Abstract
This paper presents a new Fourier-based approach to the separation or decoupling of m additive images from a time-sequence of the sum of these images where at least m−1 images are translating with distinct and unique velocity. A closed-form solution is presented for the case where m=2. A generalization is then presented which extends the theory to embrace situations where the images are not additive but are, instead, formed by the superposition of an occluding object or objects on an occluded background. That is, the approach is generalized to effect a model-free segmentation of objects undergoing translatory fronto-parallel motion in dynamic image sequences. Object velocities of one pixel per frame are sufficient to guarantee segmentation.
We also show how the technique can be applied on a local basis to compute a dense instantaneous optical flow field for the image sequence, even in relatively featureless regions. The technique is evaluated using Otte's and Nagel's benchmark image sequence, for which ground-truth data is available, and results comparable with the ground-truth flow field are achieved. RMS errors of velocity magnitude and direction are computed and reported.
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
D. Vernon, Machine Vision Prentice-Hall International, London (1991).
D. Vernon and G. Sandini, Parallel Computer Vision — The VIS a VIS System, Ellis Horwood, London (1992).
J.H. Duncan and T.-C. Chou, “On the detection and the computation of optical flow”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(3), 346–352 (1992).
H. Shariat and K.E. Price, “Motion estimation with more than two frames”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5), 417–434 (1990).
M.P. Cagigal, L. Vega, P. Prieto, “Object movement characterization from lowlight-level images”, Optical Engineering, 33(8), 2810–2812 (1994).
M.P. Cagigal, L. Vega, P. Prieto, “Movement characterization with the spatiotemporal Fourier transform of low-light-level images”, Applied Optics, 34(11), 1769–1774 (1995).
S. A. Mahmoud, M.S. Afifi, and R. J. Green, “Recognition and velocity computation of large moving objects in images”, IEEE Transactions on Acoustics, Speech, and Signal Processing, 36(11), 1790–1791 (1988).
S. A. Mahmoud, “A new technique for velocity estimation of large moving objects”, IEEE Transactions on Signal Processing, 39(3), 741–743 (1991).
S.A. Rajala, A. N. Riddle, and W.E. Snyder, “Application of one-dimensional Fourier transform for tracking moving objects in noisy environments”, Computer Vision, Graphics, and Image Processing, 21, 280–293 (1983).
D. Vernon, “Phase-Based Measurement of Object Velocity in Image Sequences using the Hough Transform”, Optical Engineering (1996).
D. J. Fleet and A.D. Jepson, “Hierarchical construction of orientation and velocity selective filters”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(3), 315–325 (1989).
D. J. Fleet and A.D. Jepson, “Computation of component image velocity from local phase information”, International Journal of Computer Vision, 5, 77–104 (1990).
D. J. Fleet and A.D. Jepson, “Stability in Phase Information”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(12), 1253–1268 (1993).
J.L. Barron, D.J. Fleet, and S. Beauchemin, “Performance of optical flow techniques”, Int. Journal of Computer Vision, 12(1), 43–77 (1994).
M. Otte and H.-H. Nagel, “Optical flow estimation: advances and comparisons”, Lecture Notes in Computer Science, J.O. Eklundh (Ed.), Computer Vision — ECCV '94, Springer-Verlag, Berlin, 51–60 (1994).
M. Tistarelli, “Multiple constraints for optical flow”, Lecture Notes in Computer Science, J.O. Eklundh (Ed.), Computer Vision — ECCV '94, Springer-Verlag, Berlin, 61–70 (1994).
L. Jacobson and H. Wechsler, “Derivation of optical flow using a spatiotemporal-frequency approach”, Computer Vision, Graphics, and Image Processing, 38, 29–65 (1987).
D. Vernon, “Decoupling Fourier Components of Dynamic Image Sequences: Theory and Application to Segmentation and Estimation of Optical Flow”, Technical Report, Department of Computer Science, National University of Ireland, Maynooth (1997).
D. Vernon, “Segmentation in Dynamic Image Sequences by Isolation of Coherent Wave Profiles”, Proceedings of the 4th European Conference on Computer Vision, Springer-Verlag, 293–303 (1996).
P.V.C. Hough, ‘Method and Means for Recognising Complex Patterns’ U.S. Patent 3,069,654, (1962).
L. Hahn, Complex Numbers and Geometry, The Mathmatical Association of America, Washington, D.C. (1994).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vernon, D. (1998). Decoupling Fourier components of dynamic image sequences: A theory of signal separation, image segmentation, and optical flow estimation. In: Burkhardt, H., Neumann, B. (eds) Computer Vision — ECCV’98. ECCV 1998. Lecture Notes in Computer Science, vol 1407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054734
Download citation
DOI: https://doi.org/10.1007/BFb0054734
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64613-6
Online ISBN: 978-3-540-69235-5
eBook Packages: Springer Book Archive