## Image Generation Process

The model equation for generation of the observed image is shown in Eq. (9.16).

where n(x, y) ~ N(0, a2) and a2 is the variance of the noise. N is the Gaussian distribution. The output synthetic image using Gaussian image generation process is shown in the Fig 9.17.

Figure 9.18 shows eight different directions that the core class of the lumen can be with respect to the crescent moon class. The darkest region is the core

Figure 9.18: a2 = 500, all directions, large noise protocol. With respect to the center of the lumen area, the core class is shown in eight different orientations. In the top row, from right to left: east, northeast, north; in the second row: northwest, southeast, south; in the third row: southwest, west, west.

Figure 9.18: a2 = 500, all directions, large noise protocol. With respect to the center of the lumen area, the core class is shown in eight different orientations. In the top row, from right to left: east, northeast, north; in the second row: northwest, southeast, south; in the third row: southwest, west, west.

Figure 9.19: Images with 10 different variances using large noise protocol. The gray scale model is perturbed with variance (a2) varying from 100 to 1000. In the top row, from right to left: a2 = 100 and 200; in the second row: a2 = 300 and 400; in the third row: a2 = 500 and 600; in the fourth row: a2 = 700 and 800; in the fifth row: a2 = 900 and 1000.

Figure 9.19: Images with 10 different variances using large noise protocol. The gray scale model is perturbed with variance (a2) varying from 100 to 1000. In the top row, from right to left: a2 = 100 and 200; in the second row: a2 = 300 and 400; in the third row: a2 = 500 and 600; in the fourth row: a2 = 700 and 800; in the fifth row: a2 = 900 and 1000.

lumen, and the next lightest region that surrounds the core is the crescent moon class. Figure 9.19 shows the core class and the crescent moon class of the lumen with perturbation. The darkest region is the core lumen, and the next lightest region that surrounds the core is the crescent moon class. The variance (a2) was varied from 100 to 1000.

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