TY - JOUR
T1 - Identification of Riccati dynamics under perspective and orthographic observations
AU - Ghosh, Bijoy K.
AU - Inaba, Hiroshi
AU - Takahashi, Satoru
N1 - Funding Information:
Manuscript received March 27, 1998; revised June 7, 1999 and October 1, 1999. Most of this research was conducted while the first author was visiting Tokyo Denki University. This work was supported in part by the DOE under Grant DE-FG02-90ER14140 and by the NSF under Grant 9720357. Recommended by Associate Editor, G. Bastin.
Funding Information:
The hospitality provided by the university and the support of the Japan Society for the promotion of science Fellowship is gratefully acknowledged. The authors would also like to thank the reviewers of this paper for their inspiring comments.
PY - 2000/7
Y1 - 2000/7
N2 - In this paper, the problem of identifying motion and shape parameters of a planar object undergoing a Riccati motion, from the associated optical flow generated on the image plane of a single CCD camera, has been studied. The optical flow is generated by projecting feature points on the object onto the image plane via perspective and orthographic projections. Riccati dynamics is to be viewed as a natural extension of the well-known affine dynamics that has been the subject of parameter estimation research for many years. An important result we show is that, under perspective projection, the parameters of a specific Riccati dynamics that extend the well-known `rigid motion' can be identified up to choice of a sign. This fact is in sharp contrast to many other results in the literature, where under perspective projection, parameters are recovered up to a possible depth ambiguity. The paper also discusses other Riccati equations obtained from quadratic extension of a rigid motion and affine motion. For each of the various motion models considered and for each of the two projection models, we show that the extent to which motion and shape parameters can be recovered from optical flow can in fact be recovered from the linear approximation of the optical flow. The quadratic part of the optical flow carries no additional information for the class of parameter identification problems considered. We also extend our analysis to a pair of cameras.
AB - In this paper, the problem of identifying motion and shape parameters of a planar object undergoing a Riccati motion, from the associated optical flow generated on the image plane of a single CCD camera, has been studied. The optical flow is generated by projecting feature points on the object onto the image plane via perspective and orthographic projections. Riccati dynamics is to be viewed as a natural extension of the well-known affine dynamics that has been the subject of parameter estimation research for many years. An important result we show is that, under perspective projection, the parameters of a specific Riccati dynamics that extend the well-known `rigid motion' can be identified up to choice of a sign. This fact is in sharp contrast to many other results in the literature, where under perspective projection, parameters are recovered up to a possible depth ambiguity. The paper also discusses other Riccati equations obtained from quadratic extension of a rigid motion and affine motion. For each of the various motion models considered and for each of the two projection models, we show that the extent to which motion and shape parameters can be recovered from optical flow can in fact be recovered from the linear approximation of the optical flow. The quadratic part of the optical flow carries no additional information for the class of parameter identification problems considered. We also extend our analysis to a pair of cameras.
UR - http://www.scopus.com/inward/record.url?scp=0034223857&partnerID=8YFLogxK
U2 - 10.1109/9.867019
DO - 10.1109/9.867019
M3 - Article
AN - SCOPUS:0034223857
VL - 45
SP - 1267
EP - 1278
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 7
ER -