{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T12:04:04Z","timestamp":1771329844166,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,11,28]],"date-time":"2012-11-28T00:00:00Z","timestamp":1354060800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Comput Vis"],"published-print":{"date-parts":[[2013,5]]},"DOI":"10.1007\/s11263-012-0595-7","type":"journal-article","created":{"date-parts":[[2012,11,29]],"date-time":"2012-11-29T12:26:19Z","timestamp":1354191979000},"page":"80-99","source":"Crossref","is-referenced-by-count":61,"title":["Divergence-Free Wavelets and High Order Regularization"],"prefix":"10.1007","volume":"103","author":[{"given":"S.","family":"Kadri-Harouna","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"D\u00e9rian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"H\u00e9as","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"M\u00e9min","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,11,28]]},"reference":[{"issue":"9","key":"595_CR1","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1109\/34.161348","volume":"14","author":"J Bergen","year":"1992","unstructured":"Bergen, J., Burt, P., Hingorani, R., & Peleg, S. (1992). A 3-frame algorithm for estimating two-component image motion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(9), 886\u2013895.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"6","key":"595_CR2","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1137\/0729097","volume":"6","author":"G Beylkin","year":"1992","unstructured":"Beylkin, G. (1992). On the representation of operator in bases of compactly supported wavelets. SIAM Journal on Numerical Analysis, 6(6), 1716\u20131740.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"595_CR3","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1002\/cpa.3160450502","volume":"45","author":"A Cohen","year":"1992","unstructured":"Cohen, A., Daubechies, I., & Feauveau, J. C. (1992). Bi-orthogonal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics, 45, 485\u2013560.","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"595_CR4","unstructured":"D\u00e9rian, P., H\u00e9as, P., Herzet, C., M\u00e9min, E. (2011). Wavelet-based fluid motion estimation. In: 3rd international conference on scale-space and variational methods in computer vision (SSVM2011). IEEE LNCS, Ein-Gedi."},{"key":"595_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/14685240500260547","volume":"7","author":"E Deriaz","year":"2006","unstructured":"Deriaz, E., & Perrier, V. (2006). Divergence-free and curl-free wavelets in 2D and 3D, application to turbulence. Journal of Turbulence, 7, 1\u201337.","journal-title":"Journal of Turbulence"},{"key":"595_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite element methods for Navier-Stokes equations: Theory and algorithms. Springer series in computational mathematics","author":"V Girault","year":"1986","unstructured":"Girault, V., & Raviart, P. (1986). Finite element methods for Navier-Stokes equations: Theory and algorithms. Springer series in computational mathematics. Berlin: Springer."},{"key":"595_CR7","doi-asserted-by":"crossref","first-page":"10962","DOI":"10.3402\/tellusa.v64i0.10962","volume":"64","author":"P Heas","year":"2012","unstructured":"Heas, P., Memin, E., Heitz, D., & Mininni, P. (2012). Power laws and inverse motion modeling: application to turbulence measurements from satellite images. Tellus A, 64, 10962. doi: 10.3402\/tellusa.v64i0.10962 .","journal-title":"Tellus A"},{"key":"595_CR8","unstructured":"Heitz, D., Carlier, J., Arroyo, G. (2007). Final report on the evaluation of the tasks of the workpackage 2, FLUID project deliverable 5.4. Technical report, INRIA-Cemagref."},{"issue":"3","key":"595_CR9","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s00348-009-0778-3","volume":"48","author":"D Heitz","year":"2010","unstructured":"Heitz, D., M\u00e9min, E., & Schn\u00f6rr, C. (2010). Variational fluid flow measurements from image sequences: Synopsis and perspectives. Experiments in fluids, 48(3), 369\u2013393.","journal-title":"Experiments in fluids"},{"key":"595_CR10","doi-asserted-by":"crossref","unstructured":"Horn, B., & Schunck, B. (1981). Determining optical flow. Artificial Intelligence, 17, 185\u2013203.","DOI":"10.1016\/0004-3702(81)90024-2"},{"key":"595_CR11","doi-asserted-by":"crossref","unstructured":"Jullien, M., Castiglione, P., & Tabeling, P. (2000). Experimental observation of batchelor dispersion of passive tracers. Physical Review Letters, 85(17), 3636\u20133639.","DOI":"10.1103\/PhysRevLett.85.3636"},{"key":"595_CR12","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1007\/3-540-44935-3_30","volume":"2695","author":"T Kohlberger","year":"2003","unstructured":"Kohlberger, T., M\u00e9min, E., & Schn\u00f6rr, C. (2003). Dense motion estimation using the Helmholtz decomposition. Scale Space Methods in Computer Vision, 2695, 432\u2013448.","journal-title":"Scale Space Methods in Computer Vision"},{"key":"595_CR13","volume-title":"Fourier series and wavelets","author":"J-P Kahane","year":"1995","unstructured":"Kahane, J.