Separate processing of local luminance and contrast in biological visual systems has been argued to be due to the independence of these two properties in natural image data. In this paper we examine spatial, retinotopic channels formed by these two quantities and use Independent Component Analysis to study the possible dependencies between the channels. As a result, oriented, localized bandpass filter pairs are learned, where one filter processes the luminance channel and the other the contrast channel. We study the relationship of the learned filters and their pairings, and show that these are due to dependencies existing between local luminance and contrast. Subsequently, our results suggest that the separate processing of local luminance and contrast can not be attributed to their independence in natural images.

Multiple visual cues are used by the visual system to analyze a scene; achromatic cues include luminance, texture, contrast and motion. Singlecell recordings have shown that the mammalian visual cortex contains neurons that respond similarly to scene structure (e.g., orientation of a boundary), regardless of the cue type conveying this information. This paper shows that cue-invariant response properties of simple- and complex-type cells can be learned from natural image data in an unsupervised manner. In order to do this, we also extend a previous conceptual model of cue invariance so that it can be applied to model simple- and complex-cell responses. Our results relate cue-invariant response properties to natural image statistics, thereby showing how the statistical modeling approach can be used to model processing beyond the elemental response properties visual neurons. This work also demonstrates how to learn, from natural image data, more sophisticated feature detectors than those based on changes in mean luminance, thereby paving the way for new data-driven approaches to image processing and computer vision.

Recently, statistical models of natural images have shown the emergence of several properties of the visual cortex. Most models have considered the nongaussian properties of static image patches, leading to sparse coding or independent component analysis. Here we consider the basic time dependencies of image sequences instead of their nongaussianity. We show that simple-cell-type receptive fields emerge when temporal response strength correlation is maximized for natural image sequences. Thus, temporal response strength correlation, which is a nonlinear measure of temporal coherence, provides an alternative to sparseness in modeling simple-cell receptive field properties. Our results also suggest an interpretation of simple cells in terms of invariant coding principles, which have previously been used to explain complex-cell receptive fields.

We show that two important properties of the primary visual cortex emerge when the principle of temporal coherence is applied to natural image sequences. The properties are simple-cell-like receptive fields and complex-cell-like pooling of simple cell outputs, which emerge when we apply two different approaches to temporal coherence. In the first approach we extract receptive fields whose outputs are as temporally co- herent as possible. This approach yields simple-cell-like receptive fields (oriented, localized, multiscale). Thus, temporal coherence is an alterna- tive to sparse coding in modeling the emergence of simple cell receptive fields. The second approach is based on a two-layer statistical generative model of natural image sequences. In addition to modeling the temporal coherence of individual simple cells, this model includes inter-cell tem- poral dependencies. Estimation of this model from natural data yields both simple-cell-like receptive fields, and complex-cell-like pooling of simple cell outputs. In this completely unsupervised learning, both lay- ers of the generative model are estimated simultaneously from scratch. This is a significant improvement on earlier statistical models of early vision, where only one layer has been learned, and others have been fixed a priori.

Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to the techniques of independent component analysis and blind source separation. In this paper, we investigate the application of sparse coding for image feature extraction. We show how sparse coding can be used to extract wavelet-like features from natural image data. As an application of such a feature extraction scheme, we show how to apply a soft-thresholding operator on the components of sparse coding in order to reduce Gaussian noise. Methods based on sparse coding have the important benefit over wavelet methods that the features are determined solely by the statistical properties of the data, while the wavelet transformation relies heavily on certain abstract mathematical properties that may be only weakly related to the properties of the natural data.

In blind source separation one tries to separate statistically independent unknown source signals from their linear mixtures without knowing the mixing coefficients. Such techniques are currently studied actively both in statistical signal processing and unsupervised neural learning. We apply neural blind separation techniques developed in our laboratory to the extraction of features from natural images and to the separation of medical EEG signals. The new analysis method yields features that describe the underlying data better than for example classical principal component analysis. We discuss difficulties related with real-world applications of blind signal processing, too.