Similarity search for 3D structure data sets is fundamental to many database applications such as molecular biology, image registration, and computer-aided design. Identifying the common 3D subtructures between two objects is an important research problem. However, it is well known that computing structural similarity is very expensive due to the 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, that is, the multiresolution Localized Co-Occurrence Model (LCM), to approximately measure the similarity between the two point-based 3D structures in linear time complexity for fast retrieval. LCM could capture both distribution characteristics and spatial structure of 3D data by localizing the point co-occurrence relationship within a predefined neighborhood system. As a step further, a novel structure query processing method called the incremental and Bounded search (iBound) is also proposed to speed up the search process. 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.