
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
G.S.J. Young, R. Chellappa, "Statistical Analysis of Inherent Ambiguities in Recovering 3D Motion from a Noisy Flow Field," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 10, pp. 9951013, October, 1992.  
BibTex  x  
@article{ 10.1109/34.159903, author = {G.S.J. Young and R. Chellappa}, title = {Statistical Analysis of Inherent Ambiguities in Recovering 3D Motion from a Noisy Flow Field}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {14}, number = {10}, issn = {01628828}, year = {1992}, pages = {9951013}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.159903}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Statistical Analysis of Inherent Ambiguities in Recovering 3D Motion from a Noisy Flow Field IS  10 SN  01628828 SP995 EP1013 EPD  9951013 A1  G.S.J. Young, A1  R. Chellappa, PY  1992 KW  3D motion recovery; image processing; inherent ambiguities; optical flow field; statistical model; CramerRao lower bound; surface orientation; field of view; aperture; feature points; image processing; optical information processing; statistical analysis VL  14 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
The inherent ambiguities in recovering 3D motion information from a single optical flow field are studied using a statistical model. The ambiguities are quantified using the CramerRao lower bound. As a special case, the performance bound for the motion of 3D rigid planar surfaces is studied in detail. The dependence of the bound on factors such as the underlying motion, surface position, surface orientation, field of view, and density of available pixels are derived as closedform expressions. A subset of the results support S. Adiv's (1989) analysis of the inherent ambiguities of motion parameters. For the general motion of an arbitrary surface. It is shown that the aperture problem in computing the optical flow restricts the nontrivial information about the 3D motion to a sparse set of pixels at which both components of the flow velocity are observable. Computer simulations are used to study the dependence of the inherent ambiguities on the underlying motion, the field of view, and the number of feature points for the motion in front of a nonplanar environment.
[1] G. Adiv, "Determining threedimensional motion and structure from optical flow generated by several moving objects,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI7, no. 4, pp. 384401, July 1985.
[2] G. Adiv, "Inherent ambiguities in recovering 3D motion and structure from a noisy flow field,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 5, pp. 477489, May 1989.
[3] J. K. Aggarwal, "Motion and timevarying imageryAn overview," inProc. IEEE Workshop Motion: Representation Anal.(Kiawah Island, SC), May 1986.
[4] J. Aloimonos and D. Shulman,Integration of Visual Modules: An Extension of the Marr Paradigm. Boston, MA: Academic, 1989.
[5] P. Anandan, "Computing dense displacement fields with confidence measures in scenes containing occlusion," inProc. DARPA Image Understanding Workshop, Oct. 1984, pp. 236246.
[6] P. Anandan, "A unified perspective on computational techniques for the measurement of visual motion," inProc. First Int. Conf. Comput. Vision(London), June 1987, pp. 219230.
[7] P. Anandan and R. Weiss, "Introducing a smoothness constraint in a matching approach for the computation of displacement fields," inProc. DARPA Image Understanding Workshop, Dec. 1985, pp. 186196.
[8] T. J. Broida, S. Chandrashekhar, and R. Chellappa, "Recursive estimation of 3D kinematics and structure from noisy monocular image sequences,"IEEE Trans. Aerosp. Electron. Syst., vol. AES26, pp. 639656, Aug. 1990.
[9] T. Broida and R. Chellappa, "Estimation of object motion parameters from noisy images,"IEEE Trans. Pattern Anal. Machine Intell, vol. PAMI8, no. 1, Jan. 1986.
[10] T. J. Broida and R. Chellappa, "Performance bounds for estimating threedimensional motion parameters from a sequence of noisy images,"J. Optical Soc. Amer. A, vol. 6, no. 6, pp. 879889, June 1989.
[11] A. R. Bruss and B. K. P. Horn, "Passive navigation,"Comput. Vision Graphics Image Processing, vol. 21, no. 1, pp. 320, Jan. 1983.
[12] B. CernuschiFriaset al., "Toward a modelbased bayesian theory for estimating and recognizing parameterized 3d objects using two or more images taken from different positions,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 10, pp. 10281052, Oct. 1989.
[13] E. Hildreth, "Computation underlying the measurement of visual motion,"Artificial Intell., vol. 23, pp. 309354, 1984.
[14] E. Hildreth,The Measurement of Visual Motion, Cambridge, MA: MIT Press, 1983.
[15] B. K. P. Horn,Robot Vision. Cambridge, MA: M.I.T. Press, 1986.
[16] B. K. P. Horn, "Motion fields are hardly ever ambiguous,"Int. J. Comput. Vision, vol. 1, pp. 259274, Oct. 1987.
[17] B. K. P. Horn, "Relative orientation,"Int. J. Computer Vision, vol. 4, no. 1, pp. 5978, 1990.
[18] H. C. LonguetHiggins, "A computer algorithm for reconstructing a scene from two projections,"Nature, vol. 293, pp. 133135, Sept. 1981.
[19] K. Prazdny, "Egomotion and relative depth map from optical flow,"Biol. Cybern., vol. 36, pp. 87102, Feb. 1980.
[20] H. W. Sorenson,Parameter Estimation, Principles and Problems. New York: Marcel Dekker, 1980.
[21] M. E. Spetsakis and J. Aloimonos, "Optimal motion estimation," inProc. Workshop Visual Motion(Irvine, CA), Mar. 1989, pp. 229237.
[22] G. Strang,Linear Algebra and Its Application. New York: Academic, 1980.
[23] R. Y. Tsai and T. S. Huang, "Uniqueness and estimation of threedimensional motion parameters of rigid objects with curved surfaces,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI6, pp. 1327, Jan. 1984.
[24] S. Ullman, "Analysis of visual motion by biological and computer systems,"Comput., vol. 14, pp. 5769, Aug. 1981.
[25] A. M. Waxman, B. KamgarParsi, and M. Subbarao, "Closedform solutions to image flow equations for 3d structure and motion,"Int. J. Comput. Vision, vol. 1, pp. 239258, Oct. 1987.
[26] J. Weng, T. S. Huang, and N. Ahuja, "Motion from images: Image matching, parameter estimation, and intrinsic stability," inProc. IEEE Workshop Visual Motion, (Irvine, CA), Mar. 2022, 1989, pp. 359366.
[27] G. S. Young and R. Chellappa, "3d motion estimation using a sequence of noisy stereo images : Models, estimation, and uniqueness results,"IEEE Trans. Patt. Anal. Machine Intell., vol. 12, no. 8, pp. 735759, Aug. 1990.