Image representations for visual learning

Science

Volumn 272, Issue 5270, 1996, Pages 1905-1909

  Beymer, David ^a   Poggio, Tomaso ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER SYSTEM; IMAGE ANALYSIS; IMAGE QUALITY; LEARNING; PRIORITY JOURNAL; THREE DIMENSIONAL IMAGING; VISUAL MEMORY;

EID: 0030056823     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.272.5270.1905     Document Type: Article

References (88)

1. Y. Lee, D. Terzopoulos, K. Waters, in SIGGRAPH Proceedings, Los Angeles, 6 to 11 August 1995 (Association for Computing Machinery, New York, 1995), pp. 55-66.
2. W. E. L. Grimson, Object Recognition by Computer: The Role of Geometric Constraints (MIT Press, Cambridge, MA, 1990).
3. A. Hurlbert and T. Poggio, Nature 321, 651 (1986).
4. S. Ullman and R. Basri, IEEE Trans. Pattern Anal. Machine Intell. 13, 992 (1991).
5. T. Poggio and S. Edelman, Nature 343, 263 (1990).
6. H. Murase and S. Nayar, in Proceedings of the Eleventh National Conference on Artificial Intelligence. Washington, DC, 11 to 15 July 1993 (American Association for Artificial Intelligence Press, Menlo Park, CA, 1993), pp. 836-843.
7. D. Pomerleau, Neural Comput. 3, 88 (1991).
8. T. Poggio, in Cold Spring Harbor Symposia on Quantitative Biology (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 1990), pp. 899-910; T. Breuel, A.I. Technical Report 1374 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1992); A. Pentland, B. Moghaddam, T. Starner, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, WA, 21 to 23 June 1994 (IEEE Computer Society Press. Los Alamitos, CA, 1994), pp. 84-91; B. A. Golomb, D. T. Lawrence, T. J. Sejnowski, in Advances in Neural Information Processing Systems 3, R, Lippmann, J. Moody, D. Touretzky, Eds. (Morgan Kaufmann, San Mateo, CA, 1991), pp. 572-577.
9. T. Poggio, in Cold Spring Harbor Symposia on Quantitative Biology (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 1990), pp. 899-910; T. Breuel, A.I. Technical Report 1374 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1992); A. Pentland, B. Moghaddam, T. Starner, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, WA, 21 to 23 June 1994 (IEEE Computer Society Press. Los Alamitos, CA, 1994), pp. 84-91; B. A. Golomb, D. T. Lawrence, T. J. Sejnowski, in Advances in Neural Information Processing Systems 3, R, Lippmann, J. Moody, D. Touretzky, Eds. (Morgan Kaufmann, San Mateo, CA, 1991), pp. 572-577.
10. T. Poggio, in Cold Spring Harbor Symposia on Quantitative Biology (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 1990), pp. 899-910; T. Breuel, A.I. Technical Report 1374 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1992); A. Pentland, B. Moghaddam, T. Starner, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, WA, 21 to 23 June 1994 (IEEE Computer Society Press. Los Alamitos, CA, 1994), pp. 84-91; B. A. Golomb, D. T. Lawrence, T. J. Sejnowski, in Advances in Neural Information Processing Systems 3, R, Lippmann, J. Moody, D. Touretzky, Eds. (Morgan Kaufmann, San Mateo, CA, 1991), pp. 572-577.
11. T. Poggio, in Cold Spring Harbor Symposia on Quantitative Biology (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 1990), pp. 899-910; T. Breuel, A.I. Technical Report 1374 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1992); A. Pentland, B. Moghaddam, T. Starner, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, WA, 21 to 23 June 1994 (IEEE Computer Society Press. Los Alamitos, CA, 1994), pp. 84-91; B. A. Golomb, D. T. Lawrence, T. J. Sejnowski, in Advances in Neural Information Processing Systems 3, R, Lippmann, J. Moody, D. Touretzky, Eds. (Morgan Kaufmann, San Mateo, CA, 1991), pp. 572-577.
