This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Novel View Synthesis by Cascading Trilinear Tensors
October-December 1998 (vol. 4 no. 4)
pp. 293-306

Abstract—We present a new method for synthesizing novel views of a 3D scene from two or three reference images in full correspondence. The core of this work is the use and manipulation of an algebraic entity termed the trilinear tensor that links point correspondences across three images. For a given virtual camera position and orientation, a new trilinear tensor can be computed based on the original tensor of the reference images. The desired view can then be created using this new trilinear tensor and point correspondences across two of the reference images.

[1] E.H. Adelson and J.R. Bergen, "The Plenoptic Function and the Elements of Early Vision," Computational Models of Visual Processing M. Landy and J.A. Movshon, eds., Chapter 1. Cambridge, Mass.: MIT Press, 1991.
[2] S. Avidan, T. Evgeniou, A. Shashua, and T. Poggio, "Image-Based View Synthesis By Combining Trilinear Tensors and Learning Techniques," VRST, 1997.
[3] S. Avidan and A. Shashua, "Tensorial Transfer: On the Representation ofn> 3 Views of a 3D Scene," Proc. ARPA Image Understanding Workshop, 1996.
[4] S. Avidan and A. Shashua, “Novel View Synthesis in Tensor Space,” Proc. Conf. Computer Vision and Pattern Recognition pp. 1034-1040, June 1997.
[5] S. Avidan and A. Shashua, "Unifying Two-View and Three-View Geometry," Proc. ARPA Image Understanding Workshop, 1997.
[6] S. Avidan and A. Shashua, "Threading Fundamental Matrices," Proc. European Conf. Computer Vision, June 1998.
[7] E.B. Barrett, P.M. Payton, and G. Gheen, "Robust Algebraic Invariant Methods with Applications in Geometry and Imaging," Proc. SPIE Remote Sensing, July 1995.
[8] T. Beier and S. Neely, "Feature Based Image Metamorphosis," Computer Graphics(Proc. Siggraph 91), ACM Press, New York, 1992, pp. 35-42.
[9] 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.
[10] D. Beymer, A. Shashua, and T. Poggio, "Example Based Image Analysis and Synthesis," M.I.T. A.I. Memo No. 1431, 1993.
[11] P.J. Burt and E.H. Adelson, “The Laplacian Pyramid as a Compact Image Code,” IEEE Trans. Comm., vol. 31, no. 4, pp. 532-540, 1983.
[12] S.E. Chen and L. Williams, “View Interpolation for Image Synthesis,” Proc. ACM SIGGRAPH '93, pp. 279-288, Aug. 1993.
[13] S.E. Chen, "QuickTime VR—An Image-Based Approach to Virtual Environment Navigation," Siggraph 95 Conf. Proc., ACM Press, New York, 1995, pp. 29-38.
[14] T. Evgeniou, "Image-Based Rendering Using Algebraic Techniques," master's thesis, Massachusetts Inst. of Tech nology, June 1996.
[15] O.D. Faugeras and T. Papadopoulo, "A Nonlinear Method for Estimating the Projective Geometry of Three Views," Proc. Int'l Conf. Computer Vision,Bombay, India, Jan. 1998.
[16] O. Faugeras, "What can be seen in three dimensions with an uncalibrated stereo rig?" Second European Conf. Computer Vision, pp. 563-578, 1992.
[17] O. Faugeras and B. Mourrain, "On the Geometry and Algebra of the Point and Line Correspondences Between N Images," Proc. Int'l Conf. Computer Vision, pp. 951-956, 1995.
[18] 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.
[19] S.J. Gortler, R. Grzeszczuk, R. Szeliski, and M.F. Cohen, “The Lumigraph,” Proc. SIGGRAPH '96, pp. 43-54, 1996.
[20] W.E.L. Grimson,“Why stereo vision is not always about 3D reconstruction,” A.I. Memo No. 1435, Artificial Intelligence Laboratory, Massachusetts Inst. of Tech nology, July 1993.
[21] C. Harris and M. Stephens, "A Combined Corner and Edge Detector," Proc. Fourth Alvey Vision Conf. Intelligence, pp. 189-192, 1988.
[22] R. Hartley, "Lines and Points in Three Views—A Unified Approach," Proc. ARPA Image Understanding Workshop, 1994.
[23] R.I. Hartley, “In Defense of the 8-Point Algorithm,” Proc. Fifth Int'l Conf. Computer Vision, pp. 1,064-1,070, June 1995.
[24] R.I. Hartley, "A Linear Method for Reconstruction From Lines and Points," Proc. Int'l Conf. Computer Vision, 1995, pp. 882-887.
[25] R. Hartley, “Minimizing Algebraic Error in Geometric Estimation Problem,” Proc. Sixth Int'l Conf. Computer Vision, pp. 469-476, 1998.
[26] A. Heyden, “Reconstruction from Image Sequences by Means of Relative Depths,” Proc. Fifth Int'l Conf. Computer Vision, June 1995.
[27] A. Heyden and K. Astrom, “Algebraic Properties of Multilinear Constraints,” Proc. Fourth European Conf. Computer Vision, B. Buxton and R. Cipolla, eds., pp. 671–682, Apr. 1996.
