Complementary Optic Flow
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Complementary OF (Zimmer et al. 2009) on the Urban sequence has an average AE of 4.64 degrees, ranking 6th in the table at the time of writing.
“The average AE is 4.64 degrees which ranks 6th in the table at the time of writing.”
From A Database and Evaluation Methodology for Optical Flow (2011) · cites this paper as Zimmer et al. 2009
Complementary OF (Zimmer et al. 2009) on the Urban sequence has an average EE of 1.78 pixels, ranking 20th in the table at the time of writing.
“The average EE is 1.78 pixels which ranks 20th at the time of writing.”
From A Database and Evaluation Methodology for Optical Flow (2011) · cites this paper as Zimmer et al. 2009
The Complementary OF algorithm (Zimmer et al. 2009) fails to correctly estimate the flow of the building in the bottom left on the Urban sequence.
“The Complementary OF algorithm (which otherwise does very well) fails to correctly estimate the flow of the building in the bottom left.”
From A Database and Evaluation Methodology for Optical Flow (2011) · cites this paper as Zimmer et al. 2009
Complementary OF's good performance on hidden texture data is presumably due to its relatively sophisticated data term, including a different robust penalization function for each channel in HSV color space.
“presumably due to the use of a relatively sophisticated data term, including the use of a different robust penalization function for each channel in HSV color space”
From A Database and Evaluation Methodology for Optical Flow (2011) · cites this paper as Zimmer et al. 2009
Complementary OF (Zimmer et al. 2009) does well on the hidden texture data (Army, Mequon, Schefflera, Wooden).
“Complementary OF (Zimmer et al. 2009) does well on the hidden texture data ( Army , Mequon , Schefflera , Wooden )”
From A Database and Evaluation Methodology for Optical Flow (2011) · cites this paper as Zimmer et al. 2009
Complementary OF (Zimmer et al. 2009) does not do as well on sequences with large motion (Urban) and complex discontinuities (Grove).
“but not as well on the sequences with large motion ( Urban ) and complex discontinuities ( Grove ).”
From A Database and Evaluation Methodology for Optical Flow (2011) · cites this paper as Zimmer et al. 2009
Cites
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 · cited 1× · see citing works
“1, we show results for the Urban3 sequence from the recent optic flow database [22] of the Middlebury University(1).”
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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 · see citing works
“Adaptive (Wedel et al. 2009) 9.2 Seg OF ( Xu et al. 2008 )6 0”
MethodInfluentialSecrets of optical flow estimation and their principles
Sun, D., Roth, S., & Black, M. J. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5539939 · Cited by 1,656 · see citing works
“Significant ones use oriented smoothness [25, 31, 33, 40], rigidity constraints [32, 33], or image segmentation [9, 21, 41, 37].”
BackgroundInfluentialLarge Displacement Optical Flow: Descriptor Matching in Variational Motion Estimation
Brox, T., & Malik, J. (2011) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2010.143 · Cited by 1,295 · see citing works
Sun, D., Roth, S., & Black, M. J. (2013) · International Journal of Computer Vision · doi:10.1007/s11263-013-0644-x · Cited by 698 · see citing works
“mation to deal with large motions [13,17], texture decomposition [65,67] or high-order filter constancy [8,17,29,39, 77] to reduce the influence of lighting changes, incremental”
BackgroundMethodInfluentialStereoscopic Scene Flow Computation for 3D Motion Understanding
Wedel, A., Brox, T., Vaudrey, T., Rabe, C., Franke, U., & Cremers, D. (2011) · International Journal of Computer Vision · doi:10.1007/s11263-010-0404-0 · Cited by 197 · see citing works
“Currently, variational techniques yield the most accurate optical flow in the literature (Wedel et al. 2008a; Werlberger et al. 2010; Zimmer et al. 2009).”
BackgroundMethodMotion detail preserving optical flow estimation
Xu, L., Jia, J.-Y., & Matsushita, Y. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5539820 · Cited by 193 · see citing works
“penalty functions [4, 21], using TV/L(1) model to reject outliers [7], minimizing energy in a continuous-discrete fashion [14], and applying advanced smoothness terms to handle motion discontinuity [26, 22, 23].”
