Alignment and Atlases

-74-Hellinger Metric• MI can be thought of as measuring a ʻdistanceʼ between two 2D histograms: thejoint distribution {r ij } and the product distribution {p i ⋅q j } MI is not a ʻtrueʼ distance: it doesnʼt satisfy triangle inequality d(a,b)+d(b,c) >d(a,c)• Hellinger metric is a true distance in distribution “space”: HM = Σ ij [ √r ij – √(p i ⋅q j ) ] 2 3dAllineate minimizes –HM with -cost hel This is the default cost functionbca