Limit laws for the diameter of a random point set

Appel, Martin J. B.; Najim, Christopher A.; Russo, Ralph P.

doi:10.1239/aap/1019160946

Cited by 14 publications

(1 citation statement)

References 6 publications

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“…The graph of p n,k for a fixed n with our geometric constraint to fall within a disc of diameter d OD . Figure 6 shows that the p n,k increase exponentially in k for a given n. This follows from the results of [21], [22] saying that the probability that the diameter of a point set is not less than a given constant decreases exponentially if the number of points tends to infinity. Note that, this diameter corresponds again to the diameter d OD of the OD.…”

Section: Constraining By Shape Characteristicsmentioning

confidence: 55%

Generalizing the Majority Voting Scheme to Spatially Constrained Voting

Hajdú

Hajdu

Jónás

et al. 2013

IEEE Trans. on Image Process.

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Abstract-Generating ensembles from multiple individual classifiers is a usual appraoch to raise the accuracy of the decision. For decision majority voting is a popular rule. In this paper, we generalize classic majority voting by letting a further constraint to decide whether a correct or false decision is made if k correct votes is present among the total n ones. This generalization is motivated by object detection problems, where the members of the ensemble are image processing algorithms giving their votes as pixels in the image domain. The shape of the desired object define a geometric constraint the votes should obey to be able to decide together. Namely, the votes in this scenarion should fall inside a region matching the shape of the object. We give several theoretical result in this new model for both dependent/indipendent classifiers, whose individual accuracies may also differ. As a real world example we present our ensemble-based system developed for the detection of the optic disc in retinal images. For this problem experimental results are shown on how our model is capable to characterize such a system and how the model can give a helping hand on the further improvability of the system, as well.

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Section: Constraining By Shape Characteristicsmentioning

confidence: 55%