Independent spectral representations of images for recognition

In recent years, studies have shown that independent components of local windows of natural images resemble the receptive fields of cells in the early stages of the mammalian visual pathway. However, the role of the independence in visual recognition is not well understood. We argue that the independence resolves the curse of dimensionality by reducing the complexity of probability models to the linear order of the dimension. In addition, we show empirically that the complexity reduction does not degrade the recognition performance on all the data sets that we have used with an independent spectral representation. In this representation, an input image is first decomposed into independent channels given by the estimated independent components from training images, and each channel's response is then summarised by using its histogram as an estimate of the underlying probability model along that dimension. We demonstrate the sufficiency of the proposed representation for image characterization by synthesizing textures and objects through sampling and for recognition by applying it to large data sets. Our comparisons show that the independent spectral representation often gives improved recognition performance.