Generalizing the Majority Voting Scheme to Spatially Constrained Voting

Generating ensembles from multiple individual classifiers is a popular approach to raise the accuracy of the decision. As a rule for decision making, majority voting is a usually applied model. In this paper, we generalize classical majority voting by incorporating probability terms pn,k to constrain the basic framework. These terms control whether a correct or false decision is made if k correct votes are present among the total number of n. 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. In this scenario, the terms pn,k can be specialized by a geometric constraint. Namely, the votes should fall inside a region matching the size and shape of the object to vote together. We give several theoretical results in this new model for both dependent and independent 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 to demonstrate the characterization capability of this system. We also investigate how the generalized model can help us to improve an ensemble with extending it by adding a new algorithm.