12. Techniques based on the assumption of a linear vector space include those of Murase and Nayar (6), who used eigenfunctions of object images; Turk and Pentland [(22), see also S. Akamatsu, T. Sasaki, H. Fukamachi, N. Masui, Y. Suenaga, International Conference on Pattern Recognition, The Hague, 30 August to 3 September 1992 (IEEE Computer Society Press, Los Alamitos, CA, 1992), pp. 217-220], who used eigenfunctions in the space of face images; and Sung and Poggio (28), who used the Mahalanobis distance in their face detection system [see also B. Moghaddam and A. Pentland, in (14), pp. 786-793; U. Fayyad, N. Weir, S. Djorgovski, in Proceedings of the Tenth International Conference on Machine Learning, University of Massachusetts, Amherst, 27 to 29 June 1993 (Morgan Kaufmann, San Mateo, CA, 1993), pp. 112-119].
13. Techniques based on the assumption of a linear vector space include those of Murase and Nayar (6), who used eigenfunctions of object images; Turk and Pentland [(22), see also S. Akamatsu, T. Sasaki, H. Fukamachi, N. Masui, Y. Suenaga, International Conference on Pattern Recognition, The Hague, 30 August to 3 September 1992 (IEEE Computer Society Press, Los Alamitos, CA, 1992), pp. 217-220], who used eigenfunctions in the space of face images; and Sung and Poggio (28), who used the Mahalanobis distance in their face detection system [see also B. Moghaddam and A. Pentland, in (14), pp. 786-793; U. Fayyad, N. Weir, S. Djorgovski, in Proceedings of the Tenth International Conference on Machine Learning, University of Massachusetts, Amherst, 27 to 29 June 1993 (Morgan Kaufmann, San Mateo, CA, 1993), pp. 112-119].
14. Techniques based on the assumption of a linear vector space include those of Murase and Nayar (6), who used eigenfunctions of object images; Turk and Pentland [(22), see also S. Akamatsu, T. Sasaki, H. Fukamachi, N. Masui, Y. Suenaga, International Conference on Pattern Recognition, The Hague, 30 August to 3 September 1992 (IEEE Computer Society Press, Los Alamitos, CA, 1992), pp. 217-220], who used eigenfunctions in the space of face images; and Sung and Poggio (28), who used the Mahalanobis distance in their face detection system [see also B. Moghaddam and A. Pentland, in (14), pp. 786-793; U. Fayyad, N. Weir, S. Djorgovski, in Proceedings of the Tenth International Conference on Machine Learning, University of Massachusetts, Amherst, 27 to 29 June 1993 (Morgan Kaufmann, San Mateo, CA, 1993), pp. 112-119].
15. A collection of objects V is a vector space if (i) for all u,v in V, au + bv is in V with a,b real numbers and (ii) there is a zero vector 0 such that for all u in V, 0u = 0 and u + 0 = u. Other axioms omitted here ensure that addition and multiplication behave as they should.
16. Measurements such as area, perimeter, and statistical estimates of color, contrast, and other properties of images are all global features used in the past. Sparse local features can also be used; there are obvious trade-offs between feature complexity and the difficulty of the correspondence step.
17. In many object recognition tasks, correspondence is not needed over the full image. Correspondence that is limited to image patches that correspond to object components is easier and yields more robust recognition and detection schemes. In this article, discussions of full image correspondence apply to components as well.
18. 2 is the number of pixels in the image (because of the three color values per pixel). Of course, it may be possible to define a sparser set of relevant feature points in the image. The term shape vector refers to the 2D shape (not 3D) relative to the reference image.
19. M. Jones and T. Poggio, in Proceedings of the Fifth International Conference on Computer Vision, Cambridge, MA, 20 to 23 June 1995 (IEEE Computer Society Press, Los Alamitos, CA, 1995), pp. 531-536.
