Theories and algorithms for 3-D root canal model construction

This paper presents theories and algorithms for 3-D root canal model construction from 2-D X-ray images in a clinically practical way: (1) the geometrical rectification algorithm for correcting distorted 2-D X-ray images, (2) the transformation algorithms from 2-D X-ray image coordinate system to unified 3-D reference coordinate system, (3) the merging algorithms and theory for obtaining spatial root canal centerline by intersecting two surfaces with assumed parallel projection, and (4) the elliptical theory for exploring the root canal crosssectional geometry. Using those theories and algorithms, three 3-D computer models constructed from teeth samples are presented to show the feasibility. The internal geometrical structure provided by 3-D computer graphics enables the clinician and the patient to comprehend root canal morphology efficiently, and the destructive access preparation before a clinician’s inspection may be avoided during clinic practice. q 2005 Elsevier Ltd. All rights reserved.