Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing

The workshop successfully brought together researchers from mathematical analysis, numerical mathematics, computer graphics and image processing. The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image and surface fairing, physical modeling of surfaces, the restoration of images and surfaces using higher order variational formulations

Surface-bounded growth modeling applied to human mandibles

From a set of longitudinal three-dimensional scans of the same anatomical structure, we have accurately modeled the temporal shape and size changes using a linear shape model. On a total of 31 computed tomography scans of the mandible from six patients, 14851 semilandmarks are found automatically using shape features and a new algorithm called geometry-constrained diffusion. The semilandmarks are mapped into Procrustes space. Principal component analysis extracts a one-dimensional subspace, which is used to construct a linear growth model. The worst case mean modeling error in a cross validation study is 3.7 mm

Generalizations, extensions and applications for principal component analysis

Principal component analysis (PCA) is one of the most important dimension reduction technique. It is widely used in many applications including economics, finance and medical research. In this research, several novel generalizations of PCA are proposed to adapt the technique to more complicated scenarios. In the first project, we propose a principal surface model for manifold-like datasets in 3D space. In the second part, a new concept of graphical intra-class correlation coefficient (GICC) is defined and a Markov Chain Monte Carlo Expectation-Maximization (mcmcEM) algorithm is used for likelihood optimization. In the third part, we propose multilevel binary principal component analysis (MBPCA) models for finding the principal components of multilevel binary dataset. A variational expectation maximization algorithm is used for likelihood optimization