Quantitative study of 3D gradient operators

An analytical and comparative study of 3D gradient operators is presented. Based on 3D models, the general formulas representing the gradient magnitude and direction responses of 3D operators are derived. The responses of several commonly used 3D operators (with different variations) as functions of the 3D edge's position and orientation are computed. By analysing the results, the performances of those operators are evaluated and compared according to our proposed judge criteria. This study shows the different behaviour between 3D operators and their 2D correspondents, and provides useful guidelines in choosing and using appropriate operators in 3D edge detection aplications.