Frequency domain analysis of general planar rigid motion with finite duration
JOSA A, Vol. 16, Issue 6, pp. 1238-1253 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001238
Acrobat PDF (699 KB)
Abstract
We present the frequency domain analysis of the most general model of planar rigid motion, i.e., motion under the joint effects of translations and rotations with polynomial-type time dependence. We show that in the frequency domain the contribution of the object’s shape and texture is separate from that of the motion parameters in this general framework. Special attention is devoted to the case of translations and rotations with constant velocity and constant acceleration, which are the most likely candidates for modeling motion in practical contexts. This work also focuses on the distinction between the effects of the motion parameters and those of time duration, a distinction that is necessary for a clear assessment of the effects of acceleration in the frequency domain. The results presented belong to the field of signal theory and may serve as a theoretical basis in the various applications of motion models in the frequency domain, which include pattern recognition, television, image registration, image sequence analysis, and classification and neural modeling of motion perception.
© 1999 Optical Society of America
OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.2960) Image processing : Image analysis
Citation
G. M. Cortelazzo, L. Lucchese, and C. M. Monti, "Frequency domain analysis of general planar rigid motion with finite duration," J. Opt. Soc. Am. A 16, 1238-1253 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-6-1238
Sort: Year | Journal | Reset
References
- J. O. Drewery, “The filtering of luminance and chrominance signals to avoid cross-colour in a PAL colour system,” British Broadcasting Corporation (BBC) Tech. Rep. RD 1975/31 (BBC, London, 1975).
- F. Kretz and J. Sabatier, “Échantillonage des images de télévision: analyse dans le domain spatio-temporel et dans le domain de Fourier,” Ann. Telecommun. 36, 231–273 (1981).
- A. M. Tekalp, Digital Video Processing (Prentice-Hall, Englewood Cliffs, N.J., 1995).
- D. I. Barnea and H. F. Silverman, “A class of algorithms for fast digital image registration,” IEEE Trans. Comput. C-21, 179–186 (1982).
- L. G. Brown, “A survey of image registration techniques,” ACM Computing Surveys 24, 325–376 (1992).
- T. S. Huang, Image Sequence Analysis (Springer-Verlag, Berlin, 1983).
- R. Wilson, A. D. Calway, and E. R. Pearson, “A generalized wavelet transform for Fourier analysis: the multiresolution Fourier transform and its application to image and audio signals analysis,” IEEE Trans. Inf. Theory 38, 674–690 (1992).
- W. Chen, G. B. Giannakis, and N. Nandhakumar, “Spatiotemporal approach for time-varying global image motion estimation,” IEEE Trans. Image Process. 5, 1448–1461 (1996).
- P. Burlina and R. Chellappa, “Analyzing looming motion components from their spatiotemporal spectral signature,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 1029–1033 (1996).
- T. R. Reed, “The analysis of motion in natural scenes using a spatiotemporal/spatiotemporal-frequency representation,” in Proceedings of IEEE 1997 International Conference on Image Processing (ICIP’97) (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. I, pp. 93–96.
- M. Bennamoun, “Application of time-frequency signal analysis to motion estimation,” in Proceedings of the IEEE 1997 International Conference on Image Processing (ICIP’97), (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. II, pp. 148–151.
- D. Casasent and D. Psaltis, “Position oriented and scale-invariant optical correlation,” Appl. Opt. 15, 1793–1799 (1976).
- D. Casasent, “Pattern recognition: a review,” IEEE Spectr., 28–33 (March 1981).
- P. E. Zwicke and I. Kiss, “A new implementation of the Mellin transform and its application to radar classification of ships,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-5, 191–198 (1983).
- Y. Sheng and J. Duvernoy, “Circular-Fourier-radial-Mellin descriptors for pattern recognition,” J. Opt. Soc. Am. A 3, 885–887 (1986).
- Y. Sheng and H. H. Arsenault, “Experiments on pattern recognition using invariant Fourier–Mellin descriptors,” J. Opt. Soc. Am. A 3, 771–776 (1986).
- A. Goshtasby, “Template-matching on rotated images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-7, 338–344 (1985).
- E. De Castro and C. Morandi, “Registration of translated and rotated images using finite Fourier transforms,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 700–703 (1987).
- S. Alliney, “Digital analysis of rotated images,” IEEE Trans. Pattern. Anal. Mach. Intell. 15, 499–504 (1993).
- B. S. Reddy and B. N. Chatterji, “An FFT-based technique for translation, rotation, and scale-invariant image registration,” IEEE Trans. Image Process. 5, 1266–1271 (1996).
- S. Alliney, G. M. Cortelazzo, and G. A. Mian, “On the registration of an object translating on a static background,” Pattern Recogn. 29, 131–141 (1996).
- D. Adolph, R. Buschmann, “1.15 Mbit/s coding of video signals including global motion compensation,” Signal Process. Image Commun. 3, 259–274 (1991).
- Y. T. Tse, R. L. Baker, “Global zoom/pan estimation and compensation for video compression,” in Proceedings of the 1991 International Conference on Acoustics, Speech and Signal Processing (ICASSP’91) (IEEE Computer Society Press, Los Alamitos Calif., 1991), Vol. 4, pp. 2725–2728.
- G. Keesman, “Motion estimation based on a motion model incorporating translation, rotation and zoom,” Signal Process. 4, 31–34 (1988).
