 The CSDL is currently updating some recently published content. During this update, the article you're looking for may not be immediately available. We anticipate this update to take no more than 4-7 days. If you cannot find your content, please try again later. We apologize for the
inconvenience.
| | This Article | | | |
| | | | Share | | | |
| | | | Bibliographic References | | | |
| | | | Add to: | | | |
 Digg
 Furl
 Spurl
 Blink
 Simpy
 Google
 Del.icio.us
 Y!MyWeb
| | | | Search | | | |
| | | | |
Relative Affine Structure: Canonical Model for 3D From 2D Geometry and Applications
September 1996 (vol. 18 no. 9) pp. 873-883
Abstract—We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work—including Euclidean, projective and affine—in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications. [1] A. Azarbayejani and A. Pentland, "Recursive Estimation of Motion, Structure and Focal Length," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 6, pp. 562-575, June 1995.
[2] E. Barrett, P.M. Payton, and G. Gheen, "Robust Algebraic Invariant Methods with Applications in Geometry and Imaging," Proc. SPIE Symp. Remote Sensing,San Diego, July 1995.
[3] J.R. Bergen, P. Anandan, K.J. Hanna, and R. Hingorani, “Hiercharchical Model-Based Motion Estimation,” Proc. European Conf. Computer Vision, pp. 237-252, 1992.
[4] D. Beymer, A. Shashua, and T. Poggio, "Example Based Image Analysis and Synthesis," M.I.T. A.I. Memo No. 1431, 1993.
[5] S. Demey, A. Zisserman, and P. Beardsley, "Affine and Projective Structure from Motion," Proc. British Machine Vision Conf., Oct. 1992.
[6] 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.
[7] R. Dutta, R. Manmatha, L.R. Williams, and E.M. Riseman, “A Data Set for Quantitative Motion Analysis,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 159–164, 1989.
[8] O. Faugeras, "What can be seen in three dimensions with an uncalibrated stereo rig?" Second European Conf. Computer Vision, pp. 563-578, 1992.
[9] O.D. Faugeras, "Stratification of Three-Dimensional Vision: Projective, Affine and Metric Representations," J. Optical Soc. of Am., vol. 12, no. 3, pp. 465-484, 1995.
[10] O. Faugeras, T. Luong, and S. Maybank, “Camera Self-Calibration: Theory and Experiments,” Proc Second European Conf. Computer Vision, pp. 321-334, May 1992.
[11] O.D. Faugeras and F. Lustman, "Let Us Suppose that the World Is Piecewise Planar," Int'l Symp. Robotics Research, O.D. Faugeras and G. Giralt, eds., pp. 33-40.Cambridge, Mass.: MIT Press, 1986.
[12] O.D. Faugeras and L. Robert, "What Can Two Images Tell Us about a Third One?" Proc. European Conf. Computer Vision, pp. 485-492,Stockholm, Sweden, May 1994.
[13] R. Hartley, “Projective Reconstruction and Invariants from Multiple Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 10, pp. 1036-1041, Oct. 1994.
[14] R. Hartley and R. Gupta, "Computing Matched-Epipolar Projections," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 1993, pp. 549-555.
[15] R. Hartley, R. Gupta, and T. Chang, “Stereo from Uncalibrated Cameras,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 761-764, June 1992.
[16] D.P. Huttenlocher and S. Ullman, “Recognizing Solid Objects by Alignment with an Image,” Int'l J. Computer Vision, vol. 5, no. 2, pp. 195-212, 1990.
[17] D. Jacobs, "Space efficient 3D model indexing," IEEE Conf. Computer Vision and Pattern Recognition, pp. 439-444, 1992.
[18] J.J. Koenderink and A.J. Van Doorn, "Affine Structure from Motion," J. Optical Soc. Am., vol. 8, pp. 377-385, 1991.
[19] R. Kumar, P. Anandan, and K. Hanna, “Direct Recovery of Shape from Multiple Views: A Parallax Based Approach,” Proc. Int'l Conf. Pattern Recognition, pp. 685-688, Oct. 1994.
[20] R. Kumar,H.S. Sawhney,, and A. R. Hanson,“3D model acquisition from monocular image sequences,” 1992 IEEE Conf. on Computer Vision and Pattern Recognition, pp. 209-215, June 1992.Los Alamitos, Calif., IEEE Computer Society Press.
[21] C.H. Lee, "Structure and Motion from Two Perspective Views via Planar Patch," Int'l Conf. Computer Vision, pp. 158-164, 1988.
[22] H.C. Longuet-Higgins, "A Computer Algorithm for Reconstructing a Scene from Two Projections," Nature, vol. 293, pp. 133-135, 1981.
[23] B.D. Lucas and T. Kanade, "An Iterative Image Registration Technique with an Application to Stereo Vision," Proc. IJCAI, pp. 674-679,Vancouver, Canada, 1981.
