Similarity search for $3$D structure data sets is fundamental to many database applications such as molecular biology, image registration and computer aided design. However, it is well known that computing structural similarity is extremely expensive due to high exponential time complexity of structure similarity measures. As the structure databases keep growing rapidly, real-time search from large structure databases becomes problematic. In this paper, we present a novel statistical model, multi-resolution \textit{Localized Co-occurrence Model} (LCM), to approximately measure the similarity between the two $3$D structures in linear time complexity for fast retrieval. LCM could capture both distribution characteristics and spatial structure of $3$D data by localizing the point co-occurrence relationship within a predefined neighborhood system. A novel structure query processing method called \textit{iBound} is also proposed for further computational reduction. iBound avoids a large amount of expensive computation at higher resolution LCMs. By superposing two LCMs, their largest common substructure can also be found quickly. Finally, our experiment results prove the effectiveness and efficiency of our methods.