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Example

Consider a toy example in 1D, as shown in figure 1. In the example there are two shapes, $ S_1$ and $ S_2$, each of different size (length) which results in the generation of four different $ G$ vectors: $ G_1(S_1)$ to $ G_2(S_2)$. Note that at the interface between the shapes, the values of $ G_1$ are between 0.0 and 1.0, representing the partial volume fraction. The transformation, $ T$, effects both the global position (and stretching) of the shapes in the image as well as the partial volume fractions.

Figure 1: Example of image model formation in 1D. The two shapes, $ S_1$ and $ S_2$, cover ten image voxels (indicated by vertical dashed lines) and generate four different $ G$ vectors: $ G_1(S_1)$ which represents the mean intensity (partial volume component) of $ S_1$; $ G_2(S_1)$ which represents the a linear intensity change across $ S_1$ (in the x-direction); and similarly for $ S_2$. The middle voxel is a partial volume voxel and shows how both the mean and linear components are multiplied by the appropriate partial volume fraction. Furthermore, note that the linear components are zero mean. Note that in 3D there would also be linear intensity changes across the y-direction and z-direction, represented by $ G_3$ and $ G_4$.
\includegraphics[width=0.7\textwidth]{egmodel.eps}


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Next: Probabilistic Forms Up: Image Generators Previous: Image Generators