The DOI matches its Crossref record.
An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences
Abstract
A mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field. In most situations, the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field. Supplementary constraints are necessary, for example the postulate that a displacement vector field varies smoothly as a function of the image position. Taken as a general requirement, this creates difficulties at gray value transitions which correspond to occluding contours. Nagel therefore introduced the ``oriented smoothness'' requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values. This contribution reports results of an investigation about how such an ``oriented smoothness'' constraint may be formulated and evaluated.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
No references could be resolved yet.
Research works printed but not linked: 29
- 1984, Informatik-Fachberichte, 87, 154, 10.1007/978-3-662-02390-7_21 · DOI
- 10.1007/978-3-662-02390-7_21 · DOI
- 0, Proc IJCAI-81, 716
- 10.1016/S0734-189X(83)80040-1 · DOI
- 10.1007/978-3-642-81935-3_23 · DOI
- 10.1007/978-3-642-81935-3_23 · DOI
- 10.1016/0004-3702(84)90018-3 · DOI · Paper page
- 10.1016/0004-3702(81)90024-2 · DOI · Paper page
- kitchen, 1980, Gray-level corner detection
- 10.1016/0167-8655(82)90020-4 · DOI
- 10.1016/0167-8655(82)90052-6 · DOI
- 10.1016/S0734-189X(83)80030-9 · DOI · Paper page
- nagel, 1983, On the estimation of dense displacement vector fields from image sequences, Proc ACM SIGGRAPH/SIGART Interdisciplinary Workshop on Motion Representation and Perception, 59
- 1984, Recent advances in image sequence analysis, Proc Premier Colloque Image?Traitement Synth�se Technologie et Applications, 545
- 10.1016/0146-664X(82)90081-8 · DOI · Paper page
- 10.1016/0734-189X(83)90029-4 · DOI
- 10.1016/0146-664X(82)90081-8 · DOI · Paper page
- 10.1145/988525.988534 · DOI
- hildreth, 1982, The integration of motion information along contours, Proc IEEE Workshop Computer Vision Representation and Control, 83
- cornelius, 1983, Adapting optical flow to measure object motion in reflectance and X-ray image sequences, Proc ACM SIGGRAPH/SIGART Workshop in Motion Representation and Perception, 50
- hildreth, 1983, The Measurement of Visual Motion
- beaudet, 1978, Rotationally invariant image operators, Proc Int Joint Conf Pattern Recognition, 579
- 0, Progress in Image Processing, 222
- nagel, 1984, Spatio-temporal modeling based on image sequences, Proc Int Symp Image Processing and Its Applications
- nagel, 1982, Investigations of second order gray value variations to estimate corner point displacements, Proc Int Conf Pattern Recognition, 768
- nagel, 1984, Towards the estimation of displacement vector fields by 'oriented smoothness' constraints, Proc Int Conf Pattern Recognition, 6
- nagel, 1983, Iterative estimation of displacement vector fields from TV-frame sequences, Proc Second European Signal Processing Conf (EUSIPCO-83), 299
- wu, 1982, Determining velocities by propagation, Proc Int Conf Pattern Recognition, 1147
- zuniga, 1983, Corner detection using the facet model, Proc IEEE Conf Comput Vision and Pattern Recognition, 30
Cited by
Performance of optical flow techniques
Barron, J. L., Fleet, D. J., & Beauchemin, S. S. (1994) · International Journal of Computer Vision · doi:10.1007/bf01420984 · Cited by 4,305
A Database and Evaluation Methodology for Optical Flow
Baker, S., Scharstein, D., Lewis, J. P., Roth, S., Black, M. J., & Szeliski, R. (2011) · International Journal of Computer Vision · doi:10.1007/s11263-010-0390-2 · Cited by 2,205
“For example, Nagel and Enkelmann [50] and Werlberger et al.”
MethodA Duality Based Approach for Realtime TV-L 1 Optical Flow
Zach, C., Pock, T., & Bischof, H. (2007) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-74936-3_22 · Cited by 1,658
Computation of component image velocity from local phase information
Fleet, D. J., & Jepson, A. D. (1990) · International Journal of Computer Vision · doi:10.1007/bf00056772 · Cited by 1,085
A computational framework and an algorithm for the measurement of visual motion
Anandan, P. (1989) · International Journal of Computer Vision · doi:10.1007/bf00158167 · Cited by 1,073
Metadata
- Authors
- Nagel, H.-H., & Enkelmann, W.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 1986-09
- Volume
- PAMI-8
- Issue
- 5
- Pages
- 565-593
- ISSN
- 0162-8828 (ISSN-L)
- 2160-9292
- 1939-3539
- OpenAlex
- W2031555400
- Cited by
- 786
- References
- 0
- FWCI
- 24.69
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences. https://app.cochat.ai/papers/10.1109/tpami.1986.4767833
- The paper
- Nagel, H.-H., & Enkelmann, W. (1986). An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/tpami.1986.4767833
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
