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Statistical shape and texture appearance models are powerful image representations, but previously had been restricted to 2D or 3D shapes with smooth surfaces and lambertian reflectance. In this thesis we present a novel 4D appearance model using image-based rendering techniques, which can represent complex lighting conditions, structures, and surfaces. We construct a light field manifold capturing the multi-view appearance of an object class and extend previous direct search algorithms to match new light fields or 2D images of an object to a point on this manifold. When matching to a 2D image the reconstructed light field can be used to render unseen views of the object. Our technique differs from previous view-based active appearance models in that model coefficients between views are explicitly linked, and that we do not model any pose variation within the deformable model at a single view. It overcomes the limitations of polygonal based appearance nodels and uses light fields that are acquired in real-time