Toward a Full Probability Model of Edges in Natural Images

We investigate the statistics of local geometric structures in natural images. Previous studies [13,14] of high-contrast 3×3 natural image patches have shown that, in the state space of these patches, we have a concentration of data points along a low-dimensional non-linear manifold that corresponds to edge structures. In this paper we extend our analysis to a filter-based multiscale image representation, namely the local 3-jet of Gaussian scale-space representations. A new picture of natural image statistics seems to emerge, where primitives (such as edges, blobs, and bars) generate low-dimensional non-linear structures in the state space of image data.