Parameterized kernel principal component analysis: Theory and applications to supervised and unsupervised image alignment

Parameterized Appearance Models (PAMs) (e.g. eigen-tracking, active appearance models, morphable models) use Principal Component Analysis (PCA) to model the shape and appearance of objects in images. Given a new image with an unknown appearance/shape configuration, PAMs can detect and track the object by optimizing the model's parameters that best match the image. While PAMs have numerous advantages for image registration relative to alternative approaches, they suffer from two major limitations: First, PCA cannot model non-linear structure in the data. Second, learning PAMs requires precise manually labeled training data. This paper proposes Parameterized Kernel Principal Component Analysis (PKPCA), an extension of PAMs that uses Kernel PCA (KPCA) for learning a non-linear appearance model invariant to rigid and/or non-rigid deformations. We demonstrate improved performance in supervised and unsupervised image registration, and present a novel application to improve the quality of manual landmarks in faces. In addition, we suggest a clean and effective matrix formulation for PKPCA.