Fig. 1.

An overview of the AdaBoost algorithm. The x vectors are the feature vectors at each voxel (there are N voxels), and the y values are the ground truth classifications (+1 for hippocampus, −1 for non-hippocampus). Weak learners are defined to be classifiers that give binary outputs regarding a voxel’s class, based on one single feature and a threshold value for that feature. Weak learners are classification functions based on any feature that can help to classify a structure correctly with an accuracy slightly better than chance. The algorithm gives an update rule for the weightings given to each of the labeled examples, in training this set of weak learners, and the epsilon terms are the sum of the weights. The D_t vector represents the importance of each example, and examples misclassified at one iteration of the algorithm receive more weight on subsequent iterations, and those that are correctly classified receive less weight in the subsequent iterations. 1 is an indicator function, returning 1 if the expression is true and 0 otherwise. The function f is a function combining the outputs of all the weak learners using weights (the alpha terms). P is a probability function that gives the Bayesian maximum a posteriori (MAP) estimate of the labeling (Morra et al., 2008c). The H function thresholds the posterior distribution P at the threshold of 1/2, returning a decision as to whether each voxel x belongs to the hippocampus (1 for yes and 0 for no).