[24] Q.-T. Luong and T. Vieville, “Canonic Representation for the Geometry of Multiple Projective Views,” Proc. European Conf. Computer Vision ECCV'94, pp. 589-600, 1994.
[25] R. Mohr, F. Veillon, and L. Quan, “Relative 3D Reconstruction Using Multiple Uncalibrated Images,” Proc. IEEE Fifth Int'l Conf. Computer Vision, pp. 543-548, 1993.
[26] T. Moons, L.J. Van Gool, M.V. Diest, and E.J. Pauwels, “Affine Reconstruction from Perspective Image Pairs Obtained by a Translating Camera,” Applications of Invariance in Computer Vision, J.L. Mundy, A. Zisserman, and D.A. Forsyth, eds., pp. 297-316, Springer-Verlag, 1994.
[27] J.L. Mundy, R.P. Welty, M.H. Brill, P.M. Payton, and E.B. Barrett, "3-D Model Alignment Without Computing Pose," Proc. ARPA Image Understanding Workshop, pp. 727-735.San Mateo, Calif.: Morgan Kaufmann, Jan. 1992.
[28] N. Navab and A. Shashua, "Algebraic Description of Relative Affine Structure: Connections to Euclidean, Affine and Projective Structure," Technical Report 270, Media Laboratory, Massachusetts Inst. of Tech nology, 1994.
[29] J. Oliensis and J.I. Thomas, "Incorporating Motion Error in Multi-Frame Structure From Motion, IEEE Workshop on Visual Motion, pp. 8-13, Princeton, N.J., Los Alamitos, Calif.: CS Press, Oct. 1991.
[30] L. Quan, "Affine Stereo Calibration for Relative Affine Shape Reconstruction," Proc. British Machine Vision Conf., pp. 659-668, 1993.
[31] L. Robert and O. Faugeras, "Relative 3D positionning and 3D convex hull computation from a weakly calibrated stereo pair," Proc. Fourth Int'l Conf. Computer Vision, pp. 540-544,Berlin, May 1993.
[32] H.S. Sawhney, "3D Geometry From Planar Parallax," Proc. CVPR '94, pp. 929-934, 1994.
[33] L.S. Shapiro, A. Zisserman, and M. Brady, "Motion from Point Matches Using Affine Epipolar Geometry," Proc. European Conf. Computer Vision, pp. 73-84,Stockholm, Sweden, May 1994.
[34] A. Shashua,“Correspondence and affine shape from two orthographic views: Motion and Recognition,” A.I. Memo No. 1327, Artificial Intelligence Laboratory, Massachusetts Inst. of Tech nology, Dec. 1991.
[35] A. Shashua, "On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views," Proc. Second Workshop on Applications of Invariance in Computer Vision, pp. 87-112, 1993.
[36] A. Shashua, "Projective Structure From Uncalibrated Images: Structure-From-Motion and Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 8, pp. 778-790, Aug. 1994.
[37] A. Shashua, “Algebraic Functions for Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 779-789, 1995.
[38] A. Shashua and N. Navab, "Relative Affine Structure: Theory and Application to 3D Reconstruction From Perspective Views," Proc. CVPR '94, pp. 483-489, 1994.
[39] G. Sparr, "An Algebraic-Analytic Method for Reconstruction from Image Correspondences," Seventh Scandinavian Conf. Image Analysis,Aalborg, Denmark, 1991.
[40] G. Sparr, "A Common Framework for Kinetic Depth, Reconstruction and Motion for Deformable Objects," Proc. European Conf. Computer Vision, pp. 471-482,Stockholm, Sweden, May 1994.
[41] R. Szeliski and S.B. Kang, "Recovering 3D Shape and Motion from Image Streams Using Non-Linear Least Squares," Technical Report D.E.C., Dec. 1992.
[42] R. Tsai,T. Huang,, and W. Zhu,“Estimating three-dimensional motion parameters of a rigid planar patch, ii: Singular value decomposition,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 30, no. 4, pp. 525-534, 1982.
[43] S. Ullman,“Aligning pictorial descriptions: An approach to object recognition,” Cognition, vol. 32, pp. 193-254, 1989. Also: in MIT AI Memo 931, Dec. 1986.
[44] D. Weinshall,“Model based invariants for 3D vision,” Int’l J. Computer Vision, vol. 10, no. 1, pp. 27-42, 1993.
[45] D. Weinshall and C. Tomasi, “Linear and Incremental Acquisition of Invariant Shape Models from Image Sequences,” Proc. Fourth Int'l Conf. Computer Vision, pp. 675-682, May 1993.
Index Terms:
Structure from motion, visual recognition, alignment, reprojection, projective reometry, algebraic and geometric invariants.
Citation:
Amnon Shashua, Nassir Navab, "Relative Affine Structure: Canonical Model for 3D From 2D Geometry and Applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 9, pp. 873-883, Sept. 1996, doi:10.1109/34.537342 Usage of this product signifies your acceptance of the Terms of Use.
|
