Abstract
Deriving three-dimensional information about a scene from its images is a challenging problem in computer vision. Multiple views of a scene/object from a moving camera can be used for this task. This paper presents a critical appraisal of the theory and algorithms for problems involving 3D geometric constraints between a scene and its multiple views. The essential constraints between the 3D shape, the view transformations and the 2D image projections are presented for various widely applicable models of projection. The recent trend in representing 3D shape in a fixed object-centered coordinate system figures prominently in this paper. It is shown how this approach nicely separates the contribution of 3D shape and motion as manifested in the image motion. This is contrasted with the traditional approach of computing 3D motion as a precursor to the computation of 3D structure. Methods that incorporate these constraints using discrete features (like points) and spatio-temporal intensity gradients are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Adiv. Determining 3D motion and structure from optical flows generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(4):384–401, 1985.
G. Adiv. Inherent ambiguities in recovering 3D information from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5):477–489, 1989.
P. Anandan, Measuring Visual Motion from Image Sequences PhD thesis, University of Massachusetts at Amherst, MA, 1987. COINS TR 87-21.
P. Anandan. A computational framework and an algorithm for the measurement of visual motion. International Journal of Computer Vision, 2(3):283–310, 1989.
A. Azarbayejani, B. Horowitz, and A. Pentland. Recursive estimation of structure and motion using relative orientation constraints. In Proc. Computer Vision and Pattern Recognition Conference, pp. 294-299, 1993.
M. Boldt, R. Weiss, and E. Riseman. Token-based extraction of straight lines. IEEE Transactions on Systems Man and Cybernetics, 19(6):1581–1594, 1989.
J.L. Crowley, P. Stelmaszyk, and C. Discours. Measuring image flow by tracking edgelines. In Proc. 2nd Intl. Conf on Computer Vision, pp. 658-664, 1988.
K. Daniilidis and H.H. Nagel. Analytical results on error sensitivity of motion estimation from two views. In Proc. 1st European Conference on Computer Vision, pp. 199-208, 1990.
K. Daniilidis and H.H. Nagel. The coupling of rotation and translation in motion estimation of planar surfaces. In Proc. Computer Vision and Pattern Recognition Conference, pp. 188-193, 1993.
R. Deriche and O. Faugeras. Tracking line segments. In Proc. 1st European Conference on Computer Vision, pp. 259-268, 1990.
R. Dutta and M.A. Snyder. Robustness of correspondence-based structure from motion. In Proc. 3rd Intl. Conf. on Computer Vision, pp. 106-110, 1990.
J.R. Bergen et al. Hierarchial model-based motion estimation. In Proc. 2nd European Conference on Computer Vision, pp. 237-252, 1992.
K.J. Hanna. Direct multi-resolution estimation of ego-motion and structure from motion. In Proc. IEEE Wkshp. on Visual Motion, pp. 156-162, 1991.
R. Hartley and R. Gupta. Computing matched epipolar projections. In Proc. Computer Vision and Pattern Recongnition Conference, pp. 549-555, 1993.
J.C. Hay. Optical motions and space perception: An extension of Gibson’s analysis. Psychological Review, 73:550–565, 1966.
D.J. Heeger and A.D. Jepson. Subspace methods for recovering rigid motion I: Algorithm and implementation. Technical Report RBCV-TR-90-35, University of Toronto, 1990.
J. Heel. Temporally integrated surface reconstruction. In Proc. 3rd Intl. Conf on Computer Vision, pp. 292-295, 1990.
B.K.P. Horn. Recovering baseline and orientation from essential matrix. Internal Report, 1990.
B.K.P. Horn. Relative orientation. International Journal of Computer Vision, 4(1):59–78, 1990.
B.K.P. Horn. Relative orientation revisited. Journal of the Optical Society of America A, 8(10):1630–1638, 1991.
B.K.P. Horn and B.G. Schunck. Determining optical flow. Artificial Intelligence, 17(1-3):185–203, 1981.
B.K.P. Horn and E.J. Weldon. Direct methods for recovering motion. International Journal of Computer Vision, 2(1):51–76, 1988.
T.S. Huang and O.D. Faugeras. Some properties of the E matrix in two-view motion estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(12):1310–1312, 1989.
J.J. Kowenderink and Andrea J. van Doorn. Affine structure from motion. Journal of the Optical Society of America A, 81:377–385, 1991.
Chia-Hoang Lee. Structure and motion from two perspective views via planar patch. In Proc. 2nd Intl. Confi on Computer Vision, pp. 158-164, 1988.
Chia-Hoang Lee and T. Huang. Finding point correspondences and determining motion of a rigid object from two weak perspective views. Computer Vision Graphics and Image Processing, 52:309–327, 1990.
H.C. Longuet-Higgins. A computer algorithm for reconstructing a scene from two projections. Nature, 293:133–135, 1981.
H.C. Longuet-Higgins and K. Prazdny. The interpretation of a moving retinal image. In Proc. Royal Society of London B, pp. 385-397, 1980.
R. Manmatha. Thesis Proposal, Univ. of Massachusetts, 1992.
R. Manmatha and J. Oliensis. Extracting affine defformations from image patches — i. finding scale and rotation. In Proc. Computer Vision and Pattern Recognition Conference, pp. 754-755, 1933.
