The issue of finding similar 3-D surface segments arises in many recent applications of spatial database systems, such as molecular biology, medical imaging, CAD, and geographic information systems. Surface segments being similar in shape to a given query segment are to be retrieved from the database. The two main questions are how to define shape similarity and how to efficiently execute similarity search queries. We propose a new similarity model based on shape approximation by multi-parametric surface functions that are adaptable to specific application domains. We then define shape similarity of two 3-D surface segments in terms of their mutual approximation errors. Applying the multi-step query processing paradigm, we propose algorithms to efficiently support complex similarity search queries in large spatial databases. A new query type, called the ellipsoid query, is utilized in the filter step. Ellipsoid queries, being specified by quadratic forms, represent a general concept for similarity search. Our major contribution is the introduction of efficient algorithms to perform ellipsoid queries on multi-dimensional index structures. Experimental results on a large 3-D protein database containing 94,000 surface segments demonstrate the successful application and the high performance of our method.
International Journal on Advances of Computer Science for Geographic Information Systems (GeoInformatica), Kluwer Academic Publishers, Vol.2, No.2, 1998, pp.113-147.