Shape Priors by Kernel Density Modeling of PCA Residual Structure

Modern image processing techniques increasingly use prior models of the expected distribution of objects. Principal component eigen-models are often selected for shape prior modeling, but are limited in capturing only the second order moment statistics. On the other hand, kernel densities can in concept reproduce arbitrary statistics, but are problematic for high dimensional data such as shapes. An evident approach is to combine these methods, using PCA to reduce the problem dimensionality, followed by kernel density modeling of the PCA coefficients. In this paper we show that useful algorithmic and editing operations can be formulated in term of this simple approach. The operations are illustrated in the context of point distribution shape models. Particular points can be rapidly evaluated as being plausible or outliers, and a plausible shape can be completed given limited operator input in a manually guided procedure. This "PCA+KD" approach is conceptually simple, scalable (becoming increasingly accurate with additional training data), provides improved modeling power, and supports useful algorithmic queries.