- M. Hoetter, “Differential estimation of the global motion parameters zoom and pan,” Signal Process. 16, 249–265 (1989).
- S. F. Wu and J. Kittler, “A differential method for simultaneous estimation of rotation, change of scale and translation,” Signal Process. Image Commun. 2, 69–80 (1990).
- A. B. Watson, A. J. Ahumada, Jr., “A look at motion in the frequency domain,” NASA Tech. Memorandum No. 84352 (NASA Ames Research Center, Moffett Field, Calif., 1983).
- D. J. Fleet and A. D. Jepson, “Computation of component image velocity from local phase information,” Int. J. Comput. Vis. 5, 77–104 (1990).
- G. Cortelazzo and M. Balanza, “Frequency domain analysis of translations with piecewise cubic trajectories,” IEEE Trans. Pattern. Anal. Mach. Intell. 15, 411–416 (1993).
- G. Cortelazzo and G. Nalesso, “A differential equation approach to the computation of the Fourier transform of images of translating objects,” IEEE Trans. Inf. Theory 40, 2049–2058 (1994).
- M. Chahine and J. Konrad, “Estimation of trajectories for accelerated motion from time-varying imagery,” in Proceedings of the IEEE 1994 International Conference on Image Processing (ICIP’94) (IEEE Computer Society Press, Los Alamitos, Calif., 1994), Vol. II, pp. 800–804.
- A. J. Patti, M. Ibrahim, and A. M. Tekalp, “Digital video standards conversion in the presence of accelerated motion,” in Proceedings of the 1994 International Conference on Acoustics Speech and Signal Processing (ICASSP’94) (IEEE Computer Society Press, Los Alamitos, Calif., 1994), Vol. 5, pp. 225–228.
- J. Weng, T. S. Huang, and N. Ahuja, “3-D motion estimation, understanding, and prediction from noisy image sequences,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 370–389 (1987).
- G.-S. J. Young and R. Chellappa, “3-D motion estimation using a sequence of noisy stereo images: models, estimation, and uniqueness results,” Trans. Pattern Anal. Mach. Intell. 12, 735–759 (1990).
- G. Cortelazzo, M. Balanza, and C. Monti, “Frequency domain analysis of rotational motion,” in Multidimensional Systems and Signal Processing, N. K. Bose, ed. (Kluwer Academic, Boston, Mass., 1993), Vol. 4, pp. 203–225.
- A. Papoulis, Systems and Transforms with Applications in Optics McGraw-Hill, New York, 1968.
- M. Abramovitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Abramovitz, New York, 1968).
- L. Lucchese, G. M. Cortelazzo, and C. Monti, “A frequency domain technique for estimating rigid planar rotations,” in Proceedings of the IEEE 1996 International Symposium on Circuits and Systems (ISCAS’96) (IEEE Computer Society Press, Los Alamitos, Calif., 1996), Vol. 2, pp. 774–777.
- L. Lucchese, G. M. Cortelazzo, and M. Rizzato, “A phase correlation technique for estimating rigid planar rotations,” in Proceedings of the 5^{th} International Workshop on Time-Varying Image Processing and Moving Object Recognition (Elsevier Science B.V., Amsterdam, 1996), pp. 244–249.
- L. Lucchese, G. M. Cortelazzo, and C. Monti, “High resolution estimation of planar rotations based on Fourier transform and radial projections,” in Proceedings of the IEEE 1997 International Symposium on Circuits and Systems (ISCAS’97) (IEEE Computer Society Press, Los Alamitos, Calif., 1997), Vol. II, pp. 1181–1184.
- J. J. Koenderink and J. Van Doorn, “Affine structure from motion,” J. Opt. Soc. Am. A 8, 377–385 (1991).
- L. Lucchese and G. M. Cortelazzo, “Frequency domain analysis of affine motion with linear time-dependence and finite duration,” in Proceedings of the IASTED (International Association of Science and Technology for Development) International Conference on Signal Processing and Communications (IASTED/Acta Press, Anaheim, Calif., 1998), pp. 28–31.
- L. Lucchese, G. M. Cortelazzo, and C. Monti, “Estimation of affine transformations between image pairs via Fourier transform,” in Proceedings of the IEEE 1996 International Conference on Image Processing (ICIP’96) (IEEE Computer Society Press, Los Alamitos, Calif., 1996), Vol. III, pp. 715–718.
- L. Lucchese and G. M. Cortelazzo, “Frequency domain estimation of 3-D rigid motion based on range and intensity data,” in Proceedings of the International Conference on Recent Advances in 3-D Digital Imaging and Modeling (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 107–112.
- G. M. Cortelazzo, G. Doretto, L. Lucchese, and S. Totaro, “A frequency domain method for registration of range data,” in Proceedings of the IEEE 1998 International Symposium on Circuits and Systems (ISCAS’98) (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. 5, pp. 518–521.
- G. M. Cortelazzo, G. Doretto, and L. Lucchese, “Free-form textured surfaces registration by a frequency domain technique,” in Proceedings of the IEEE 1998 International Conference on Image Processing (ICIP’98) (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. I, pp. 813–817.
- A. Erdélyi, W. Magnus, and F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
« Previous Article | Next Article »
OSA is a member of CrossRef.