BackgroundMethodFreehand HDR Imaging of Moving Scenes with Simultaneous Resolution Enhancement
Zimmer, H., Bruhn, A., & Weickert, J. (2011) · Computer graphics forum (Print) · doi:10.1111/j.1467-8659.2011.01870.x · Cited by 179 · see citing works
“The alignment of such an exposure series comes down to displacement vector fields ( u k , v k ) between images g k and a reference image g r , where r := ⌈ m/ 2 ⌉ for simplicity. model To ease presentation, we describe our for greyscale images, but also sketch the extension to colour images.”
Self-citationA survey of variational and CNN-based optical flow techniques
Tu, Z., Xie, W. C., Zhang, D., Poppe, R. W., Veltkamp, R. C., Li, B., & Yuan, J. (2018) · Signal Processing Image Communication · doi:10.1016/j.image.2018.12.002 · Cited by 149 · see citing works
“[88] exploited a joint image- and flowdriven smoothness term to avoid artifacts of over-smoothing and over-segmentation.”
BackgroundMethodEstimation of slipping organ motion by registration with direction-dependent regularization
Schmidt-Richberg, A., Werner, R., Handels, H., & Ehrhardt, J. (2012) · Medical Image Anal. · doi:10.1016/j.media.2011.06.007 · Cited by 105 · see citing works
Multi-modal and Multi-spectral Registration for Natural Images
Shen, X.-Y., Xu, L., Zhang, Q., & Jia, J.-Y. (2014) · European Conference on Computer Vision · doi:10.1007/978-3-319-10593-2_21 · Cited by 100 · see citing works
“In modern methods, the data term usually enforces brightness or gradient constancy [5,6,41].”
BackgroundMethodJoint Estimation of Motion, Structure and Geometry from Stereo Sequences
Valgaerts, L., Bruhn, A., Zimmer, H., Weickert, J., Stoll, C., & Theobalt, C. (2010) · European Conference on Computer Vision · doi:10.1007/978-3-642-15561-1_41 · Cited by 95 · see citing works
“In [27] the authors demonstrate that the linearised brightness constancy assumption for optical flow can be interpreted geometrically as a weighted distance of the estimated flow to the line described by the optical flow constraint.”
BackgroundInfluentialSelf-citationLayered RGBD scene flow estimation
Sun, D., Sudderth, E. B., & Pfister, H. (2015) · Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2015.7298653 · Cited by 73 · see citing works
“Some notable variants include image-dependent, non-local motion priors to recover sharp motion boundaries [38, 47, 51], fusion moves to reach stronger local minima [24], embedding feature matching to track small, fast-moving objects [10, 45, 49], exploiting the epipolar constraint for egocentric scenes [50], and real-…”
BackgroundIllumination-Robust Optical Flow Using a Local Directional Pattern
Mohamed, M. A., Rashwan, H. A., Mertsching, B., García, M. Á., & Puig, D. (2014) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2014.2308628 · Cited by 68 · see citing works
Object Tracking in Satellite Videos Based on a Multiframe Optical Flow Tracker
Du, B., Cai, S., & Wu, C. (2019) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2019.2917703 · Cited by 99 · see citing works
“[56] and realized by Baker et al.”
Fractional-order variational optical flow model for motion estimation
Chen, D.-L., Sheng, H., Chen, Y., & Xue, D.-Y. (2013) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2012.0148 · Cited by 56 · see citing works
Bootstrap optical flow confidence and uncertainty measure
Kybic, J., & Nieuwenhuis, C. (2011) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2011.06.008 · Cited by 53 · see citing works
“For example, the two OF algorithms with the best results on the Middlebury database [3] both minimize a criterion of this type [41,44].”
MethodConstrained Optical Flow Estimation as a Matching Problem
Mozerov, M. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2244221 · Cited by 49 · see citing works
Optical Flow via Locally Adaptive Fusion of Complementary Data Costs
Kim, T. H., Lee, H. S., & Lee, K. M. (2013) · IEEE International Conference on Computer Vision · doi:10.1109/iccv.2013.415 · Cited by 46 · see citing works
“Although previous works [6, 27, 25] showed that more complementary models provide more accurate results, they are computationally inefficient.”
Sparsity model for robust optical flow estimation at motion discontinuities
Shen, X.-H., & Wu, Y. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5539944 · Cited by 44
“Such a connection was further explored by [29], which introduced the complementarity of these two terms.”
BackgroundDemetz, O., Hafner, D., & Weickert, J. (2013) · British Machine Vision Conference · doi:10.5244/c.27.50 · Cited by 41 · see citing works
“These results are remarkable, since they prove that the invariant data term of our simple model includes hardly less information than the combined grey value and gradient information of [3, 27].”
