Learning Low Dimensional Invariant Signature of 3-D Object under Varying View and Illumination from 2-D Appearances

In this paper, we propose an invariant signature representation for appearances of 3-D object under varying view and illumination, and a method for learning the signature from multi-view appearance examples. The signature, a nonlinear feature, provides a good basis for 3-D object detection and pose estimation due to its following properties: (1) Its location in the signature feature space is a simple function of the view and is insensitive or invariant to illumination. (2) It changes continuously as the view changes, so that the object appearances at all possible views should constitute a known simple curve segment (manifold) in the feature space. (3) The coordinates of the object appearances in the feature space are correlated in a known way according to a predefined function of the view. The first two properties provide a basis for object detection and the third for view (pose) estimation. To compute the signature representation from input, we present a nonlinear regression method for learning a nonlinear mapping from the input (e.g. image) space to the feature space. The ideas of the signature representation and the learning method are illustrated with experimental results for the object of human face. It is shown that the face object can be effectively modeled compactly in a 10-D nonlinear feature space. The 10-D signature presents excellent insensitivity to changes in illumination for any view. The correlation of the signature coordinates is well determined by the predefined parametric function. Applications of the proposed method in face detection and pose estimation are demonstrated.