Analytic Bilinear Appearance Subspace Construction for Modeling Image Irradiance under Natural Illumination and Non-Lambertian Reflectance

Conventional subspace construction approaches suffer from the need of "large-enough" image ensemble rendering numerical methods intractable. In this paper, we propose an analytic formulation for low-dimensional subspace construction in which shading cues lie while preserving the natural structure of an image sample. Using the frequencyspace representation of the image irradiance equation, the process of finding such subspace is cast as establishing a relation between its principal components and that of a deterministic set of basis functions, termed as irradiance harmonics. Representing images as matrices further lessen the number of parameters to be estimated to define a bilinear projection which maps the image sample to a lowerdimensional bilinear subspace. Results show significant impact on dimensionality reduction with minimal loss of information as well as robustness against noise.