This Article 
 Bibliographic References 
 Add to: 
Space and Time Bounds on Indexing 3D Models from 2D Images
October 1991 (vol. 13 no. 10)
pp. 1007-1017

Model-based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses, which are then verified. In order to accelerate recognition considerably, the model groups can be arranged in an index space (hashed) offline such that feasible matches are found by indexing into this space. For the case of 2D images and 3D models consisting of point features, bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated. It is proved that, even in the absence of image error, each model must be represented by a 2D surface in the index space. This places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image. Theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined, and an implementation of indexing for measuring this speedup empirically is presented. It is found that indexing can produce only a minimal speedup on its own. However, when accompanied by a grouping operation, indexing can provide significant speedups that grow exponentially with the number of features in the groups.

[1] N. Ayache and O. D. Faugeras, "HYPER: A new approach for the recognition and positioning of two-dimensional objects,"IEEE Trans. Patt. Anal. Machine Intell., vol. 8, no. 1, pp. 44-54, 1986.
[2] R. Bolles and R. Cain "Recognizing and locating partially visible objects: The local-feature-focus method,"Int. J. Robotics Res., vol. 1, no. 3, pp. 57-82, 1982.
[3] T. Breuel "Indexing for visual recognition from a large model base," MIT AI Memo 1108, 1990.
[4] R. Brooks, "Symbolic reasoning among 3-D models and 2-D images."Artificial Intell., vol. 17, pp. 85-348, 1981.
[5] J. Burns, R. Weiss, and E. Riseman, "View variation of point set and line segment features," inProc. DARPA IU Workshop, 1990, pp. 650-659.
[6] D. Clemens, "The recognition of two-dimensional modeled objects in images," Master's thesis, Mass. Inst. Technol., Dept. Elec. Eng. Comput. Sci., 1986.
[7] D. Clemens, "Model-group indexing for recognition," inProc. DARPA IU Workshop, 1990, pp. 604-613.
[8] M. A. Fischler and R. C. Bolles, "Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,"Commun. ACM, vol. 24, no. 6, pp. 381-395, 1981.
[9] D. Forsythe, J. Mundy, A. Zisserman, and C. Brown, "Invariance: A new framework for vision." inProc. Third Int. Conf. Comput. Vision, 1990, pp. 598-605.
[10] W. E. L. Grimson, D. Huttenlocher, and D. Jacobs, "Affine matching with bounded sensor error: A study of geometric hashing and alignment," MIT AI Memo 1250, 1991.
[11] B. K. P. Horn,Robot Vision. New York: McGraw-Hill, 1986.
[12] D. P. Huttenlocher and S. Ullman, "Recognizing solid objects by alignment with an image,"J. Comput. Vision, vol. 5, no. 2, pp. 195-212, 1990.
[13] D. Jacobs, "Grouping for recognition," MIT AI Memo 1177, 1989.
[14] A. Kalvin, E. Schonberg, J. Schwartz, and M. Sharir, "Two-dimensional, model-based, boundary matching using footprints."Int. J. Robotics Res., vol. 5, no. 4, pp. 38-55, 1986.
[15] Y. Lamdan, J. T. Schwartz, and H. J. Wolfson, "Object recognition by affine invariant matching," inProc. CVPR 88, 1988.
[16] Y. Lamdan and H. J. Wolfson, "Geometric hashing: A general and efficient model-based recognition scheme," inProc. 2nd Int. Conf. Computer vision, 1988.
[17] D. Lowe, Perceptual Organization And Visual Recognition. Boston: Kluwer, 1985.
[18] J. T. Schwartz and M. Sharir, "Identification of objects in two and three dimensions by matching noisy characteristic curves,"Int. J. Robotics Res., vol. 6, no. 2, pp. 29-44, 1987.
[19] D. Thompson and J. Mundy, "Three dimensional model matching from an unconstrained viewpoint,"Proc. Int. Conf. Robotics Automation, 1987, pp. 208-220.
[20] A. Wallace, "Matching segmented scenes to models using pairwise relationships between features,"Image Vision Comput., vol. 5, no. 2, pp. 114-120, 1987.

Index Terms:
3D model indexing; space bounds; model-based recognition; feature extraction; time bounds; 2D images; visual recognition systems; image features; model features; grouping operation; computerised pattern recognition; computerised picture processing
D.T. Clemens, D.W. Jacobs, "Space and Time Bounds on Indexing 3D Models from 2D Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 10, pp. 1007-1017, Oct. 1991, doi:10.1109/34.99235
Usage of this product signifies your acceptance of the Terms of Use.