20. A. Blake and M. Isard, in SIGGRAPH Proceedings, Orlando, FL, 24 to 29 July 1994 (Association for Computing Machinery, New York, 1994), pp. 185-192.
21. T. F. Cootes, C. J. Taylor, A. Lanitis, D. H. Cooper, J. Graham, in Proceedings of the Fourth International Conference on Computer Vision, Berlin, 11 to 14 May 1993 (IEEE Computer Society Press, Los Alamitos, CA, 1993), pp. 242-246.
22. T. Poggio, Technical Report 9005-03 (Istituto per la Ricerca Scientifica e Tecnologica, Povo, Italy, 1990),
23. I. Craw and P. Cameron, in Proceedings British Machine Vision Conference, University of Glasgow, UK, 24 to 26 September 1991 (Springer-Verlag, London, 1991), pp. 367-370.
24. J. J. Koenderink and A. J. van Doorn, Biol. Cybern. 32, 211 (1979).
25. T. Vetter, A. Hurlbert, T. Poggio, Cereb. Cortex 3, 261 (1995).
26. M. Kirby and L. Sirovich, IEEE Trans. Pattern Anal. Machine Intell. 12, 103 (1990).
27. M. Turk and A. Pentland, J. Cogn. Neurosci. 3, 71 (1991).
28. T. Vetter and T. Poggio, A.I. Memo 1531 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1995).
29. D. Beymer and T. Poggio, in (14), pp. 500-507.
30. In this framework, principal components analysis is just one of the several tools provided by the mathematical structure of a vector space, which is the actual key property here.
31. A. Lanitis, C. J. Taylor, T. F. Cootes, in (14), pp. 368-373.
32. T. Poggio and R. Brunelli, A.I. Memo 1354 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1992).
33. K. K. Sung and T. Poggio, in Proceedings of the Image Understanding Workshop, Monterey, CA, 13 to 16 November 1994 (Morgan Kaufmann, San Mateo, CA, 1994), pp. 843-850.
34. H.A. Rowley, S. Baluja, T. Kanade, Technical Report CMU-CS-95-158 (Carnegie Mellon University, Pittsburgh, PA, 1995); H. Murase and S. K. Nayar, Int. J. Comput. Vision 14, 5 (1995).
35. H.A. Rowley, S. Baluja, T. Kanade, Technical Report CMU-CS-95-158 (Carnegie Mellon University, Pittsburgh, PA, 1995); H. Murase and S. K. Nayar, Int. J. Comput. Vision 14, 5 (1995).
36. T. F. Cootes and C. J. Taylor, in Proceedings British Machine Vision Conference, Leeds, UK, 22 to 24 September 1992 (Springer-Verlag, London, 1992), pp. 266-275.
37. A. Shashua, A.I. Technical Report 1401 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1992); thesis, Massachusetts Institute of Technology (1992).
38. T. Poggio and T. Vetter, A.I Memo 1347 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1992).
39. M. Lades et al., IEEE Trans. Comput. 42, 300 (1993).
40. D. Beymer, A.I. Memo 1537 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1995).
41. C. Tomasi and T. Kanade, Int. J. Comput. Vision 9, 137 (1992).
42. A. Shashua, IEEE Trans. Pattern Anal. Machine Intell. 17, 779 (1995).
43. S. Laveau and O. Faugeras, Technical Report 2205 (Institut National de Recherche en Informatique et en Automatique, France, 1994); S. Avidan and A, Shashua, Technical Report CIS-9602 (Technion, Haifa, Israel, 1996); T. Evgeniou, thesis. Massachusetts Institute of Technology (1996).
44. S. Laveau and O. Faugeras, Technical Report 2205 (Institut National de Recherche en Informatique et en Automatique, France, 1994); S. Avidan and A, Shashua, Technical Report CIS-9602 (Technion, Haifa, Israel, 1996); T. Evgeniou, thesis. Massachusetts Institute of Technology (1996).