S. Maybank, Theory of Reconstruction from Image Motion. Springer-Verlag, 1993.
R. Mohr, F. Veillon, and L. Quan. Relative 3D reconstruction using multiple uncalibrated images. In Proc. Computer Vision and Pattern Recongnition Conference, pp. 543-548, 1993.
J.L. Mundy and A. Zisserman, Geometric Invariance in Computer Vision. The MIT Press, MA, 1992.
S. Negahdaripour and B.K.P. Horn. Direct passive navigation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9(1):168–176, 1987.
J. Oliensis and J.I. Thomas. Incorporating motion error in multi-frame structure from motion. In Proc. IEEE Wkshp. on Visual Motion, pp. 8-13. 1991.
C.J. Poelman and T. Kanade. A paraperspective factorization method for shape and motion recovery. Technical Report CMU-CS-92-208, Carnegie Mellon University, 1992.
K. Rangarajan and M. Shah. Establishing motion correspondence. In Proc. Computer Vision and Pattern Recognition Conference, pp. 103-108, 1991.
J.H. Rieger and D.T. Lawton. Processing differential image motion. Journal of the Optical Society of America A, 2(2):354–360, 1985.
H.S. Sawhney and A.R. Hanson. Comparative results of some motion algorithms on real image sequences. In Proc. DARPA Image Understanding Workshop, 1990.
H.S. Sawhney and A.R. Hanson. Identification and 3D description of “shallow” environmental structure in a sequence of images. In Proc. Computer Vision and Pattern Recognition Conference, pp. 179-186, 1991.
H.S. Sawhney and A.R. Hanson. Trackability as a cue for potential obstacle identification and 3D description. International Journal of Computer Vision, 1993.
H.S. Sawhney J. Oliensis, and A.R. Hanson. Image description and 3D reconstruction from image trajectories of rotational motion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9), 1993.
Harpreet S. Sawhney. Spatial and Temporal Grouping in the Interpretation of Image Motion. PhD thesis, University of Massachusetts at Amherst, MA, 1992. COINS TR 92-05.
S.K. Sethi and R. Jain. Finding trajectories of feature points in a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9(1):56–73, 1987.
Amnon Shashua. Correspondence and affine shape from two orthographic views: Motion and recognition. Technical Report AI Meno No. 1327, Massachusetts Institute of Technology, 1991.
M. Spetsakis and Y. Aloimonos. A multi-frame approach to visual motion perception. International Journal of Computer Vision, 6(3):245–255, 1991.
M.E. Spetsakis and J. Aloimonos. Optimal computing of structure from motion using point correspondences in two frames. In Proc. 2nd Intl. Conf. on Computer Vision, pp. 449-453, 1988.
R. Szeliski and S.B. Kang. Recovering 3D shape and motion from image streams using non-linear least squares. In Proc. Computer Vision and Pattern Recognition Conference, pp. 752-753, 1993.
R. Szeliski and S.B. Kang. Recovering 3D shape and motion from image streams using non-linear least squares. Technical Report CRL93/3, DEC Cambridge Research Lab., 1993.
J.I. Thomas, A. Hanson, and J. Oliensis. Understanding noise: The critical role of motion error in scene reconstruction. In Proc. 4th Intl. Conf On Computer Vision, pp. 325-329, 1993.
C. Tomasi. Shape and Motion from Image Streams: A Factorization Method. PhD thesis, Carnegie Mellon University, 1991. CMU-CS-91-172.
C. Tomasi and T. Kanade. Shape and motion from image streams under orthography: A factorization method. International Journal of Computer Vision, 9(2):137–154, 1992.
R.Y. Tsai and T.S. Huang. Uniqueness and estimation of 3D motion parameters and surface structures of rigid objects. In Whitman Richards and Shimon Ullman, editors, Image Understanding 1984, pp. 135–171. Ablex Corporation, NJ, 1984.
S. Ullman. The Interpretation of Visual Motion. The MIT Press, Cambridge, MA, 1979.
A. Verri and T. Poggio. Motion field and optical flow: Qualitative properties. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5):490–498, 1989.
D. Weinshall. Model based invariants for 3D vision. International Journal of Computer Vision, 10(1):27–42, 1993.
D. Weinshall and C. Tomasi. Linear and incremental acquisition of invariant shape models from image sequences. In Proc. 4th Intl. Conf. On Computer Vision, pp. 675-682, 1993.
P. Werkhoven and J.J. Koenderink. Extraction of motion parallax structure in the visual system I. Biological Cybernetics, 59, 1990.
L.R. Williams and A.R. Hanson. Translating optical flow into token matches and depth from looming. In ICCV, pp. 441-448, 1988.
Z. Zhang and O. Faugeras. 3D Dynamic Scene Analysis: A Stereo Approach. Springer, Berlin, Heidelberg, 1992.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sawhney, H.S., Anandan, P. (1996). 3D Constraints on Monocular Image Sequences: Theory and Algorithms. In: Sanz, J.L.C. (eds) Image Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58288-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-58288-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63528-1
Online ISBN: 978-3-642-58288-2
eBook Packages: Springer Book Archive