Subspace Regression: Predicting a Subspace from One Sample

Subspace methods have been extensively used to solve a variety of problems in computer vision including object detection, recognition, and tracking. Typically, subspaces are learned from a training set that contains different configurations of a particular object (e.g., variations on shape or appearance). However, in some situations it is not possible to have access to data with multiple configurations of an object. For instance, consider the problem of predicting a person-specific subspace of the pose variation from only a frontal face image, by learning a mapping between frontal images and the corresponding pose subspaces in training samples. We refer to this problem as subspace regression. Subspace regression is a challenging problem for two main reasons: (i) it involves a mapping between high-dimensional spaces, (ii) it is unclear how to parameterize the mapping between one sample and a subspace. We propose four methods to learn a mapping from one sample to a subspace: Individual Mapping on Images, Direct Mapping to Subspaces, Regression on Subspaces, and Direct Subspace Alignment. We show the validity of our approaches to build a person-specific face subspace of pose or illumination, and its applications to face tracking and recognition.