45. S. Laveau and O. Faugeras, Technical Report 2205 (Institut National de Recherche en Informatique et en Automatique, France, 1994); S. Avidan and A, Shashua, Technical Report CIS-9602 (Technion, Haifa, Israel, 1996); T. Evgeniou, thesis. Massachusetts Institute of Technology (1996).
46. D. Beymer, A. Shashua, T. Poggio, A.I. Memo 1431 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1993); T. Ezzat, thesis, Massachusetts Institute of Technology (1996); S. Lines, thesis. Massachusetts Institute of Technology (1996).
47. D. Beymer, A. Shashua, T. Poggio, A.I. Memo 1431 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1993); T. Ezzat, thesis, Massachusetts Institute of Technology (1996); S. Lines, thesis. Massachusetts Institute of Technology (1996).
48. D. Beymer, A. Shashua, T. Poggio, A.I. Memo 1431 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1993); T. Ezzat, thesis, Massachusetts Institute of Technology (1996); S. Lines, thesis. Massachusetts Institute of Technology (1996).
49. S. Seitz and C. Dyer, in Proc. IEEE Workshop on the Representation of Visual Scenes, Cambridge, MA, 24 June 1995 (IEEE Computer Society Press, Los Alamitos, CA, 1995), pp. 18-25; S. Chen and L. Williams, in SIGGRAPH Proceedings, Anaheim, CA, 1 to 6 August 1993 (Association for Computing Machinery, New York, 1993), pp. 279-288; L. McMillan and G. Bishop, in (1), pp. 39-46.
50. S. Seitz and C. Dyer, in Proc. IEEE Workshop on the Representation of Visual Scenes, Cambridge, MA, 24 June 1995 (IEEE Computer Society Press, Los Alamitos, CA, 1995), pp. 18-25; S. Chen and L. Williams, in SIGGRAPH Proceedings, Anaheim, CA, 1 to 6 August 1993 (Association for Computing Machinery, New York, 1993), pp. 279-288; L. McMillan and G. Bishop, in (1), pp. 39-46.
51. S. Seitz and C. Dyer, in Proc. IEEE Workshop on the Representation of Visual Scenes, Cambridge, MA, 24 June 1995 (IEEE Computer Society Press, Los Alamitos, CA, 1995), pp. 18-25; S. Chen and L. Williams, in SIGGRAPH Proceedings, Anaheim, CA, 1 to 6 August 1993 (Association for Computing Machinery, New York, 1993), pp. 279-288; L. McMillan and G. Bishop, in (1), pp. 39-46.
52. T. Werner, R. Hersch, V. Hlaváč, in (14), pp. 957-962.
53. T. Poggio and F. Girosi, A.I. Memo 1140 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1989). See also T. Poggio and F. Girosi, Science 247, 978 (1990).
54. T. Poggio and F. Girosi, A.I. Memo 1140 (Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, 1989). See also T. Poggio and F. Girosi, Science 247, 978 (1990).
55. F. Girosi, M. Jones, T. Poggio, Neural Comput. 7, 219 (1995).
56. D. S. Broomhead and D. Lowe, Complex Systems 2, 321 (1988).
57. 2 criterion is used for training (42).
58. J. R. Bergen, P. Anandan, K. J. Hanna, R. Hingorani, in Proceedings of the Second European Conference on Computer Vision, Santa Margherita Ligure, Italy, 19 to 22 May 1992 (Springer-Verlag, Berlin, 1992), pp. 237-252. See also B. Lucas and T. Kanade, in Proceedings IJCAI. Vancouver, British Columbia, 24 to 28 August 1981 (American Association for Artificial Intelligence, Menlo Park, CA, 1981), pp. 674-679.
59. J. R. Bergen, P. Anandan, K. J. Hanna, R. Hingorani, in Proceedings of the Second European Conference on Computer Vision, Santa Margherita Ligure, Italy, 19 to 22 May 1992 (Springer-Verlag, Berlin, 1992), pp. 237-252. See also B. Lucas and T. Kanade, in Proceedings IJCAI. Vancouver, British Columbia, 24 to 28 August 1981 (American Association for Artificial Intelligence, Menlo Park, CA, 1981), pp. 674-679.
