Statistical Analysis of Spatial Structure in Natural Images

When a sample of natural images is taken and compared with a set of noise images, the two are obviously distinguishable. Even when the noise images are set to have the same power spectral characteristics as the natural images, there is no doubt which is a normal image and which is a noise image. In the study to be reported, we have examined the nature of the spatial characteristics of natural images that allow them to be so discriminated from noise images.

The approach is to process large sets of images belonging to various categories through mechanisms that have some similarities to known operations in biological visual systems. Thus, the images are filtered at various spatial scales and at various orientations; the filter outputs are combined into local energy maps; and features are detected in such processed images. The result of these calculations is the distribution of values of some parameter which describes a particular image characteristics for each set of images. Parameters that could support adequate discrimination between two sets of images, for example natural images and noise images, will have largely non-overlapping distributions.

In practice it is found that no simple parameters can distinguish obviously different sets of images, but parameters that encapsulate spatial patterns, especially those related to non-accidental image properties, can do so. It is concluded that filter outputs must be followed by nontrivial spatial operations. Suggestions are made as to what are the most plausible.