The 'tree-dependent components' of natural scenes are edge filters
Daniel Zoran, Yair Weiss · 2009
We propose a new model for natural image statistics. Instead of minimizing de-pendency between components of natural images, we maximize a simple form of dependency in the form of tree-dependencies. By learning filters and tree struc-tures 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. 1 Introduction and related work Many models of natural image statistics have been proposed in recent years [1, 2, 3, 4]. A common goal of many of these models is finding a representation in which components or sub-components of the image are made as independent or as sparse as possible [5, 6, 2]. This has been found to be a difficult goal, as natural images have a highly intricate structure and removing dependencies between