Criticisms of Mutual Information

Mutual information and its normalized variants have been criticized for failing to take account of the spatial coherence of information in images. By analogy with communication theory, all the voxel values are sent down a communication channel one after another, with all spatial information about their relative positions being lost. This can be nicely illustrated

3An affine transformation maps parallel lines to parallel lines. It includes skew and scaling as well as the rigid body degrees of freedom.

FIGURE 4 Example unregistered sagittal images that can be registered using mutual information.

FIGURE 5 (Top row) Unregistered MR (left) and CT (right) images. The MR images are shown in the original sagittal plane and reformatted coronal plane; the CT images, in the original oblique plane and reformatted sagittal plane. Note the different field of view of the images. (Bottom row) MR images in sagittal, coronal, and axial planes with the outline of bone, thresholded from the registered CT scan, overlaid. The registration transformation has 10 degrees of freedom to correct for errors in the machine-supplied voxel dimensions and gantry tilt angle.

FIGURE 5 (Top row) Unregistered MR (left) and CT (right) images. The MR images are shown in the original sagittal plane and reformatted coronal plane; the CT images, in the original oblique plane and reformatted sagittal plane. Note the different field of view of the images. (Bottom row) MR images in sagittal, coronal, and axial planes with the outline of bone, thresholded from the registered CT scan, overlaid. The registration transformation has 10 degrees of freedom to correct for errors in the machine-supplied voxel dimensions and gantry tilt angle.

by randomizing the positions of all voxels in an image, such that it looks like noise. Provided the same randomization function is applied to both images being registered, the mutual information will be unchanged. For image registration, it is not a single value of mutual information that is of interest, i.e., the value of mutual information of just one estimate of the image transformation T. Rather, it is the change in mutual information as T is iterated that influences the success of the measure. There is, therefore, some implicit spatial information involved in registration by maximizing mutual information because the spatial transformation estimates are being changed. There are, nevertheless, examples of data that mutual information cannot register. Clinical scenarios in which this arise include registration of a very small number of slices of one image with a second. In this case the joint PDF is quite sparse, and there are too few voxels to estimate mutual information robustly. Also, although mutual information is fairly robust to shading across images, frequently caused by RF inhomogeneity in MR scans, it can fail to register images where the shading is very severe. In this case there is no functional relationship between the intensity values of an object in both images. It is also easy to design a pair of simulated images that mutual information fails to register in a sensible way. Figure 8 is an example put forward by Roche et al. [30]. In this example, there would appear to be an intuitively correct translation that would correctly align the images, yet mutual information produces multiple identical maxima with a period of one pixel.

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