BackgroundSelf-citationConsistent Binocular Depth and Scene Flow with Chained Temporal Profiles
Hung, C.-H., Xu, L., & Jia, J.-Y. (2012) · International Journal of Computer Vision · doi:10.1007/s11263-012-0559-y · Cited by 38 · see citing works
“We turn to an anisotropic smoothness method (Xiao et al. 2006; Sun et al. 2008; Zimmer et al. 2009) to provide critical constraints for edge-preserving regularization.”
BackgroundMethodAdaptive Integration of Feature Matches into Variational Optical Flow Methods
Stoll, M., Volz, S., & Bruhn, A. (2012) · Asian Conference on Computer Vision · doi:10.1007/978-3-642-37431-9_1 · Cited by 32 · see citing works
“In direction of the maximal change, r1, we follow [24] and use the Perona-Malik penalizer [5]”
BackgroundMethodInfluentialSelf-citationOptical flow estimation with adaptive convolution kernel prior on discrete framework
Lee, K. J., Kwon, D., Yun, I., & Lee, S.-U. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5539953 · Cited by 32 · see citing works
“Recently a new diffusion tensor combining both image and flow structure [19] is introduced and its modification [31] shows state-of-the-art performance on the Middlebury evaluation site [1].”
BackgroundObject Tracking in Satellite Videos Based on a Multi-Frame Optical Flow Tracker
Du, B., Cai, S., Wu, C., Zhang, L., & Tao, D.-C. (2018) · arXiv.org · doi:10.48550/arxiv.1804.09323 · Cited by 31
“We implement HSV representation by using the sophisticated approaches that proposed by Zimmer et al [45] and realized by Baker et al[39].”
MethodA fractional order variational model for the robust estimation of optical flow from image sequences
Kumar, P., Kumar, S., & Raman, B. (2016) · Optik · doi:10.1016/j.ijleo.2016.05.118 · Cited by 31 · see citing works
Optical Flow Estimation Using Laplacian Mesh Energy
Li, W., Cosker, D., Brown, M. A., & Tang, R. (2013) · 2013 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2013.315 · Cited by 31 · see citing works
“The former is a continuous approach [5, 6, 18] to estimate optical flow based on modifications of Horn and Schunck’s framework proposed in [9].”
MethodOptical Flow Estimation with Deep Learning, a Survey on Recent Advances
Savian, S., Elahi, M., & Tillo, T. (2020) · Unsupervised and Semi-Supervised Learning · doi:10.1007/978-3-030-32583-1_12 · Cited by 29 · see citing works
Control of the Effects of Regularization on Variational Optic Flow Computations
Belhachmi, Z., & Hecht, F. (2011) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-010-0239-x · Cited by 27 · see citing works
Variational Optical Flow Estimation Based on Stick Tensor Voting
Rashwan, H. A., García, M., & Puig, D. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2253481 · Cited by 26 · see citing works
Fast Optical Flow Estimation Based on the Split Bregman Method
Chen, J., Cai, Z., Lai, J., & Xie, X.-H. (2018) · IEEE transactions on circuits and systems for video technology (Print) · doi:10.1109/tcsvt.2016.2615324 · Cited by 24 · see citing works
“[13] later presented an efficient algorithm that achieved near-real-time performance on a GPU by using the fast explicit diffusion scheme [27] for the Euler–Lagrange framework.”
MethodZhu, Y., Li, K., & Jiang, J.-M. (2014) · Signal processing. Image communication · doi:10.1016/j.image.2014.06.005 · Cited by 24
Multi-frame super-resolution algorithm for complex motion patterns.
Kanaev, A., & Miller, C. W. (2013) · Optics Express · doi:10.1364/oe.21.019850 · Cited by 23 · see citing works
A nonlinear modeling of fractional order based variational model in optical flow estimation
Khan, M., & Kumar, P. (2022) · Optik · doi:10.1016/j.ijleo.2022.169136 · Cited by 20 · see citing works
A Flow-based Motion Perception Technique for an Autonomous Robot System
Pinto, A., Moreira, A., Correia, M., & Costa, P. (2013) · Journal of Intelligent and Robotic Systems · doi:10.1007/s10846-013-9999-z · Cited by 17 · see citing works
“Furthermore, the normalized brightness and gradient constraints are employed in [41] and were recently improved by [40].”
