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Face Processing with Whitney Reduction Networks

This paper investigates the application of the Whitney Reduction Network (WRN) to the low-dimensional characterization of digital images human faces. Motivated by Whitney's Embedding theorem from diierential topology the WRN provides a non-linear parameterization of m dimensional manifolds. Based on this, the reduction of the high-dimensional raw image data consists of two-stages. First, a low-dimensional representation is constructed using an optimal projection. Secondly, a nonlinear inverse from the image of the projection to the null-space of the projection is approximated to permit the (almost) perfect reconstruction of the data. This architecture is applied to problem of representing a family of digital images, i.e., faces. We compare this method with the well-known eigenpicture approach, which may be viewed as a special limiting case of the WRN.