60. Dense correspondence can be computed at video rate by machines such as the Carnegie Mellon University video-rate stereo machine [T. Kanade, H. Kano, S. Kimura, A. Yoshida, K. Oda, in Proceedings of the International Conference on Intelligent Robotics and Systems, Pittsburgh, PA, 5 to 9 August 1995 (IEEE Computer Society Press, Los Alamitos, CA, 1995), pp. 95-100] or the David Sarnoff Vision Front End [ P. Anandan, P. Burt, J. Pearson, in Proceedings of the Image Understanding Workshop, Palm Springs, CA, 12 to 15 February 1996 (Morgan Kaufmann, San Mateo, CA. 1996)]
61. Dense correspondence can be computed at video rate by machines such as the Carnegie Mellon University video-rate stereo machine [T. Kanade, H. Kano, S. Kimura, A. Yoshida, K. Oda, in Proceedings of the International Conference on Intelligent Robotics and Systems, Pittsburgh, PA, 5 to 9 August 1995 (IEEE Computer Society Press, Los Alamitos, CA, 1995), pp. 95-100] or the David Sarnoff Vision Front End [ P. Anandan, P. Burt, J. Pearson, in Proceedings of the Image Understanding Workshop, Palm Springs, CA, 12 to 15 February 1996 (Morgan Kaufmann, San Mateo, CA. 1996)]
62. S. Mukherjee and S. K. Nayar, in (14), pp. 794-800.
63. i are computed by solving the linear system of Eqs. 1 over the training data.
64. G. Wolberg, Digital Image Warping (IEEE Computer Society Press, Los Alamitos, CA, 1990).
65. S. Librande, thesis, Massachusetts Institute of Technology (1992). See also the Cartoon-o-Matic Web page, http://www.nfx.com.
66. A different approach to rendering a face with a focus on the text-to-speech component can be found in K. Waters and T. M. Levergood. Technical Report CRL 93/4 (Cambridge Research Laboratory, Digital Equipment Corporation, Cambridge, MA, 1993).
67. J. Y. A. Yang and E. H. Adelson, IEEE Trans. Imag. Proc. 3, 625 (1994).
68. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
69. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
70. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
71. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
72. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
73. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
74. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
75. k's of Eqs. 4 to 8. Given a novel image, the parameters that correspond to the best fit of the model are estimated by minimizing an error measure between the novel image and the flexible model after rendering it as an image. For instance, parameters can be found that minimize the function equation presented
76. A. Blake, R. Curwen, A. Zisserman, Int. J. Comput. Vision 11, 127 (1993).
77. Other matching techniques for object recognition are closely related to optical flow algorithms, even if the connection is not always made explicit. For instance, the functional minimized in the technique of von der Marlsburg and co-workers (33) is closely related to the regularization functional [T. Poggio, V. Torre, C. Koch, Nature 317, 314 (1985)] used in many optical flow algorithms.
78. Optical flow techniques work between images with sufficiently low disparities. When correspondence is desired between images that are quite different, other techniques are required [P. Lipson, thesis, Massachusetts Institute of Technology (1993); I. Bachelder, thesis, Massachusetts Institute of Technology (1991); A. Witkin, D. Terzopoulos, M. Kass, Int. J. Comput. Vision 1, 133 (1987)]. We do not imply that dense correspondence is always needed in vision and graphics tasks. Symbolic techniques should be used in general to guide the low-level correspondence algorithms we have used in this work.
79. Optical flow techniques work between images with sufficiently low disparities. When correspondence is desired between images that are quite different, other techniques are required [P. Lipson, thesis, Massachusetts Institute of Technology (1993); I. Bachelder, thesis, Massachusetts Institute of Technology (1991); A. Witkin, D. Terzopoulos, M. Kass, Int. J. Comput. Vision 1, 133 (1987)]. We do not imply that dense correspondence is always needed in vision and graphics tasks. Symbolic techniques should be used in general to guide the low-level correspondence algorithms we have used in this work.
