We present a framework for representing and matching multi-scale, qualitative feature hierarchies. The coarse shape of an object is captured by a set of blobs and ridges, representing compact and elongated parts of an object. These parts, in turn, map to nodes in a directed acyclic graph, in which parent/child edges represent feature overlap, sibling edges join nodes with shared parents, and all edges encode geometric relations between the features. Given two feature hierarchies, represented as directed acyclic graphs, we present an algorithm for computing both similarity and node correspondence in the presence of noise and occlusion. Similarity, in turn, is a function of structural similarity, contextual similarity (geometric relations among neighboring nodes), and node contents similarity. Moreover, the weights of these components can be varied on a node by node basis, allowing a graph-based model to effectively parameterize the saliency of its constraints. We demonstrate the approach on two domains: gesture recognition and face detection.