-P., & Lemari\u00e9-Rieusset, P.-G. (1995). Fourier series and wavelets. Luxembourg: Gordon and Breach."},{"key":"595_CR14","doi-asserted-by":"crossref","first-page":"221","DOI":"10.4171\/RMI\/123","volume":"8","author":"P-G Lemari\u00e9-Rieusset","year":"1992","unstructured":"Lemari\u00e9-Rieusset, P.-G. (1992). Analyses multir\u00e9solutions non orthogonales, commutation entre projecteurs et d\u00e9rivation et ondelettes vecteurs \u00e0 divergence nulle. Revista Matematica Iberoamericana, 8, 221\u2013237.","journal-title":"Revista Matematica Iberoamericana"},{"key":"595_CR15","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1017\/S0022112008003273","volume":"614","author":"T Liu","year":"2008","unstructured":"Liu, T., & Shen, L. (2008). Fluid flow and optical flow. Journal of Fluid Mechanics, 614, 253\u2013291.","journal-title":"Journal of Fluid Mechanics"},{"key":"595_CR16","volume-title":"A wavelet tour of signal processing: The sparse way","author":"S Mallat","year":"2008","unstructured":"Mallat, S. (2008). A wavelet tour of signal processing: The sparse way. Orlando: Academic Press."},{"key":"595_CR17","volume-title":"Numerical optimization. Springer series in operations research","author":"J Nocedal","year":"1999","unstructured":"Nocedal, J., & Wright, S. J. (1999). Numerical optimization. Springer series in operations research. New York: Springer."},{"key":"595_CR18","unstructured":"Papadakis, N., Corpetti, T., & M\u00e9min., E,. (2007). Dynamically consistent optical flow estimation. Rio de Janeiro, Brasil: IEEE International Conference on Computer Vision."},{"key":"595_CR19","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s00348-006-0220-z","volume":"42","author":"P Ruhnau","year":"2007","unstructured":"Ruhnau, P., & Schn\u00f6rr, C. (2007). Optical stokes flow estimation: An imaging-based control approach. Experiments in Fluids, 42, 61\u201378.","journal-title":"Experiments in Fluids"},{"key":"595_CR20","first-page":"79","volume":"1","author":"M Sass-Hansen","year":"2009","unstructured":"Sass-Hansen, M., Larsen, R., & Christensen, N.-V. (2009). Curl-gradient image warping-introducing deformation potentials for medical image registration using Helmholtz decomposition. VISSAPP, 1, 79\u2013185.","journal-title":"VISSAPP"},{"key":"595_CR21","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1109\/34.3886","volume":"10","author":"PY Simard","year":"1998","unstructured":"Simard, P. Y., & Mailloux, G. E. (1998). A projection operator for the restoration of divergence-free vector fields. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10, 248\u2013256.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"595_CR22","unstructured":"Steinbruecker, F., Pock, T., Cremers, D. (2009). Large displacement optical flow computation without warping. In: IEEE International Conference on Computer Vision (ICCV). Kyoto."},{"key":"595_CR23","unstructured":"Suter, D. (1994). Motion estimation and vector splines. In: Proceeding conference computer vision pattern recognition (pp. 939\u2013942). Seattle."},{"key":"595_CR24","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1109\/TPAMI.1986.4767807","volume":"8","author":"D Terzopoulos","year":"1986","unstructured":"Terzopoulos, D. (1986). Regularization of inverse visual problems involving discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, 413\u2013424.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"2","key":"595_CR25","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1023\/A:1008101718719","volume":"38","author":"Y Wu","year":"2000","unstructured":"Wu, Y., Kanade, T., Li, C., & Cohn, J. (2000). Image registration using wavelet-based motion model. International Journal of Computer Vision, 38(2), 129\u2013152.","journal-title":"International Journal of Computer Vision"},{"key":"595_CR26","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10851-007-0014-9","volume":"28","author":"J Yuan","year":"2007","unstructured":"Yuan, J., Schn\u00f6rr, C., & M\u00e9min, E. (2007). Discrete orthogonal decomposition and variational fluid flow estimation. Journal of Mathematical Imaging and Vision, 28, 67\u201380.","journal-title":"Journal of Mathematical Imaging and Vision"}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-012-0595-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11263-012-0595-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-012-0595-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T12:16:50Z","timestamp":1559391410000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-012-0595-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,28]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["595"],"URL":"https:\/\/doi.org\/10.1007\/s11263-012-0595-7","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11,28]]}}}