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Discusses two functions for retrieving 3D images from large collections. One proposed representation is referred to as the 3D spatial orientation graph (SOG). SOG is a fully-connected, undirected, weighted graph. The time complexity of this SOG-based spatial similarity (SIM3D) algorithm is Θ(|Eq|+|Ed|), where |Eq| and |Ed| are the number of edges, respectively, in the query or database images. The other proposed representation is referred to as the 3D surface normal list (SNL). The surface normal is the unit vector perpendicular to the plane formed by three space objects. A list with surface normals is used to represent an image. This SNL-based SIM3D algorithm has linear time complexity based on the total number of objects in the query and the database images. We expect both the SOG- and SNL-based SIM3D algorithms to be quite useful in multimedia retrieval applications such as architectural design, interior design and real-estate marketing. The original SOG algorithm has been improved to recognize rotational variant images and arbitrary variants involving a composition of translation, scaling and rotation. For the SNL algorithm, the choice of the base point is significant. It cannot recognize the difference between objects unevenly scaled along the line to the base point of an image. To overcome these limitations, an improved SNL algorithm was worked on. The improved algorithm is very robust, but it has Θ(n2) time complexity. It is effective when used for a small database or for refining the search result of the original SNL algorithm.