[28] W. Hoff and N. Ahuja, "Surfaces From Stereo: Integrating Feature Matching, Disparity Estimation, and Contour Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 2, pp. 121-136, Feb. 1989.
[29] S. Laveau and O. Faugeras, “Oriented Projective Geometry for Computer Vision,” Proc. European Conf. Computer Vision ECCV'96, pp. 147-156, 1996.
[30] S. Laveau and O.D. Faugeras, "3-D Scene Representation as a Collection of Images," Proc. Int'l Conf. Pattern Recognition, 1994.
[31] M. Levoy and P. Hanrahan, “Light Field Rendering,” Proc. SIGGRAPH '96, pp. 31-42, 1996.
[32] 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.
[33] L. McMillan and G. Bishop, "Plenoptic Modeling: An Image-Based Rendering System," Siggraph 95 Conf. Proc., ACM Press, New York, 1995, pp. 39-46.
[34] P.A. Beardsley, A. Zisserman, and D.W. Murray, “Sequential Updating of Projective and Affine Structure from Motion,” Int'l J. Computer Vision, vol. 23, pp. 235–259, June 1997.
[35] S. Peleg and J. Herman, “Panoramic Mosaics by Manifold Projection,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 338-343, June 1997.
[36] P.H.S. Torr, A. Zisserman, and D. Murray, "Motion Clustering Using the Trilinear Constraint Over Three Views," Proc. Workshop Geometrical Modeling and Invariants for Computer Vision, 1995.
[37] T. Poggio and R. Brunelli, "A Novel Approach to Graphics," Technical Report A.I. Memo No. 1354, Artificial Intelligence Laboratory, Massachusetts Inst. of Tech nology, 1992.
[38] M. Irani, R. Kumar, P. Anandan, J. Bergen, and K. Hanna, "Representation of Scenes from Collections of Images," Proc. IEEE Workshop Representation of Visual Scenes, 1995.
[39] B. Rousso, S. Avidan, A. Shashua, and S. Peleg, “Robust Recovery of Camera Rotation from Three Frames,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, 1996.
[40] S.M. Seitz and C.R. Dyer, "Physically-Valid View Synthesis By Image Interpolation," Proc. IEEE Workshop Representation of Visual Scenes, 1995.
[41] S.M. Seitz and C.R. Dyer, “View Morphing,” ACM SIGGRAPH, pp. 21-30, 1996.
[42] A. Shashua, “Algebraic Functions for Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 779-789, 1995.
[43] A. Shashua and P. Anandan, "The Generalized Trilinear Constraints and the Uncertainty Tensor," Proc. ARPA Image Understanding Workshop, 1996.
[44] A. Shashua and S. Avidan, "The Rank4 Constraint in Multiple View Geometry," Proc. European Conf. Computer Vision,Cambridge, UK, Apr. 1996.
[45] A. Shashua and S.J. Maybank, "Degenerate n Point Configurations of Three Views: Do Critical Surfaces Exist?" Technical Report TR 96-19, Hebrew Univ. of Jerusalem, Nov. 1996.
[46] A. Shashua and S. Toelg, "The Quadric Reference Surface: Applications in Registering Views of Complex 3D Objects," Proc. European Conf. Computer Vision, 1994.
[47] A. Shashua and M. Werman, "Trilinearity of Three Perspective Views and Its Associated Tensor," Proc. Int'l Conf. Computer Vision, June 1995.
[48] M.E. Spetsakis and J. Aloimonos, “Structure from Motion Using Line Correspondences,” Int'l J. Computer Vision, vol. 4, pp. 171-183, 1990.
[49] M.E. Spetsakis and J. Aloimonos, "A Unified Theory of Structure from Motion," Proc. ARPA Image Understanding Workshop, 1990.
[50] G.P. Stein and A. Shashua, “Model-Based Brightness Constraints: On Direct Estimation of Structure and Motion,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 400-406, 1997.
[51] R. Szeliski and S.B. Kang, “Direct Methods for Visual Scene Reconstruction,” Proc. Workshop Representations of Visual Scenes, 1995.
[52] P.H.S. Torr and A. Zisserman, "Robust Parameterization and Computation of the Trifocal Tensor," Image and Vision Computing, vol. 15, pp. 591-607, 1997.
[53] B. Triggs, Matching Constraints and the Joint Image Proc. Int'l Conf. Computer Vision, pp. 338-343, 1995.
[54] J. Weng, T.S. Huang, and N. Ahuja, Motion and Structure from Line Correspondences: Closed-Form Solution, Uniqueness, and Optimization Trans. Pattern and Machine Intelligence, vol. 14, no. 3, pp. 318-336, Mar. 1992.
[55] T. Werner, R.D. Hersch, and V. Hlavac, "Rendering Real-World Objects Using View Interpolation," Proc. Int'l Conf. Computer Vision, 1995.
[56] G. Wolberg, Digital Image Warping, IEEE CS Press, 1990.

Index Terms:
Image-based rendering, trilinear tensor, virtual reality, image manipulation.
Citation:
Shai Avidan, Amnon Shashua, "Novel View Synthesis by Cascading Trilinear Tensors," IEEE Transactions on Visualization and Computer Graphics, vol. 4, no. 4, pp. 293-306, Oct.-Dec. 1998, doi:10.1109/2945.765324
Usage of this product signifies your acceptance of the Terms of Use.