research-article

On Functionals with Greyvalue-Controlled Smoothness Terms for Determining Optical Flow

Author:

C. SchnörrAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 15, Issue 10

Pages 1074 - 1079

https://doi.org/10.1109/34.254064

Published: 01 October 1993 Publication History

Abstract

The modification by H.H. Nagel (1987) of the approach developed by B.K.P. Horn and B.G. Schunck (1981) for determining optical flow is generalized to the case where local motion information is given by more than one constraint equation. Applying this scheme to three constraint equations reported in the literature, as a special case, a generalization of Nagel's approach is obtained. An existence and uniqueness result of solutions under very general conditions that, in turn, ensures the applicability of standard techniques to compute an approximate solution is presented.

References

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{18} C. Schnörr, "Untersuchung von modifizierten Ansätzen zur Ermittlung von örtlichen und zeitlichen Ableitungen bei der Schätzung des Optischen Flusses in Bildfolgen," Master thesis, Fakultät für Elektrotechnik der Universität Karlsruhe (TH), Nov. 1987.

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Cited By

Hafner DDemetz OWeickert JReiβel M(2015)Mathematical Foundations and Generalisations of the Census Transform for Robust Optic Flow ComputationJournal of Mathematical Imaging and Vision10.1007/s10851-014-0529-952:1(71-86)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1007/s10851-014-0529-9
Rashwan HPuig DGarcia M(2012)Improving the robustness of variational optical flow through tensor votingComputer Vision and Image Understanding10.1016/j.cviu.2012.04.006116:9(953-966)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.1016/j.cviu.2012.04.006
Zimmer HBruhn AWeickert J(2011)Optic Flow in HarmonyInternational Journal of Computer Vision10.1007/s11263-011-0422-693:3(368-388)Online publication date: 1-Jul-2011
https://dl.acm.org/doi/10.1007/s11263-011-0422-6
Show More Cited By

On Functionals with Greyvalue-Controlled Smoothness Terms for Determining Optical Flow
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision tasks
  2. Computer graphics
    1. Animation

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Published In

cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 15, Issue 10

October 1993

129 pages

ISSN:0162-8828

Issue’s Table of Contents

Copyright © Copyright © 1993 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

Publication History

Published: 01 October 1993

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Cited By

Hafner DDemetz OWeickert JReiβel M(2015)Mathematical Foundations and Generalisations of the Census Transform for Robust Optic Flow ComputationJournal of Mathematical Imaging and Vision10.1007/s10851-014-0529-952:1(71-86)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1007/s10851-014-0529-9
Rashwan HPuig DGarcia M(2012)Improving the robustness of variational optical flow through tensor votingComputer Vision and Image Understanding10.1016/j.cviu.2012.04.006116:9(953-966)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.1016/j.cviu.2012.04.006
Zimmer HBruhn AWeickert J(2011)Optic Flow in HarmonyInternational Journal of Computer Vision10.1007/s11263-011-0422-693:3(368-388)Online publication date: 1-Jul-2011
https://dl.acm.org/doi/10.1007/s11263-011-0422-6
Demetz OWeickert JBruhn AZimmer H(2011)Optic flow scale spaceProceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision10.1007/978-3-642-24785-9_60(713-724)Online publication date: 29-May-2011
https://dl.acm.org/doi/10.1007/978-3-642-24785-9_60
Jodoin PMignotte M(2009)Optical-flow based on an edge-avoidance procedureComputer Vision and Image Understanding10.1016/j.cviu.2008.12.005113:4(511-531)Online publication date: 1-Apr-2009
https://dl.acm.org/doi/10.1016/j.cviu.2008.12.005
Guo XXu ZFeng YWang YWang Z(2006)Optical flow computation with fourth order partial differential equationsProceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition10.1007/11815921_30(279-286)Online publication date: 17-Aug-2006
https://dl.acm.org/doi/10.1007/11815921_30
Bruhn AWeickert JSchnörr C(2005)Lucas/Kanade meets Horn/SchunckInternational Journal of Computer Vision10.5555/1028916.103541761:3(211-231)Online publication date: 21-Feb-2005
https://dl.acm.org/doi/10.5555/1028916.1035417
Ruhnau PYuan JSchnörr C(2004)On variational methods for fluid flow estimationProceedings of the 1st international conference on Complex motion10.5555/1758712.1758722(124-145)Online publication date: 12-Oct-2004
https://dl.acm.org/doi/10.5555/1758712.1758722
Spies HGarbe C(2002)Dense Parameter Fields from Total Least SquaresProceedings of the 24th DAGM Symposium on Pattern Recognition10.5555/648287.754105(379-386)Online publication date: 16-Sep-2002
https://dl.acm.org/doi/10.5555/648287.754105
Weickert JSchnörr C(2001)A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image MotionInternational Journal of Computer Vision10.1023/A:101361431797345:3(245-264)Online publication date: 1-Dec-2001
https://dl.acm.org/doi/10.1023/A%3A1013614317973
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