BackgroundSpatial and temporal constraints in variational correspondence methods
Ralli, J., Díaz, J., & Ros, E. (2013) · Machine Vision and Applications · doi:10.1007/s00138-011-0360-x · Cited by 15 · see citing works
“There are more complex and elaborated ways of combining both the image- and flow information in order to achieve excellent results [32], and we expect that using such regularization terms would further improve the results obtained in this paper.”
BackgroundMethodRegularization Strategies for Discontinuity-Preserving Optical Flow Methods
Monzón, N., Salgado, A., & Sánchez, J. (2016) · IEEE Transactions on Image Processing · doi:10.1109/tip.2016.2526903 · Cited by 14 · see citing works
“Some examples in the use of diffusion tensors with robustification functions are given in [6] and [32].”
BackgroundSelf-citationFALDOI: A New Minimization Strategy for Large Displacement Variational Optical Flow
Palomares, R. P., Meinhardt-Llopis, E., Ballester, C., & Haro, G. (2016) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-016-0688-y · Cited by 14 · see citing works
“On the other hand, global or variational methods [2,9,24,50,62,64] provide a dense solution by minimizing a global energy.”
BackgroundDense Scene Flow Based on Depth and Multi-channel Bilateral Filter
Zhang, X., Chen, D.-P., Yuan, Z.-J., & Zheng, N. (2012) · Asian Conference on Computer Vision · doi:10.1007/978-3-642-37431-9_11 · Cited by 14
“[8] and [9] applied anisotropic regularization in optical flow estimation, then it is introduced in scene flow estimation[10] by applying smoothness constraints only within segments in the image plane.”
MethodImproving the robustness of variational optical flow through tensor voting
Rashwan, H. A., Puig, D., & García, M. (2012) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2012.04.006 · Cited by 14 · see citing works
Software for Non-Parametric Image Registration of 2-Photon Imaging DataPreprint
Flotho, P., Nomura, S., Kuhn, B., & Strauss, D. (2021) · bioRxiv · doi:10.1101/2021.07.25.453381 · Cited by 13 · see citing works
“We normalize the dataterm according to Zimmer et al. [14] and apply the recommended good practices proposed by Sun et al. [8].”
BackgroundMethodHigh-Quality Correspondence and Segmentation Estimation for Dual-Lens Smart-Phone Portraits
Shen, X.-Y., Gao, H., Tao, X., Zhou, C., & Jia, J.-Y. (2017) · IEEE International Conference on Computer Vision · doi:10.1109/iccv.2017.353 · Cited by 13 · see citing works
“The involved data terms are used to satisfy color or gradient constancy [10, 12, 53].”
MethodDense Descriptors for Optical Flow Estimation: A Comparative Study
Baghaie, A., D'Souza, R., & Yu, Z.-Y. (2017) · Journal of Imaging · doi:10.3390/jimaging3010012 · Cited by 13 · see citing works
“[5], higher order derivatives proposed in [6] and color models with photometric invariant channels [7,8], have been investigated before.”
BackgroundAn Adaptive Approach for the Segmentation and the TV-Filtering in the Optic Flow Estimation
Belhachmi, Z., & Hecht, F. (2016) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-015-0608-6 · Cited by 13
Imaging with multi-spectral mosaic-array cameras.
Kanaev, A., Kutteruf, M. R., Yetzbacher, M. K., DePrenger, M. J., & Novak, K. (2015) · Applied Optics · doi:10.1364/ao.54.00f149 · Cited by 13
Low complexity optical flow using neighbor-guided semi-global matching
Xiang, J., Li, Z., Blaauw, D., Kim, H.-S., & Chakrabarti, C. (2016) · International Conference on Information Photonics · doi:10.1109/icip.2016.7533208 · Cited by 12 · see citing works
“[4], typically require a large number of nonlinear computations.”
BackgroundToward robust estimation of specular flow
Adato, Y., Zickler, T., & Ben-Shahar, O. (2010) · British Machine Vision Conference · doi:10.5244/c.24.22 · Cited by 12
“Numerous studies have also focused on improving the smoothness term, for example by incorporating motion segmentation [2], by modeling scene motion [11], by using spatiotemporal regularization [6, 7], or by combining anisotropic smoothing [16, 22, 24].”
