Statistical models of images and early vision

A fundamental question in visual neuroscience is: Why are the receptive fields and response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input. In this paper, we will review work on modelling statistical regularities in ecologically valid visual input (“natural images”) and the obtained functional explanation of the properties of visual neurons. A seminal statistical model for natural images was linear sparse coding which is equivalent to the model called independent component analysis (ICA). Linear features estimated by ICA resemble wavelets or Gabor functions, and provide a very good description of the properties of simple cells in the primary visual cortex. We have introduced extensions of ICA that are based on modelling dependencies of the ”independent” components estimated by basic ICA. The dependencies of the components are used to define either a grouping or a topographic order between the components. With natural image data, these models lead to emergence of further properties of visual neurons: the topographic organization and complex cell receptive fields. We have also modelled the temporal structure of natural image sequences, which provides an alternative approach to the sparseness used in most models. These models can be combined in a unifying framework that we call bubble coding. Finally, we will discuss a promising new direction of research: predictive visual neuroscience. There, the goal is to try to predict response properties of neurons in areas that are poorly understood, still based on statistical modelling of natural input.