Learning Variance Statistics of Natural Images

In this paper, we show how a nonlinear transformation can be applied to model the variance statistics of natural images resulting in a sparse distributed representation of image structures. A variance representation of the input is learned from raw natural image patches using likelihood maximization. The simulation results demonstrate that the model can not only learn new families of basis functions, including multi-scale blobs, Gabor-like gratings and ridge-like basis functions, but also captures more abstract properties of the image, such as statistical similarity of regions within natural images. Moreover, in contrast to traditional linear model, such as sparse coding and ICA, responses show only very little residual dependencies.