Test Model

The test model is one dimensional and consists of 2 known shapes, an area of unknown intensity and some background. Only global translation will be considered for the spatial transformation, $T$. The sizes and intensities of the shapes are shown in figure 3. Note that the contrast between shapes 1 and 2 is quite small, which is typical in many applications. The measured image is taken to have 256 voxels, each of 1mm width. The position of the field of view of the measured image is varied across the object, over a 100mm range, to demonstrate the effect of partial object-image overlap on the similarity functions.

The portion of the object to the left of shape 1 is modelled using a set of small `voxel-shapes' (each 1mm wide) to account for unknown object structure in this region. To the right of shape 3 there is no object and this is therefore modelled by a single extra shape to account for potential constant background intensity (common in MRI where the background noise is strictly Rician, not Gaussian, and hence not zero mean).

Figure 3: Shape model used for the experimental tests.