Zhou Shaohua Kevin, Aggarwal Gaurav, Chellappa Rama, Jacobs David W
Integrated Data Systems Department, Siemens Corporate Research, Princeton, NJ 08540, USA.
IEEE Trans Pattern Anal Mach Intell. 2007 Feb;29(2):230-45. doi: 10.1109/TPAMI.2007.25.
Traditional photometric stereo algorithms employ a Lambertian reflectance model with a varying albedo field and involve the appearance of only one object. In this paper, we generalize photometric stereo algorithms to handle all appearances of all objects in a class, in particular the human face class, by making use of the linear Lambertian property. A linear Lambertian object is one which is linearly spanned by a set of basis objects and has a Lambertian surface. The linear property leads to a rank constraint and, consequently, a factorization of an observation matrix that consists of exemplar images of different objects (e.g., faces of different subjects) under different, unknown illuminations. Integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account. The effectiveness of the linear Lambertian property is further investigated by using it for the problem of illumination-invariant face recognition using just one image. Attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in Lambert's law. This enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources. Experimental results using standard data sets are presented.
传统的光度立体算法采用具有变化反照率场的朗伯反射模型，并且只涉及单个物体的外观。在本文中，我们通过利用线性朗伯特性，将光度立体算法进行推广，以处理一类中所有物体的所有外观，特别是人脸类别。线性朗伯物体是由一组基物体线性张成且具有朗伯表面的物体。这种线性特性导致一个秩约束，进而导致对一个观测矩阵进行分解，该观测矩阵由不同物体（例如不同主体的面部）在不同的、未知光照下的示例图像组成。利用可积性和对称性约束，通过一种考虑了变化反照率场的新颖线性化算法来完全恢复子空间基。通过将线性朗伯特性用于仅使用一幅图像的光照不变人脸识别问题，进一步研究了其有效性。通过仔细处理朗伯定律中固有的非线性，将附着阴影纳入模型。这使我们能够扩展算法，以便在存在多个光照源的情况下进行人脸识别。给出了使用标准数据集的实验结果。
