The Applicability of Green's Theorem to Computation of Rate of Approach

International Journal of Computer Vision - Tập 31 Số 1 - Trang 83-98 - 1999
Duric, Zoran1, Rosenfeld, Azriel2, Duncan, James3
1Department of Computer Science, George Mason University, Fairfax, USA
2Center for Automation Research, University of Maryland, College Park, USA
3Department of Mechanical Engineering, University of Maryland, College Park, USA

Tóm tắt

The rate of approach (ROA) of a moving observer toward a scene point, as estimated at a given instant, is proportional to the component of the observer's instantaneous velocity in the direction of the point. In this paper we analyze the applicability of Green's theorem to ROA estimation. We derive a formula which relates three quantities: the average value of the ROA for a surface patch in the scene; a surface integral that depends on the surface slant of the patch; and the contour integral of the normal motion field around the image of the boundary of the patch. We analyze how much larger the ROA on the surface patch can be than the value of the contour integral, for given assumptions about the variability of the distance to points on the surface patch. We illustrate our analysis quantitatively using synthetic data, and we also validate it qualitatively on real image sequences.

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Tài liệu tham khảo

citation_journal_title=IEEE Transactions on Pattern Analysis and Machine Intelligence; citation_title=Determining three-dimensional motion and structure from optical flow generated by several moving objects; citation_author=G. Adiv; citation_volume=7; citation_publication_date=1985; citation_pages=384-401; citation_id=CR1

citation_journal_title=IEEE Transactions On Systems, Man, and Cybernetics; citation_title=Outline for a theory of intelligence; citation_author=J.S. Albus; citation_volume=21; citation_publication_date=1991; citation_pages=473-509; citation_id=CR2

citation_journal_title=International Journal of Computer Vision; citation_title=Estimating the heading direction using normal flow; citation_author=Y. Aloimonos, Z. Duric; citation_volume=13; citation_publication_date=1994; citation_pages=33-56; citation_id=CR3

Ancona, N. and Poggio, T. 1993. Optical flow from 1D correlation: Application to a simple time-to-crash detector. In Proc. ARPA Image Understanding Workshop, pp. 673–682.

citation_title=An Introduction to Numerical Analysis; citation_publication_date=1989; citation_id=CR5; citation_author=K.E. Atkinson; citation_publisher=John Wiley and Sons

citation_journal_title=Computer Vision, Graphics, and Image Processing; citation_title=Passive navigation; citation_author=A. Bruss, B.K.P. Horn; citation_volume=21; citation_publication_date=1983; citation_pages=3-20; citation_id=CR6

citation_journal_title=IEEE Transactions on Pattern Analysis and Machine Intelligence; citation_title=Analyzing looming motion components from their spatiotemporal spectral signature; citation_author=P. Burlina, R. Chellappa; citation_volume=18; citation_publication_date=1996; citation_pages=1029-1034; citation_id=CR7

citation_journal_title=International Journal of Computer Vision; citation_title=Temporal analysis of motion in video sequences through predictive operators; citation_author=P. Burlina, R. Chellappa; citation_volume=28; citation_publication_date=1998; citation_pages=175-192; citation_id=CR8

Cipolla, R. and Blake, A. 1992. Surface orientation and time to contact from image divergence and deformation. In Proc. European Conference on Computer Vision, pp. 187–202.

citation_journal_title=Image and Vision Computing; citation_title=Derivation of qualitative information in motion analysis; citation_author=E. Francois, P. Bouthemy; citation_volume=8; citation_publication_date=1990; citation_pages=279-288; citation_id=CR10

citation_journal_title=Artificial Intelligence; citation_title=Determining optical flow; citation_author=B.K.P. Horn, B.G. Schunck; citation_volume=17; citation_publication_date=1981; citation_pages=189-203; citation_id=CR11

citation_journal_title=Artificial Intelligence; citation_title=Shape from regular patterns; citation_author=K. Ikeuchi; citation_volume=22; citation_publication_date=1984; citation_pages=49-75; citation_id=CR12

citation_journal_title=Optica Acta; citation_title=Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer; citation_author=J.J. Koenderink, A.J. Van Doorn; citation_volume=22; citation_publication_date=1975; citation_pages=773-791; citation_id=CR13

citation_journal_title=Phil. Trans. Royal Society London; citation_title=The optical flow field: The foundation of vision; citation_author=D.N. Lee; citation_volume=B290; citation_publication_date=1980; citation_pages=169-179; citation_id=CR14

citation_journal_title=Proc. Royal Society London; citation_title=The interpretation of a moving retinal image; citation_author=H.C. Longuet-Higgins, K. Prazdny; citation_volume=B208; citation_publication_date=1980; citation_pages=385-397; citation_id=CR15

citation_title=Vector Calculus; citation_publication_date=1976; citation_id=CR16; citation_author=J.E. Marsden; citation_author=A.J. Tromba; citation_publisher=W.H. Freeman and Company

citation_journal_title=Image and Vision Computing; citation_title=Apparent area of a rigid moving body; citation_author=S.J. Maybank; citation_volume=5; citation_publication_date=1987; citation_pages=111-113; citation_id=CR17

Meyer, F. and Bouthemy, P. 1992. Estimation of time-to-collision maps from first order motion models and normal flows. In Proc. 11th Int. Conf. on Pattern Recognition, pp. 78–82.

citation_journal_title=Vision Research; citation_title=Biological image motion processing: A review; citation_author=K. Nakayama; citation_volume=25; citation_publication_date=1985; citation_pages=625-660; citation_id=CR19

citation_journal_title=IEEE Transactions on Pattern Analysis and Machine Intelligence; citation_title=Obstacle avoidance using flow field divergence; citation_author=R.C. Nelson, J. Aloimonos; citation_volume=11; citation_publication_date=1989; citation_pages=1102-1106; citation_id=CR20

citation_title=Green theorems and qualitative properties of the optical flow; citation_publication_date=1991; citation_id=CR21; citation_author=T. Poggio; citation_author=A. Verri; citation_author=V. Torre; citation_publisher=MIT

Sharma, R. 1992. Active vision in robot navigation: Monitoring time-to-collision while tracking. In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems.

citation_journal_title=Computer Vision, Graphics, and Image Processing; citation_title=Bounds on time-to-collision and rotational component from first-order derivatives of image flow; citation_author=M. Subbarao; citation_volume=50; citation_publication_date=1990; citation_pages=329-341; citation_id=CR23

citation_journal_title=IEEE Transactions on Pattern Analysis and Machine Intelligence; citation_title=On the advantages of polar and logpolar mappings for direct estimation of time-to-impact from optical flow; citation_author=M. Tistarelli, G. Sandini; citation_volume=15; citation_publication_date=1993; citation_pages=401-410; citation_id=CR24

Verri, A. and Poggio, T. 1987. Against quantitative optical flow. In Proc. International Conference on Computer Vision, pp. 171–180.

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International Journal of Computer Vision

Tập 31 Số 1

83-98

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