Discrete & Computational Geometry
Topology for Computing
Form representions and means for landmarks: A survey and comparative study
Computer Vision and Image Understanding
Lipschitz Functions Have L p -Stable Persistence
Foundations of Computational Mathematics
Persistent homology: an introduction and a new text representation for natural language processing
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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A method for the use of persistent homology in the statistical analysis of landmark-based shape data is given. Three-dimensional landmark configurations are used as input for separate filtrations, persistent homology is performed, and persistence diagrams are obtained. Groups of configurations are compared using distances between persistence diagrams combined with dimensionality reduction methods. A three-dimensional landmark-based data set is used from a longitudinal orthodontic study, and the persistent homology method is able to distinguish clinically relevant treatment effects. Comparisons are made with the traditional landmark-based statistical shape analysis methods of Dryden and Mardia, and Euclidean Distance Matrix Analysis.