a gray-scale image f (i, j), into a binary image g(i, j), based on a threshold value, T . The process is summarized as:

g(i, j) = 1	for f (i, j) > T,
g(i, j) = 0	for f (i, j) ≤ T.	(5.4)

In its simplest form thresholding is a manual process in which the user interactively selects a threshold value (T ), based on the distribution of gray-levels in the image histogram, to create a binary image similar to those shown in Fig. 5.5.

Manual thresholding, like all subjective processes, is open to inter and intraoperator variability. Figure 5.5c, d are examples of alternative segmentation results that were obtained using alternative threshold values.

At the outset, some authors used manual thresholding to quantify fat in MR image. However, in an effort to reduce subjectivity, Chan et al. [11] set a strict protocol for threshold selection. The threshold was selected as the minima between the soft tissue and fat peaks in the image histogram. Chan’s method shows good correlation with BMI for a sample group of patients [11]. One drawback of this

5 Fat Segmentation in Magnetic Resonance Images

97

Fig. 5.5 (a) T1-Weighted GE image (b) manually thresholded image (c) over-thresholded (d) under-thresholded (e) image histogram

approach is that MR image histograms can have multiple minima between tissue peaks as a result of random noise and inhomogeneities. This can cause ambiguity when manually selecting a threshold value. Another approach used in the literature is to preset a threshold for all subjects based on the manual analysis of a group of healthy controls [13, 36]. This system of segmentation is very rigid and can require user interaction to reclassify mislabelled pixels [13]. One way to avoid variability is to automate the process of thresholding to select an optimum threshold value.

5.4.2 Selecting the Optimum Threshold

Subjectively choosing an image threshold is a relatively simple task. However, the objective selection of an optimum threshold can be much more complex. Many

98	D.P. Costello and P.A. Kenny

algorithms have been developed for the automated selection of optimum thresholds (see, e.g., Zhang et al. [37], Sezgin et al. [38]). Six categories of automated thresholding, including histogram shape information, clustering and entropy methods have been proposed [38]. Histogram–shape–based methods threshold an image based on the peaks, valleys, or curvature of the smoothed images histogram. Clustering–based methods group the elements of an image histogram into two or more tissue classes based on a predefined model. A variety of techniques have been proposed in the literature for automatic threshold selection in gray-scale images. These methods include shape-based algorithms including peak and valley thresholding [39, 40] and clustering methods such as the Otsu method [41].

The Otsu method is one of the most referenced thresholding methods in the literature for finding an optimal threshold [41,42]. This method is a non-parametric, unsupervised clustering algorithm used for the automatic selection of an optimal threshold [41]. Optimal thresholds are calculated by minimizing the weighted sum of within-class variance of the foreground and background pixels. The weighted sum of within-class variance, σw2, can be expressed as:

σw2 = Wbσ 2	+ Wf σ 2	,	(5.5)
b	f

where Wb and Wf are the number of voxels in the background and foreground, respectively, and σb2 and σ f2 are the variance in the background and foreground.

Otsu’s thresholding is an iterative algorithm which calculates all possible threshold values for the image and the corresponding variance on each side of the

threshold. The threshold is then set as the value which gives the maximum value for σw2.

Otsu Algorithm

•Compute histogram

•Set up initial threshold value

•Step through all possible thresholds

– Compute σw2 for each one

•The optimum threshold corresponds to the maximum σw2

Thresholding using this method gives satisfactory results when the number of voxels in each class is similar. MR images used for the analysis of body fat usually contain at least three tissue classes, soft tissue, fat and background. An extension of the Otsu method known as Multilevel Otsu thresholding can be used to segment images with more than two tissue classes. The Otsu method was used in Fig. 5.6 to segment fat, soft tissue and background.

Using Multilevel Otsu thresholding complete segmentation is not always possible as illustrated in Fig. 5.6b. To compensate, a morphological hole–filling operation was carried out resulting in Fig. 5.6c. Lee and Park [43] found that when foreground area in an image is small relative to the background, segmentation errors will occur. The Otsu method also breaks down in images with a low SNR.

5 Fat Segmentation in Magnetic Resonance Images

99

Fig. 5.6 (a) T1w GE image containing fat and soft tissue, (b) image segmentation using a MultiOtsu method and (c) segmented image corrected using morphological operator

In MRI, the water signal can sometimes obscure the fat peak in the image histogram and make it difficult to use histogram–based global–segmentation techniques to locate the optimum threshold. WS sequences such as b-SSFP (or FISP) and T1w FSE can be used to simplify the image segmentation process [19]. Peng et al. [19] compared Water-suppressed T1w TSE and WS b-SSFP and found that SNR and contrast were superior in WS b-SSFP. In later work, Peng et al. [44] introduced a simple automated method to quantify fat in water saturated MR images. This technique is based on an ideal model of the image histogram and global thresholding. Figure 5.7 illustrates the effect of water saturation on the image histogram.

Peng’s segmentation model assumes that all voxels beyond the peak fat value (Smax) in Fig. 5.7e are fat and all voxels between 0 and Smax are partial volume fat voxels. On average, partial volume fat voxels are 50% fat [16]. Therefore, the threshold value, Sth, is set to Smax/2. Once a threshold value is calculated classification of subcutaneous and visceral fat is completed manually. Using water– saturated MR images removes the obstacle of overlapping peaks from the image histogram, which facilitates simple thresholding. Segmentation results shown in Fig. 5.7e, f are very different because of the improved contrast in (d), demonstrating that an optimal imaging protocol can greatly simplify the segmentation process.