BackgroundMethodInfluentialComputer vision-based video signal fusion using deep learning architectures
Ghyabi, M., & Lattanzi, D. (2025) · Journal of Civil Structural Health Monitoring · doi:10.1007/s13349-024-00891-w · Cited by 10 · see citing works
“1 Overall data fusion approach while the other part aims to achieve the expected variations in the general motion [12, 49–51].”
SuperWarp: Supervised Learning and Warping on U-Net for Invariant Subvoxel-Precise Registration
Young, S. I., Balbastre, Y., Dalca, A. V., Wells, W., Iglesias, J., & Fischl, B. (2022) · Workshop on Biomedical Image Registration · doi:10.48550/arxiv.2205.07399 · Cited by 11
“Oriented regularization terms [21–25] regularize the fl ow only along the direction tangent to the image gradient while non-local terms [26–29] regularize fl ow even across disconnected pixels subject to similar motion.”
BackgroundKumar, P., & Kumar, S. (2016) · AEU - International Journal of Electronics and Communications · doi:10.1016/j.aeue.2015.12.002 · Cited by 11 · see citing works
Wang, X., Zhang, K., Zhang, X., Li, S., & Yan, J. (2021) · Infrared Physics & Technology · doi:10.1016/j.infrared.2021.103790 · Cited by 12 · see citing works
Locally Oriented Optical Flow Computation
Niu, Y., Dick, A., & Brooks, M. J. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2177847 · Cited by 10 · see citing works
A vision based motion estimation in underwater images
Kumar, P., Kumar, S., & Balasubramanian, R. (2015) · International Conference on Advances in Computing, Communications and Informatics · doi:10.1109/icacci.2015.7275771 · Cited by 9 · see citing works
Motion Estimation—A Video Coding Viewpoint
Pesquet-Popescu, B., Cagnazzo, M., & Dufaux, F. (2014) · Academic press library in signal processing · doi:10.1016/b978-0-12-420149-1.00002-8 · Cited by 9 · see citing works
Determining shape and motion from monocular camera: A direct approach using normal flows
Hui, T., & Chung, R. (2015) · Pattern Recognition · doi:10.1016/j.patcog.2014.08.012 · Cited by 8 · see citing works
Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition
Duits, R., Becciu, A. A., Janssen, B. J. A., Florack, L., van Assen, H. V., & Romeny, B. M. T. H. (2011) · International Workshop on Statistical Atlases and Computational Models of the Heart · doi:10.1007/978-3-642-28326-0_27 · Cited by 8
“A similar scheme has been employed in more recent and sophisticated techniques by Bruhn et al. [6] and Zimmer et al.[52], who used an anisotropic smoothness term and carried out tests on the Yosemite sequence and Middlebury benchmark outperforming the results of most of the current optic flow methods.”
Optical flow estimation on image sequences with differently exposed frames
Bengtsson, T., McKelvey, T., & Lindström, K. (2015) · Optical Engineering · doi:10.1117/1.oe.54.9.093103 · Cited by 7 · see citing works
“[51] that only includes smoothing constraint along image edges, and not across image edges [52,75].”
BackgroundDuits, R., Janssen, B., Becciu, A. A., & Assen, V. (2012) · doi:10.1090/s0033-569x-2012-01313-0 · Cited by 7
“For further extensions/improvements see [6, 19, 55, 59, 63].”
On improving the robustness of differential optical flow
Rashwan, H. A., Puig, D., & García, M. (2011) · IEEE International Conference on Computer Vision · doi:10.1109/iccvw.2011.6130344 · Cited by 7 · see citing works
“In turn, the structure tensor, which is applied in [5] and [11], makes the assumption that gradients change in a neighborhood slowly.”
BackgroundMethodInfluentialFeature invariance versus change estimation in variational motion estimation
Demetz, O. (2015) · doi:10.22028/d291-26623 · Cited by 6
“These results are remarkable in the sense that they prove our invariant data term to include hardly less information than the combined grey value and gradient information of [Brox et al., 2004; Zimmer et al., 2009].”
