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 al-ternative approaches, they suffer from two major limita-tions: First, PCA cannot model non-linear structure in the data. Second, learning PAMs requires precise manually la-beled training data. This paper proposes Parameterized Kernel Principal Component Analysis (PKPCA), an exten-sion 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 perfor-mance 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. 1