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 frequency-space 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 lower-dimensional bilinear subspace. Results show significant impact on dimensionality reduction with minimal loss of information as well as robustness against noise.