80. Optical flow techniques work between images with sufficiently low disparities. When correspondence is desired between images that are quite different, other techniques are required [P. Lipson, thesis, Massachusetts Institute of Technology (1993); I. Bachelder, thesis, Massachusetts Institute of Technology (1991); A. Witkin, D. Terzopoulos, M. Kass, Int. J. Comput. Vision 1, 133 (1987)]. We do not imply that dense correspondence is always needed in vision and graphics tasks. Symbolic techniques should be used in general to guide the low-level correspondence algorithms we have used in this work.
81. This procedure is similar to training a network with input-output pairs of prototypical views representing each prototype in the initial and in the desired pose. Then, for a new input image, the network synthesizes a virtual view in the desired pose. If the network is trained with pairs of prototype images as inputs (represented as 2D shape vectors) and their 3D shape as output, it will effectively compute 3D shape for novel images of the same class [see (23, 32) and compare the approach of J. Atick, P. Griffin, N. Reidlich, Network: Comput. Neural Syst. 7, 1 (1996)]. The linear class assumption induces a linear combination of the 2D shape vectors but not of the corresponding texture vectors, not even for Lambertian reflectance and uniform albedo ( A. Yuille, personal communication).
82. This procedure is similar to training a network with input-output pairs of prototypical views representing each prototype in the initial and in the desired pose. Then, for a new input image, the network synthesizes a virtual view in the desired pose. If the network is trained with pairs of prototype images as inputs (represented as 2D shape vectors) and their 3D shape as output, it will effectively compute 3D shape for novel images of the same class [see (23, 32) and compare the approach of J. Atick, P. Griffin, N. Reidlich, Network: Comput. Neural Syst. 7, 1 (1996)]. The linear class assumption induces a linear combination of the 2D shape vectors but not of the corresponding texture vectors, not even for Lambertian reflectance and uniform albedo ( A. Yuille, personal communication).
83. An approach in the same spirit was used earlier by Pomerleau to increase the number of training examples in his system that learns to steer a vehicle from images of the road (7).
84. It is not surprising that a small set of corresponding images constitutes a powerful representation for recognition and graphics, because complete 3D structure can be recovered from a small number of views in correspondence (three orthographic and two perspective views are sufficient).
85. T. Poggio and S. Ullman, in preparation.
86. H. H. Bülthoff and S. Edelman, Proc. Natl. Acad. Sci. U.S.A. 89, 60 (1992); N. Logothetis, J. Pauls, T. Poggio, Curr. Biol. 5, 552 (1995).
87. H. H. Bülthoff and S. Edelman, Proc. Natl. Acad. Sci. U.S.A. 89, 60 (1992); N. Logothetis, J. Pauls, T. Poggio, Curr. Biol. 5, 552 (1995).
88. We thank H. Bülthoff, F. Girosi, P. Dayan, M. Jordan, T. Vetter, T. Sejnowski, D. Glaser, A. Shashua, E. Grimson, M. Jones, R. Romano, and especially S. Ullman, C. Tomasi, C. Koch, A. Blake, D. Terzopoulos, and T. Kanade for reading the manuscript and for many insightful and constructive comments. Sponsored by grants from the Office of Naval Research and the Advanced Research Projects Agency under contracts N00014-93-1-0385 and N00014-92-J-1879, Support for CBCL is provided in part by grants from NSF under contract ASC-9217041, by the Multidisciplinary University Research Initiative under contract N00014-95-1-0600, and by Siemens, Daimler-Benz, Eastman Kodak, and ATR. T.P. is supported by the Uncas and Helen Whitaker Chair at Whitaker College, Massachusetts Institute of Technology. D.B. was supported in part by a Howard Hughes Doctoral Fellowship from the Hughes Aircraft Company.