Goodness of Prediction for Principal Components of Shape A Correlation Measure

The wide variety of statistical shape models available in image analysis and computer vision calls for some criteria and procedure to evaluate them for their effectiveness. In this paper, we introduce a formal correlation measure called goodness of prediction that allows evaluating statistical shape models in terms of their predictive power: the ability to describe an unseen member of the population. Most applications of statistical shape models such as segmentation and classification rely on their predictive power particularly heavily. The correlation measure is designed to analyze statistical shape models that use principal component analysis (PCA) to characterize shape variability. As some geometric shape representations like the m-rep do not form a vector space, the correlation measure initially defined in linear vector space is generalized to a nonlinear manifold by interpreting the measure in terms of geodesic distance in space. Through a systematic procedure for calculating the measure, we analyze the predictive power of statistical shape models as a function of training sample size. Our approach is demonstrated with two different shape representations: the Supported primarily by NCI P01 CA47982, R01 CA095749-01A1 and NIBIB EB000219 Ja-Yeon Jeong · Xiaoxiao Liu · Stephen M. Pizer Medical Image Display & Analysis Group, University of North Carolina, Chapel Hill, NC USA Ja-Yeon Jeong e-mail: jeong@cs.unc.edu, jayeon.j@gmail.com Surajit Ray Department of Mathematics and Statistics, Boston University, Boston, MA USA Qiong Han Center for Visualization & Virtual Environments Lexington, KY USA Keith E. Muller Epidemiology and Health Policy Research, University of Florida, Gainesville, FL USA m-rep and the point distribution model. Our experiment results show the usefulness and the benefit of our evaluation method.