This Article 
 Bibliographic References 
 Add to: 
Model-Based Recognition of 3D Objects from Single Images
February 2001 (vol. 23 no. 2)
pp. 116-128

Abstract—In this work, we treat major problems of object recognition which have received relatively little attention lately. Among them are the loss of depth information in the projection from a 3D object to a single 2D image, and the complexity of finding feature correspondences between images. We use geometric invariants to reduce the complexity of these problems. There are no geometric invariants of a projection from 3D to 2D. However, given certain modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions can be either a particular model or a generic assumption about a class of models. Here, we use such assumptions for single-view recognition. We find algebraic relations between the invariants of a 3D model and those of its 2D image under general projective projection. These relations can be described geometrically as invariant models in a 3D invariant space, illuminated by invariant “light rays,” and projected onto an invariant version of the given image. We apply the method to real images.

[1] E. Barrett, personal communication. 1998.
[2] P.A. Beardsley, P. Torr, and A.P. Zisserman, “3D Model Acquisition from Extended Image Sequences,” Proc. Fourth European Conf. Computer Vision, B.F. Buxton and R. Cipolla, eds., Apr. 1996.
[3] J. Ben-Arie, Z. Wang, and K.R. Rao, "Iconic Recognition With Affine-Invariant Spectral Signatures," Proc. 1996 IAPR/IEEE Int'l Conf. Pattern Recognition (ICPR '96), vol. 1, pp. 672-676,Vienna, Austria, Aug. 1996.
[4] T.O. Binford and T.S. Levitt, “Model-Based Recognition of Objects in Complex Scenes,” Proc. DARPA Image Understanding Workshop, pp. 89-100, 1996.
[5] A. Bruckstein, E. Rivlin, and I. Weiss, “Scale Space Invariants for Recognition,” Machine Vision and Applications, vol. 15, pp. 335-344, 1997.
[6] J. B. Burns, R. Weiss, and E.M. Riseman, “View Variation of Point Set and Line Segment Features,” Proc. DARPA Image Understanding Workshop, pp. 650-659, 1990.
[7] S. Carlsson, “Relative Positioning from Model Indexing,” Image and Vision Computing, vol. 12, pp. 179-186, 1994.
[8] S. Carlsson and D. Weinshall, Dual Computation of Projective Shape and Camera Positions from Multiple Images Int'l J. Computer Vision, vol. 27, no. 3, pp. 227-241, May 1998.
[9] R.W. Curwen and J.L. Mundy, “Grouping Planar Projective Symmetries,” Proc. DARPA Image Understanding Workshop, pp. 595-605, 1997.
[10] R. Deriche, Z. Zhang, Q.-T. Luong, and O. Faugeras, “Robust Recovery of the Epipolar Geometry for an Uncalibrated Stereo Rig,” Proc. Third European Conf. Computer Vision, 1994.
[11] H. Guggenheimer, Differential Geometry. New York: Dover, 1963.
[12] G.R. Hjaltason and H. Samet, “Ranking in Spatial Databases,” Proc. Fourth Int'l Symp. Large Spatial Databases, pp. 83-95, 1995.
[13] J.P. Hopcroft, D.P. Huttenlocher, and P.C. Wayner, “Affine Invariants for Model-Based Recognition,” Geometric Invariance in Machine Vision, J.L. Mundy and A. Zisserman, eds. Cambridge, Mass.: MIT Press, 1992.
[14] D. Jacobs, "Space efficient 3D model indexing," IEEE Conf. Computer Vision and Pattern Recognition, pp. 439-444, 1992.
[15] D. Jacobs and R. Basri, “3D to 2D Recognition with Regions,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 547-553, 1997.
[16] D. Keren, R. Rivlin, I. Shimshoni, and I. Weiss, “Recognizing 3D Objects Using Tactile Sensing and Curve Invariants,” Technical Report CS-TR-3812, Univ. of Maryland, 1997.
[17] S.J. Maybank, “Relation between 3D Invariants and 2D Invariants,” Image and Vision Computing, vol. 16, pp. 13-20, 1998.
[18] P. Meer and I. Weiss, “Point/Line Correspondence under Projective Transformations,” Proc. Int'l Conf. Pattern Recognition, vol. A, pp. 399-402, 1992.
[19] R. Mohr, L. Quan, and F. Veillon, Relative 3D Reconstruction Using Multiple Uncalibrated Images Int'l J. Robotics Research, vol. 14, no. 6, pp. 619-632, Dec. 1995.
[20] Y. Moses and S. Ullman, “Generalization to Novel Views: Universal, Class-Based and Model-based Processing,” Int'l J. Computer Vision, vol. 29, pp. 233-253, 1988.
