Joint Histograms

A joint histogram is a useful tool for visualizing the relationship between the intensities of corresponding voxels in two or more images. Such histograms are widely used with multi-spectral data (e.g., dual echo MR images) as the basis for statistical classifiers for image segmentation, and are used as co-occurrence matrices for texture analysis. For two images A and B, the joint histogram is two-dimensional and is constructed by plotting the intensity a of each voxel in image A against the intensity b of the corresponding voxel in image B. The value of each histogram location h(a, b) will therefore correspond to the number of image voxels with intensity a in modality A and intensity b in modality B. For the dual echo MR image just mentioned, there are the same number of voxels in each image, and there is complete overlap between image volumes. When a joint histogram is being produced from two images of different modalities, the resolution and field of view are likely to be different. Before calculating a joint histogram, it is necessary to resample one of the images so that they both have the same sample spacing, and it is also necessary to

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