Abstract
A new algorithm is presented for interpreting two-dimensional (2D) line drawings as three-dimensional (3D) objects without models. Even though no explicit models or additional heuristics are included, the algorithm tends to reach the same 3D interpretations of 2D line drawings that humans do. The algorithm explicitly calculates the partial derivatives of Marill's Minimum Standard Deviation of Angles (MSDA) with respect to all adjustable parameters, and follows this gradient to minimize SDA. For an image with lines meeting atm points formingn angles, the gradient descent algorithm requiresO(n) time to adjust all the points, while Marill's method requiredO(mn) time to do so. Experimental results on various line drawing objects show that this gradient descent algorithm running on a Macintosh II is one to two orders of magnitude faster than the MSDA algorithm running on a Symbolics, while still giving comparable results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Baird and P.S.P. Wang, “3-D Object Recognition Using Gradient Descent and the Universal 3-D Array Grammar,”SPIE, 1607, Intelligent Robotic and Computer Vision, pp. 711–719, 1992.
R. Basri, “Viewer-centered representation in object recognition—a computational approach,” inHandbook of Pattern recognition and Computer Vision (ed. by C.H. Chen, L.F. Paul, and P.S.P. Wang), WSP, pp. 863–882, 1993.
I. Chakravarty and H. Freeman, “Characteristic views as a base for 3D object recognition,”SPIE Robot Vision, pp. 37–45, 1982.
R.T. Chin and C.R. Dyer, “Model-based recognition in robot vision,”ACM Computing Surveys, Vol. 18, No. 1, pp. 67–108, 1986.
S.J. Dickinson, A.P. Pentland, and A. Rosenfeld, “3D shape recovery using distributed aspect matching,”IEEE-PAMI, Vol. 14, No. 2, pp. 174–198, 1992.
Y.G. Leclerc and M.A. Fischler, “An Optimization-Based Approach to the Interpretation of Single Line Drawings as 3D Wire Frames,”I.J. of Computer Vision, Vol. 9, No. 2, pp. 113–136, 1992.
T. Marill, “Emulating the Human Interpretation of Line-Drawings and 3-D Objects,”IJCV, Vol. 6, No. 2, pp. 147–161, 1991.
T. Marill, “Computer Perception of Three-Dimensional Objects,” MIT A.I. Memo 1136, 1989.
T. Marill, “Recognizing Three-Dimensional Objects Without the Use of Models,” MIT A.I. Memo 1157, 1989.
S. Ullman and R. Basri, “Recognition by linear combination of models,”IEEE-PAMI, Vol. 13, No. 10, pp. 992–1006, 1991.
K. Sugihara,Machine Interpretation of Line Drawings, MIT Press, Cambridge, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baird, L., Wang, P. 3D object perception using gradient descent. J Math Imaging Vis 5, 111–117 (1995). https://doi.org/10.1007/BF01250523
Issue date:
DOI: https://doi.org/10.1007/BF01250523