The Dimensionality of Scene Appearance

Low-rank approximation of image collections (e. g., via PCA) is a popular tool in many areas of computer vision. Yet, surprisingly little is known justifying the observation that images of an object or scene tend to be low dimensional, beyond the special case of Lambertian scenes. This paper considers the question of how many basis images are needed to span the space of images of a scene under real-world lighting and viewing conditions, allowing for general BRDFs. We establish new theoretical upper bounds on the number of basis images necessary to represent a wide variety of scenes under very general conditions, and perform empirical studies to justify the assumptions. We then demonstrate a number of novel applications of linear models for scene appearance for Internet photo collections. These applications include, image reconstruction, occluder-removal, and expanding field of view.