A spatial discrepancy measure between voxel sets in brain imaging

Functional Magnetic Resonance Imaging serves to identify networks and regions in the brain engaged in various mental activities, represented as a set of voxels in the 3D image. It is important to be able to measure how similar two selected voxel sets are. The major flaw of the currently used correlation-based and overlap-based measures is that they disregard the spatial proximity of the selected voxel sets. Here, we propose a measure for comparing two voxel sets, called Spatial Discrepancy, based upon the average Hausdorff distance. We demonstrate that Spatial Discrepancy can detect genuine similarities and differences where other commonly used measures fail to do so. A simulation experiment was carried out where distorted copies of the same voxel sets were compared, varying the level of distortion. The experiment revealed that the proposed measure correlates better with the level of distortion than any of the other measures. Data from a 10-subject experiment were used to demonstrate the advantages of the Spatial Discrepancy measure in multi-subject studies.