Summary: Principal component analysis models are widely used to model shapes in medical image analysis, computer vision, and other fields. The “Laplacian” spline approaches including thin-plate splines are also used for this purpose. These alternative approaches have complementary advantages and weaknesses: a low-rank principal component analysis model has some “knowledge” of the data being modeled, but cannot exactly fit arbitrary data, whereas spline models can fit arbitrary data but have only a generic smoothness assumption about the character of the data. In this contribution we show that the data fitting problem for these two approaches can be put into a common form, by making use of a relation between the data covariance and the Laplacian. This suggests the possibility of a unified approach that combines the advantages of each.
For the entire collection see [Zbl 1300.00038].