The "tree-dependent components" of natural scenes are edge filters

We propose a new model for natural image statistics. Instead of minimizing dependency between components of natural images, we maximize a simple form of dependency in the form of tree-dependencies. By learning filters and tree structures which are best suited for natural images we observe that the resulting filters are edge filters, similar to the famous ICA on natural images results. Calculating the likelihood of an image patch using our model requires estimating the squared output of pairs of filters connected in the tree. We observe that after learning, these pairs of filters are predominantly of similar orientations but different phases, so their joint energy resembles models of complex cells.