Learning bilinear models for two-factor problems in vision

In many vision problems, we want to infer two (or more) hidden factors which interact to produce our observations. We may want to disentangle illuminant and object colors in color constancy; rendering conditions from surface shape in shape-from-shading; face identity and head pose in face recognition; or font and letter class in character recognition. We refer to these two factors generically as "style" and "content". Bilinear models offer a powerful framework for extracting the two-factor structure of a set of observations, and are familiar in computational vision from several well-known lines of research. This paper shows how bilinear models can be used to learn the style-content structure of a pattern analysis or synthesis problem, which can then be generalized to solve related tasks using different styles and/or content. We focus on three tasks: extrapolating the style of data to unseen content classes, classifying data with known content under a novel style, and translating data from novel content classes and style to a known style or content. We show examples from color constancy, face pose estimation, shape-from-shading, typography and speech.