Homogeneous Eigenspace for Photometric Analyses and Recognition

Eigenspaces are often utilized in computer vision for various applications. However, careful manipulations are required for sensitive applications in photometric analyses and human interface applications. While several formulations have already been utilized in each application, a unified framework of eigenspace manipulations should be created for further progress of computer vision. This paper provides a concept of homogeneous eigenspaces for this purpose. After brief discussion of eigenspace construction, this paper focuses on how an optimal projection of an input image should be done. Three approaches are presented for the projection and normalization in order to minimize the effects of noise. Both the theoretical and experimental comparisons show that the normalization after projection can suppress the effects of noise more effectively than the other methods. The normalization-after-projection formulation can be reformulated by the homogeneous eigenspace. In the framework of homogeneous eigenspace, a projection onto the normalized eigenspace is accomplished without using an explicit normalization. Furthermore, an optimal partial projection to the normalized eigenspace is also reduced to linear mapping in this framework. Two applications are also discussed for illumination analysis and for photometric classification. These problems are efficiently solved by partial projections onto homogeneous eigenspaces.