Unsupervised Learning of Hierarchical Spatial Structures in Images

Abstract

The visual world demonstrates organized spatial patterns, among objects or regions in a scene, object-parts in an object, and low-level features in object-parts. These classes of spatial structures are inherently hierarchical in nature. Although seemingly quite different these spatial patterns are simply manifestations of different levels in a hierarchy. In this work, we present a unified approach to unsupervised learning of hierarchical spatial structures from a collection of images. Ours is a hierarchical rule-based model capturing spatial patterns, where each rule is represented by a star-graph. We propose an unsupervised EM-style algorithm to learn our model from a collection of images. We show that the inference problem of determining the set of learnt rules instantiated in an image is equivalent to finding the minimum-cost Steiner tree in a directed acyclic graph. We evaluate our approach on a diverse set of data sets of object categories, natural outdoor scenes and images from complex street scenes with multiple objects.