The shock graph is an emerging shape representation for object recognition, in which a 2-D silhouette is decomposed into a set of qualitative parts, captured in a directed acyclic graph. Although a number of approaches have been proposed for shock graph matching, these approaches do not address the equally important indexing problem. We extend our previous work in both shock graph matching and hierarchical structure indexing to propose the first unified framework for view-based 3-D object recognition using shock graphs. The heart of the framework is an improved spectral characterization of shock graph structure that not only drives a powerful indexing mechanism (to retrieve similar candidates from a large database), but also drives a matching algorithm that can accommodate noise and occlusion. We describe the components of our system and evaluate its performance using both unoccluded and occluded queries. The large set of recognition trials (over 25,000) from a large database (over 1400 views) represents one of the most ambitious shock graph-based recognition experiments conducted to date.