[21] R. Mohan, D. Weinshall, and R. Sarukkai, "3D Object Recognition by Indexing Structural Invariants from Multiple Views," Proc. Int'l Conf. Computer Vision, pp. 264-268,Berlin, May 1993.
[22] R.C. Nelson and H. Samet, “A Population Analysis for Hierarchical Data Structures,” Proc. SIGMOD Conf., pp. 270-277, 1987.
[23] S. Peleg, A. Shashua, D. Weinshall, M. Werman, and M. Irani, “Multisensor Representation of Extended Scenes Using Multiview Geometry,” Proc. DARPA Image Understanding Workshop, pp. 79-83, 1997.
[24] E. Rivlin and I. Weiss, “Local Invariants for Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 3, pp. 226-238, Mar. 1995.
[25] E. Rivlin and I. Weiss, “Recognizing Objects Using Deformation Invariants,” Computer Vision and Image Understanding, vol. 65, pp. 95-108, 1997.
[26] K.D. Wagner and T.W. Williams, "Design for Testability of Mixed Signal Integrated Circuits," Proc. Int'l Test Conf., IEEE CS Press, 1988, pp. 823-829.
[27] H. Samet, The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.
[28] J. Sato and R. Cipolla, “Affine Integral Invariants for Extracting Symmetry Axes,” Image and Vision Computing, vol. 15, pp. 627-635, 1997.
[29] A. Shashua and N. Navab, “Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, pp. 873-883, 1996.
[30] G. Sparr, “Projective Invariants for Affine Shapes of Point Configurations,” Proc. First Workshop Invariance, pp. 151-170, 1991.
[31] C.E. Springer, Geometry and Analysis of Projective Spaces. San Francisco: Freeman, 1994.
[32] P.F. Stiller, C.A. Asmuth, and C.S. Wan, “Invariant Indexing and Single View Recognition,” Proc. DARPA Image Understanding Workshop, pp. 1423-1428, 1994.
[33] B. Strumpel, Algorithms in Invariant Theory. New York: Springer Verlag, 1993.
[34] C. Tomasi and T. Kanade, "Shape and Motion From Image Streams Under Orthography: A Factorization Method," Int'l J. Computer Vision, vol. 9, no. 2, pp. 137-154, 1992.
[35] S. Ullman and R. Basri, "Recognition by Linear Combinations of Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 992-1006, 1991.
[36] L. Van Gool, T. Moons, E. Pauwels, and A. Oosterlinck, “Vision and Lie's Approach to Invariance,” Image and Vision Computing, vol. 13, pp. 259-277, 1995.
[37] T. Vieville, O. Faugeras, and Q.T. Luong, “Motion of Points and Lines in the Uncalibrated Case,” Int'l J. Computer Vision, vol. 17, pp. 7-41, 1996.
[38] B. Vijayakumar, D. Kriegman, and J. Ponce, "Structure and Motion of Curved 3D Objects From Monocular Silhouettes," Proc. Conf. Computer Vision and Pattern Recognition, pp. 327-334, 1996.
[39] D. Weinshall,“Model based invariants for 3D vision,” Int’l J. Computer Vision, vol. 10, no. 1, pp. 27-42, 1993.
[40] I. Weiss, “Geometric Invariants of Shapes,” Proc. Computer Vision and Image Processing, pp. 291-297, 1988.
[41] I. Weiss,“Noise-resistant invariants of curves,” IEEE Trans. Pattern Anal. and Machine Intelligence, vol. 15, no. 9, pp. 943-948, Sept. 1993.
[42] I. Weiss, “Geometric Invariants and Object Recognition,” Int'l J. Computer Vision, vol. 10, no. 3, pp. 201-231, June 1993.
[43] I. Weiss, “Local Projective and Affine Invariants,” Annals of Math. and Artificial Intelligence, vol. 13, pp. 203-225, 1995.
[44] I. Weiss, “3D Curve Reconstruction from Uncalibrated Cameras,” Technical Report CS-TR-3605, Univ. of Maryland, 1996.
[45] I. Weiss, “Model-Based Recognition of 3D Curves from One View,” J. Math. Imaging and Vision, vol. 10, pp. 1-10, 1999.
[46] M. Zerroug and R. Nevatia, “Using Invariance and Quasi-invariance for the Segmentation and Recovery of Curved Objects,” Lecture Notes in Computer Science 825, Berlin: Springer-Verlag, 1994.
[47] A. Zisserman, D. Forsyth, J. Mundy, C. Rothwell, J. Liu, and N. Pillow, “3D Object Recognition Using Invariance,” Artificial Intelligence, vol. 78, nos. 1-2, pp. 239-288, 1995.

Index Terms:
Object recognition, invariance, model-based.
Isaac Weiss, Manjit Ray, "Model-Based Recognition of 3D Objects from Single Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 2, pp. 116-128, Feb. 2001, doi:10.1109/34.908963
Usage of this product signifies your acceptance of the Terms of Use.