Landmark-based algorithms for group average and pattern recognition.

Highlights • A robust landmark-based algorithm for finding the geometric median (group average) of a group of shapes with heavy outliers is proposed. • The underlying Log and Exp maps of the proposed algorithm belong to a class of efficient geodesic shooting algorithms for template matching. • Once the group average is found, the Hamiltonian metric computed between the group average and each member of the group can be used for clustering analysis. • The proposed algorithms, as a tool of feature extraction, extract information about momentum at each landmark during the process of finding the geometric median. • The local momenta found by the proposed algorithm are useful for some classification purposes that cannot be achieved by using the landmark locations. Abstract We introduce a class of mathematical algorithms with the aim of establishing a framework of finding a group average and extracting prominent features in a group of landmark represented shapes or image templates. A group average is an estimator that is said to best represent the common features of the group being studied. The proposed algorithms, as a tool of feature extraction, extract information about momentum at each landmark through the process of template matching. Once the convergence criterion is satisfied numerically, the algorithms produce a group average and a local coordinate system for each member of the observing group, in terms of the residual momentum. We present several examples to illustrate the use of the proposed algorithms for finding a group average. Using the metrics computed between the group average and each member of the group, we successfully run a cluster analysis for datasets that contain a heavy percentage of outliers. Finally, we apply the collected residual momenta computed in the proposed algorithms in some statistical methods to demonstrate a potential application of the algorithms for detecting structure abnormality. [ABSTRACT FROM AUTHOR]