A Design Method for Relaxation Labeling Applications

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A Design Method for Relaxation Labeling Applications
Robert a Hummel
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. That we seek: for i and j distinct neighbors, we set a = r. . (1, 1) and b = r. . (1, 2). Applying the conditions for strict consistency to each of the patterns listed above leads to the single condition a > b.
What other unambiguous local patterns are consistent in this scheme? Let n, be the number of 1-labels among the six neighbors of a central object, and n2 be the number of 2-labels. Then the support for label 1 is s(l) = anj^ + bn2 and the supporc for label 2 is s(2) = an2 + bn, . A loc
...al pattern with a central object labeled with a "1" is strictly consistent if s(l) > s(2)> ieec, n^^ > . 19. (Note that a-b > 0). Similarly, "2" is consistent for the central object of a local pattern if n2 > ni.
Remarkably, the same set of patterns are consistent whatever the values of a and b, as long as a > b. This confirms empirical evidence of the robustness of simple relaxation labeling applications to modifications of the compatibilities.
A global unambiguous labeling will be strictly consistent in this model if every object is labeled with the majority label as voted by the six neighbors.


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