ResultLi, Z., Xiang, J., Gong, L., Blaauw, D., Chakrabarti, C., & Kim, H.-S. (2019) · IEEE transactions on circuits and systems for video technology (Print) · doi:10.1109/tcsvt.2018.2854284 · Cited by 5 · see citing works
Effects of texture addition on optical flow performance in images with poor texture
Andalibi, M., Hoberock, L. L., & Mohamadipanah, H. (2015) · Image and Vision Computing · doi:10.1016/j.imavis.2015.04.008 · Cited by 5
Improving the Optical Flow Accuracy Based on the Total Variation of Local-Global method
Zhang, Y., Fan, H.-N., Zheng, J., & Zhang, C. (2018) · 2018 IEEE International Conference on Big Data (Big Data) · doi:10.1109/bigdata.2018.8622420 · Cited by 4 · see citing works
“The use of diffusion tensors in combination with robustification functions are given in [6] and [29], with a motion tensor introduced into the data term and a regularization tensor introduced into the smoothness term.”
MethodQuantitative motion analysis for non-contact affective and neurocognitive assessment
Flotho, P., & Strauss, D. (2017) · International IEEE/EMBS Conference on Neural Engineering · doi:10.1109/ner.2017.8008303 · Cited by 3
“Energy based optical flow methods can be implemented efficiently on graphic cards [4] and are suitable for real time applications.”
MethodInfluentialEnhancement of imagery of objects with highly dynamic brightness and large rotational motion.
Kanaev, A., Miller, C. W., Seanor, C. J., & Murray-Krezan, J. (2014) · Applied Optics · doi:10.1364/ao.53.000c32 · Cited by 3 · see citing works
Improving Motion Estimation Using Image-Driven Functions and Hybrid Scheme
Nguyen, D., & Jeon, J. (2011) · Pacific-Rim Symposium on Image and Video Technology · doi:10.1007/978-3-642-25367-6_7 · Cited by 3 · see citing works
“Both the coarse-to-fine scheme [3,5,12,14] and the multigrid scheme [11,15,16,17] have been used so far to solve (11) effectively.”
BackgroundMethodOptical Flow with Harmonic Constraint and Oriented Smoothness
Zhao, J., Wang, Y.-Q., & Wang, H. (2011) · 2011 Sixth International Conference on Image and Graphics · doi:10.1109/icig.2011.122 · Cited by 3 · see citing works
“Bruhn and Weikert [4] later improved this idea by introducing a separate robust penalisation of the brightness constancy assumption and the gradient constancy assumption.”
BackgroundIntermediate Flow Field Filtering in Energy Based Optic Flow Computations
Hoeltgen, L., Setzer, S., & Breuß, M. (2011) · Energy Minimization Methods in Computer Vision and Pattern Recognition · doi:10.1007/978-3-642-23094-3_23 · Cited by 3
“[2,3,4,5,6,7,8,9,10,11] for some influential publications.”
BackgroundMethodInfluentialOptical Flow: Traditional Approaches
Brox, T. (2020) · Computer Vision · doi:10.1007/978-3-030-03243-2_600-1 · Cited by 3 · see citing works
Holzer, S., & Ilic, S. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-37431-9 · Cited by 3
On the Generalization of Optical Flow: Quantifying Robustness to Dataset Shifts
Bauer, K., Bruhn, A., & Schmalfuss, J. (2025) · 2025 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW) · doi:10.1109/iccvw69036.2025.00054 · Cited by 2 · see citing works
“Traditionally, optical flow robustness focused on specific challenging conditions including varying illumination [30, 43, 75], large object motion [8, 70], occlusion [33], motion blur [45], image noise [7] or rain [34].”
Self-citationOn parameterizing higher-order motion for behaviour recognition
Sun, Y., Hare, J. S., & Nixon, M. S. (2020) · Pattern Recognition · doi:10.1016/j.patcog.2020.107710 · Cited by 5 · see citing works
“The alternative forms of the data term are the correlation between frames [25] and colour space [26].”
BackgroundEfficiency of Bilateral Filter Application in Problems of Optical Flow Calculation
Titkov, V., Panin, S., Lyubutin, P., & Chemezov, V. O. (2017) · Optoelectronics Instrumentation and Data Processing · doi:10.3103/s8756699017060073 · Cited by 2 · see citing works
Illumination-Aware Large Displacement Optical Flow
Stoll, M., Maurer, D., Volz, S., & Bruhn, A. (2017) · Energy Minimization Methods in Computer Vision and Pattern Recognition · doi:10.1007/978-3-319-78199-0_10 · Cited by 2 · see citing works
Self-citationVariational Large Displacement Optical Flow Without Feature Matches
Stoll, M., Maurer, D., & Bruhn, A. (2017) · Energy Minimization Methods in Computer Vision and Pattern Recognition · doi:10.1007/978-3-319-78199-0_6 · Cited by 2 · see citing works
Self-citationBregman Iteration for Correspondence Problems: A Study of Optical Flow
Hoeltgen, L., & Breuß, M. (2015) · arXiv.org · doi:10.48550/arxiv.1510.01130 · Cited by 2
“During this period of time, many efforts have been spent to improve the models cf. [4,8,10,42,44,60,65,68,74–76] for an account of that field.”
