F approach proposal and comparisons of methods used in missing landmark estimation

Statistical shape analysis involves methods that use geometric information obtained from objects. The most important input to the use of geometric information in statistical shape analysis is landmarks. Missing data in shape analysis occurs when there is a loss of information about landmark coordinates. The loss of data in the cartesian coordinates of landmarks makes that landmark unusable and causes the releated unit to be dropped out of the survey. Performances are evaluated for the following methods used in the estimation of missing data; EM algorithm, multiple regression imputation, Bayesian principal component analysis, probabilistic principal component analysis, Inverse non-linear principal component analysis, non-linear estimation by iterative partial least squares principal component analysis and proposed Min(F) and Max(F) approaches in the thesis. Landmark counts were taken as 3, 6, 9, 12 and sample sizes were taken as 30, 50, 100 in the simulation study. The data are generated based on multivariate normal distribution from isotropic and non-isotropic models and 10 different simulation scenarios are considered. The best and the most different result in the performance evaluation according to small, medium and large sample sizes is the Min(F) criterion of the F-approximation algorithm proposed in the thesis study.