Two experiments were designed to evaluate the performance of the QHCF algorithm. The first experiment used a phantom image to determine segmentation

Figure 8.4: A phantom study of the MRF segmentation problem with adaptive ICM and QHCF. (a) Original phantom image. (b) Phantom is processed with additive Gaussian random noise. (c) Segmented image with Pappas' adaptive ICM algorithm. (d) Segmented result with proposed QHCF algorithm. (e) The difference between (a) and (c). Number of dark pixels is 120. (f) The difference image between (a) and (d). Number of dark pixels is 92.

accuracy. In this study, a phantom was used as the ground truth shown in Fig. 8.4(a). By applying additive Gaussian noise, a test image was created as shown in Fig. 8.4(b). It was segmented with adaptive ICM [20] and the QHCF algorithms individually. The results are shown in Figs. 8.4(c) and 8.4(d). Comparison of the segmented images with the original phantom images yielded difference images (Figs. 8.4(e) and 8.4(f)). QHCF had 92 pixel errors, while adaptive ICM had 120 pixel errors. Ten phantom image comparisons had been conducted and the QHFC algorithm sustained 24.7% fewer edge pixel errors than the ICM algorithm. We can also see from the shape of the ICM-segmented object that merging of the two parts has occurred, while the proposed QHFC algorithm sustains the separation. This is due to the edge constraint in the QHCF energy function that makes it more sensitive at boundaries. However, in the analysis of the difference image (Fig. 8.4(f)) we note that most errors occur at the boundary of the segments creating a rough contour. Further work is indicated to solve this problem.

The second experiment was designed to evaluate the sensitivity of the segmentation result with differing initial conditions. We compared QHCF and uniform grid initialized HCF [19] (UGHCF) on human carotid MR images with a size of 128 pixels by 128 pixels. As UGHCF needs a predefined grid size, we chose 10, 20, and 30 pixels respectively. For the QHCF algorithm, the standard deviation of Quad-Tree region's intensity was used as RC Vrc, and the threshold was adjusted at 5, 10, and 20 intensity levels, respectively. Other constraint parameters, such as p1 and p2 have same values for the two algorithms. Figure 8.5 is an example of the segmentation result processed with the above initial conditions. Although the overall performance of the two segmentation results seem quite similar given various input RC values, QHCF gives more consistent results than UGHCF (for example, the partitioned regions within the white dotted line circles are stable in QHCF under differing initialization).

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