## 2 Materials and Methods
### Image Segmentation Methods for the Identification of Regions of Interest
#### 2.4.1 Image Segmentation with Threshold and Level Set Methods (TLSM)
Figure 9: Generation of automatic initial contour for the segmentation of gel-pad region: (**a**) The original MR image (upper part); (**b**) result of the application of the edge indicator function; (**c**) binary image obtained after the application of a threshold of 0.2 in a grayscale of 256 levels between 0 and 1; (**d**) complement of the mask obtained from the image in Figure 9c; (**e**) gel-pad area identification; (**f**) extracted gel-pad area (mask); (**g**) result of the application of the gel-pad mask in the original MR image; (**h**) the automatic initial contour obtained after the application of a threshold of 0 in a grayscale of 256 levels between 0 and 255; (**i**) final contour; (**j**) segmented MR image (upper part). After the segmentation of the air and gel-pad regions, a resulting region is enclosed between them. This region is the segmented tissue region, as shown in Figures 8d and 9j. Therefore, an appropriate segmentation of the tissue region depends on the performance of the segmentation methods for the air and gel-pad regions. Segmentation of Transducer and Water Regions  
The transducer region in the lower part of the MR image, shown in Figure 6b, was segmented in the same way as the gel-pad region, using two level set methods independently: the GAC method [7] and the DRLSE method [8]. In the GAC method, the constant velocity \(c\) can be varied, so it will be considered in the parametric study described in Section 2.6. Hereinafter this parameter will be called _c_transducer_. In the DRLSE method, the weighted area coefficient \(\alpha\) can be varied, so it will be considered in the parametric study described in Section 2.6. Hereinafter this parameter will be called _a_transducer_. The initial contour \(\phi_{0}\), for both the GAC and DRLSE methods, was the binary step function suggested in [8] and is defined as  
\[\phi_{0}(x)=\left\{ \begin{array}{cl}&-c_{0},&\text{ if }x\in R_{0}\\ &c_{0},&\text{ otherwise}\end{array} \right. \tag{10}\]  
where:  
\(c_{0}\) is a constant and \(c_{0}>0\). For this constant, a fixed value of 2 was considered. This value was used in the implementation for the DRLSE method reported in [10]. \(R_{0}\) is a region in the domain of the image. The obtained initial contour with the binary step function is shown in Figure 10a. The final contour has the shape of the found object as shown in Figure 10b, and the segmented region is shown in Figure 10c. The background of the segmented region is the water region. The threshold method was also used for the segmentation of the transducer region in the lower part of the MR image. From Figure 11a, a total of nine thresholds were equidistantly defined between the two maximal peaks in the histogram of the image, with the first and last defined thresholds as the two maximal peaks. A threshold, between the nine defined, can be chosen to perform segmentation as shown in Figure 11b, so it will be considered in the parametric study described in Section 2.6. Hereinafter this parameter will be called _Tn_transducer_. Finally, the segmented transducer is shown in Figure 11c. Figure 10: Segmentation of transducer region: (**a**) initial contour obtained from the binary step function; (**b**) final contour; (**c**) image with segmented transducer (shown in gray color). The segmented water region is the white background of this image. The final segmented image is built from the individual segmented regions. This image is shown in Figure 12.