BackgroundGilliocq-Hirtz, D., & Belhachmi, Z. (2015) · arXiv.org · doi:10.48550/arxiv.1508.02977 · Cited by 2
Experimental study of image representation spaces in variational disparity calculation
Ralli, J., Díaz, J., Guzmán, P., & Ros, E. (2012) · EURASIP Journal on Advances in Signal Processing · doi:10.1186/1687-6180-2012-254 · Cited by 2 · see citing works
A review on vision-based motion estimation
Liu, H., & Wang, H. (2024) · arXiv.org · doi:10.48550/arxiv.2407.14478 · Cited by 1
“…term were also useful to preserve edges, such as the image-driven term in (Alvarez, Weickert, and S ´ anchez 2000), integrating intensity gradient into the smoothness term, the flow-driven term in (Weickert and Schn ¨ orr 2001), the combined term in (Zimmer, Bruhn, Weickert, et al. 2009).”
Dense Optical Flow Estimation from RGB-D
Lv, J.-X., Mohamed, M. A., & Yuan, H.-W. (2018) · International Conference on Instrumentation and Measurement, Computer, Communication and Control · doi:10.1109/imccc.2018.00076 · Cited by 1
“Furthermore, Zimmer et al. [15] combined the data term and the smoothness term in a synergistic model.”
BackgroundVariational optical flow estimation for images with spectral and photometric sensor diversity
Bengtsson, T., McKelvey, T., & Lindström, K. (2015) · International Conference on Graphic and Image Processing · doi:10.1117/12.2180109 · Cited by 1
Enhancing accuracy and sharpness of motion field with adaptive scheme and occlusion-aware filter
Nguyen, D., & Jeon, J. (2013) · IET Image Processing · doi:10.1049/iet-ipr.2012.0563 · Cited by 1 · see citing works
Object Class Recognition (Categorization)
Lazebnik, S. (2014) · Springer eBooks · doi:10.1007/978-0-387-31439-6_337 · Cited by 2 · see citing works
How to improve local optima of optical flow energies using discrete matchesPreprint
Palomares, R. P., Meinhardt-Llopis, E., Ballester, C., & Haro, G. (2016) · arXiv.org · doi:10.48550/arxiv.1602.08960
“On the other hand, global or variational methods [21, 2, 9, 57, 59, 45] provide a dense solution by minimizing a global energy.”
BackgroundMahala, N. K., Khan, M., & Kumar, P. (2026) · Applied Mathematical Modelling · doi:10.1016/j.apm.2026.117165
Arain, M. B., Amur, K., Tantawy, S., Alburaikan, A., Khalifa, H., Ishtiaq, U., & Popa, I. (2025) · Scientific Reports · doi:10.1038/s41598-025-25291-y
“A general variational denoising model seeks to optimize an energy functional of the form 29,34–38,53, where R ( u ) is a regularization term that promotes smoothness, and λ is a scaling parameter that scales the fidelity M ( u, f ) and regularization.”
A nonlinear fractional order variational model for the robust estimation of optical flow
Kumar, A., Singh, B., Khan, M., & Kumar, P. (2024) · 2024 OPJU International Technology Conference (OTCON) on Smart Computing for Innovation and Advancement in Industry 4.0 · doi:10.1109/otcon60325.2024.10687886
“Moreover, the effectiveness of an optical flow model is typically assessed based on its ability to handle flow discontinuities, and large motions [5], [13]–[16].”
BackgroundFlotho, P., Romero-Santiago, A., Schwerdtfeger, K., Hulser, M., Haab, L., & Strauss, D. (2017) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society · doi:10.1109/embc.2017.8037834
“[10] to reduce the weight of large gradients, which are often caused by noise.”
