Abstract
A theory is developed for determining the motion of an observer given the motion field over a full 360 degree image sphere. The method is based on the fact that for an observer translating without rotation, the projected circular motion field about any equator can be divided into disjoint semicircles of clockwise and counterclockwise flow, and on the observation that the effects of rotation decouple around the three equators defining the three principal axes of rotation. Since the effect of rotation is geometrical, the three rotational parameters can be determined independently by searching, in each case, for a rotational value for which the derotated equatorial motion field can be partitioned into 180 degree arcs of clockwise and counterclockwise flow. The direction of translation is also obtained from this analysis. This search is two dimensional in the motion parameters, and can be performed relatively efficiently. Because information is correlated over large distances, the method can be considered a pattern recognition rather than a numerical algorithm. The algorithm is shown to be robust and relatively insensitive to noise and to missing data. Both theoretical and empirical studies of the error sensitivity are presented. The theoretical analysis shows that for white noise of bounded magnitude M, the expected errors is at worst linearly proportional to M. Empirical tests demonstrate negligible error for perturbations of up to 20% in the input, and errors of less than 20% for perturbations of up to 200%.
Similar content being viewed by others
References
Adiv G (1985) Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. Proceedings of the 1985 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 70-77
Clocksin WF (1978) Perception of surface slant and edge labels from optical flow: a computational approach. University of Edinburgh, DAI Working Paper no 33
Gibson JJ (1950) The perception of the visual world. Houghton Mifflin, Boston, Mass
Horn BKP, Schunk BG (1981) Determining optical flow. Artif Intell 17: 185–204
Kanatani K (1984) Tracing planar surface motion from projection without knowing the correspondence. Comput Vis Graphics Image Process 29: 1–12
Koenderink JJ (1986) Optic flow. Vision Res 26: 161–180
Koenderink JJ, van Doorn AJ (1975) Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer. Optica Acta 22: 773–791
Longuet-Higgins HC (1981) A computer algorithm for reconstructing a scene from two projections. Nature 293: 133–135
Longuet-Higgins HC, Prazdny K (1984) The interpretation of a moving retinal image. Proc R Soc London Ser B 208: 385–397
Prazdny K (1980) Egomotion and relative depth map from optical flow. Biol Cybern 36: 87–102
Prazdny K (1981) Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer. Comput Graphics Image Process 17: 238–248
Thompson WB, Kearney JK (1986) Inexact Vision Workshop on Motion. Representation, and Analysis, May 1986, 15–22
Tsai RY, Huang TS (1981) Estimating 3-D motion parameters of a rigid planar patch. I. IEEE Trans Acoust Speech Signal Process ASSP-30: 525–534
Tsai RY, Huang TS (1984) Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces. IEEE Trans PAMI- 6: 13–26
Ullman S (1981) Analysis of visual motion by biological and computer systems. IEEE. Comput 14: 57–69
Verri A, Poggio T (1987) Against quantitative optical flow. Proceedings of the 1987 International Conference on Computer Vision, June 1987
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nelson, R.C., Aloimonos, J. Finding motion parameters from spherical motion fields (or the advantages of having eyes in the back of your head). Biol. Cybern. 58, 261–273 (1988). https://doi.org/10.1007/BF00364131
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00364131