  Principal component analysis (PCA) is a popular tool for linear
dimensionality reduction and feature extraction. Kernel PCA is the nonlinear
form of PCA, which better exploits the complicated spatial structure of
high-dimensional features. In this paper, we first review the basic ideas of
PCA and kernel PCA. Then we focus on the reconstruction of pre-images for
kernel PCA. We also give an introduction on how PCA is used in active shape
models (ASMs), and discuss how kernel PCA can be applied to improve traditional
ASMs. Then we show some experimental results to compare the performance of
kernel PCA and standard PCA for classification problems. We also implement the
kernel PCA-based ASMs, and use it to construct human face models.
