Fig. 1

Illustration of the optimizations used in calculating the average distance(AVD). In 1 and 2, the images A and B, defined on the same grid, are to be compared using the AVD. In 3, the intersection of the images is identified. In 4, the pairwise distance between point in the intersection is zero, therefore these distances are excluded from the calculation. In 5, to find the minimum distance from a point in A to the the image B, only the boundary voxels of B are considered. In 6, likewise to find the minimum distance from a point in B to the A, only the boundary voxels of A considered. In 7 and 8, the boundary voxels of a real segmentation of the edema of a brain tumor. In 9, to reduce the search space when searching the nearest neighbor, a search sphere with radius r is found by moving from the query q toward the mean m and considering the first point crossed on the boundary