Segmentation and classification are important problems with applications in areas like textural analysis and pattern recognition. Th is paper describes a single-0stage approach to solve the image segmentation/classification problem down to the pixel level, using energy density functions based on the wavelet transform. The energy density functions obtained, called Pseudo Power Signatures, are essentially functions of the scale and orientation, and are obtained using separable approximations to the 2D wavelet transform. A significant advantage of these representations is that they are invariant to signal magnitude, and spatial location within the object of interest. Further, they lend themselves to fast and simple classification routines. We provide a complete formulation of the signature determination problem for 2D, and propose an effective, albeit simple, technique based on a tensor singular value analysis, to solve the problem, We present an efficient computational algorithm, and a simulation result reflecting the strengths and limitations of this approach. We next present a detailed analysis of a more sophisticate method based on orthogonal projections to obtain signatures which are better representations of the underlying data.