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- In mathematics, the matching distance is a metric on the space of size functions. The core of the definition of matching distance is the observation that theinformation contained in a size function can be combinatorially stored in a formal series of lines and points of the plane, called respectively cornerlines and cornerpoints. Given two size functions and , let (resp. ) be the multiset ofall cornerpoints and cornerlines for (resp. ) counted with theirmultiplicities, augmented by adding a countable infinity of points of thediagonal . The matching distance between and is given bywhere varies among all the bijections between and and Roughly speaking, the matching distance between two size functions is the minimum, over all the matchingsbetween the cornerpoints of the two size functions, of the maximumof the -distances between two matched cornerpoints. Sincetwo size functions can have a different number of cornerpoints,these can be also matched to points of the diagonal . Moreover, the definition of implies that matching two points of the diagonal has no cost. (en)
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- In mathematics, the matching distance is a metric on the space of size functions. The core of the definition of matching distance is the observation that theinformation contained in a size function can be combinatorially stored in a formal series of lines and points of the plane, called respectively cornerlines and cornerpoints. Given two size functions and , let (resp. ) be the multiset ofall cornerpoints and cornerlines for (resp. ) counted with theirmultiplicities, augmented by adding a countable infinity of points of thediagonal . (en)
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