BackgroundMethodInfluentialPanin, S., Titkov, V., Lyubutin, P., Chemezov, V. O., & Eremin, A. (2016) · AIP conference proceedings · doi:10.1063/1.4966475
Complex algorithm of optical flow determination by weighted full search
Panin, S., Chemezov, V. O., & Lyubutin, P. (2016) · AIP conference proceedings · doi:10.1063/1.4966472
Incorporating discontinuity preserving approach for optical flow estimation
Kumar, P., Kumar, S., & Balasubramanian, R. (2014) · Confluence · doi:10.1109/confluence.2014.6949319
“Currently, in optical flow estimation the variational optical flow models have obtained much success to compute the optical flow field and give their advantage in modeling, estimation and quality [4], [5], [15], [20].”
MethodSuper-Resolution Based Demosaicking For Full Motion Video SWIR Multi-Spectral Sensor
Kanaev, A., Yetzbacher, M., Kutteruf, M., Deprenger, M. J., Novak, K., Miller, C., & Downes, T. (2014) · doi:10.1364/isa.2014.iw4c.2
Reliable optical flow estimation in motion-blurred regions
Koh, Y., Lee, C., Sim, J.-Y., & Kim, C.-S. (2013) · IEEE International Workshop on Multimedia Signal Processing · doi:10.1109/mmsp.2013.6659321
“Also, gradient and/or color constancy constraints have been employed to enhance the robustness of optical flow estimation against lighting variations between image frames [8], [10].”
MethodKanaev, A., Miller, C. W., Seanor, C. J., & Murray-Krezan, J. (2013) · Defense, Security, and Sensing · doi:10.1117/12.2016393
The analysis and development of computed 2D optical flow velocity based on phantom data
Cai, F., van Triest, H. J. W., & Kang, Y. (2012) · International Conference on Computerized Healthcare · doi:10.1109/icch.2012.6724469
“After nearly 30 years of research, these methods have obtained an impressive level of reliability and accuracy [11, 12, 13, 16].”
BackgroundOptical flow estimation with parameterized data term and warping
Xu, J., Feng, Z.-R., & Lu, N. (2012) · Proceedings of the 10th World Congress on Intelligent Control and Automation · doi:10.1109/wcica.2012.6359357
“There are also some other technologies to solve the problem of the noise and illumination changes [6, 8, 12].”
BackgroundDirectionally Weakened Diffusion for Optical Flow
Zhao, J., Wang, H., & Wang, Y.-Q. (2011) · doi:10.4028/www.scientific.net/amr.403-408.2449
“…there have been many improvements, these improvements include refining the smoothness terms with discontinuity-preserving constraints [2, 3, 4] or spatial regularization [5], using higher-order smoothness terms [6, 7], using improved data terms with modified constraints [8, 9] and…”
BackgroundNonlocal Regularizing Constraints in Variational Optical Flow
Duran, J., & Buades, A. (2017) · VISIGRAPP · doi:10.5220/0006098501510161
“Although this filtered-data constraint can be advantageous for very noisy sequences, it significantly blurs motion discontinuities, where this assumption fails (Zimmer et al., 2011).”
BackgroundInfluentialPeriodicity-Based Computation of Optical Flow
Khachaturov, G., González-Brambila, S. B., & Trejo, J. I. G. (2015) · Computación y Sistemas · doi:10.13053/cys-18-4-1557
- Authors
- Zimmer, H., Bruhn, A., Weickert, J., Valgaerts, L., Salgado, A., Rosenhahn, B., & Seidel, H.-P.
- Affiliations
- Max Planck Institute for Informatics (DE)
- Saarland University (DE)
- Universidad de Las Palmas de Gran Canaria (ES)
- Leibniz University Hannover (DE)
- Venue
- Lecture Notes in Computer Science
- Publisher
- Springer Berlin Heidelberg
- Published
- 2009
- Pages
- 207-220
- ISSN
- 0302-9743 (ISSN-L)
- 1611-3349
- OpenAlex
- W2143485281
- Cited by
- 107
- References
- 0
- Citations by year
- 2025: 5 · 2023: 5 · 2022: 4 · 2021: 3 · 2020: 3 · 2019: 1 · 2018: 6 · 2017: 4 · 2016: 9 · 2015: 10 · 2014: 9 · 2013: 14 · 2012: 9
- FWCI
- 9.26
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Lecture notes in computer science (publishedVersion)
- Max Planck Digital Library (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Vision and Imaging
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Video Surveillance and Tracking Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Video Stabilization
- Keywords
- optical flow, variational methods, complementarity, data term, smoothness term, anisotropic smoothing, Middlebury benchmark
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