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Enhancement of synthetic schlieren image resolution using total variation optical flow: application to thermal experiments in a Hele-Shaw cell

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Abstract

We present an improvement to the standard synthetic schlieren technique to obtain the temperature distribution of a fluid inside of a Hele-Shaw cell. We aim to use the total variation \(L^1\)-norm optical flow method to treat experimental images and to obtain quantitative results of the development of thermal convection inside a cell, by detecting the gradients of the optical refractive index. We present a simple algorithm to set the optical flow parameters, which is based on the comparison between the optical flow output and the result obtained by digital PIV using the structural index metric. As an example of the application of the proposed method, we analyze laboratory experiments of thermal convection in porous media using a Hele-Shaw cell. We demonstrate that the application of the proposed method produces important improvements versus digital PIV, for the quantification of the gradients of the refractive index including the detection of small-scale convective structures. In comparison with correlation-based digital methods, we demonstrate the advantages of the proposed method, such as denoising and edge capture. These features allow us to obtain the temperature, for this experimental setting, with better image resolution than other techniques reported in the literature.

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References

  • Atchenson B, Heidrich W, Ihrke I (2009) An evaluation of optical flow algorithms for background oriented schlieren imaging. Exp Fluids 46:467–476. doi:10.1007/s00348-008-0572-7

    Article  Google Scholar 

  • Backhaus S, Turitsyn K, Ecke R (2011) Convective instability and mass transport of diffusion layers in a Hele-Shaw geometry. Phys Rev Lett 106(104):501. doi:10.1103/PhysRevLett.106.104501

    Google Scholar 

  • Baker S, Scharstein D, Lewis JP, Roth S, Black MJ, Szeliski R (2011) A database and evaluation methodology for optical flow. Int J Comput Vis 92:1–31. doi:10.1007/s11263-010-0390-2

    Article  Google Scholar 

  • Barron J, Fleet D, Beauchemin S (1994) Performance of optical flow techniques. Int J Comput Vis 12:43–77

    Article  Google Scholar 

  • Benson S, Cook P et al (2005) Underground geological storage. In: Metz B, Davidson O, de Coninck H, Loss M, Meyer L (eds) Special report on carbon dioxide capture and storage, chap 5, Cambridge University Press, Cambridge, pp 195–276

  • Brox T, Bruhn A, Papenberg N, Weickert J (2004) High accuracy optical flow estimation based on a theory for warping. In: Pajdla T, Matas J (eds) Proceedings of 8th European conference on computer vision, 4, Springer, Berlin, pp 25–36

  • Chambolle A (2004) An algorithm for total variation minimization and applications. J Math Imaging Vis 20:89–97

    Article  MathSciNet  Google Scholar 

  • Chan TF, Osher S, Shen J (2001) The digital TV filter and nonlinear denoising. IEEE Trans Image Process 10:231–241. doi:10.1109/83.902288

    Article  MATH  Google Scholar 

  • Clausnitzer V, Bayer U, Fuhrmann J (2001) Large-scale thermal convective instability in sedimentary basins. Eur Geophys Soc, Geophys Res Abstracts HS02-02

  • Cooper C, Crews J, Schumer R, Breitmeyer R, Voepel H, Decker D (2014) Experimental investigation of transient thermal convection in porous media. Transp Porous Media 104:335–347. doi:10.1007/s11242-014-0337-0

    Article  Google Scholar 

  • Corpetti T, Heitz D, Arroyo G, Memin E, Santa-Cruz A (2005) Fluid experimental flow estimation based on an optical flow scheme. Exp Fluids 40:80–97. doi:10.1007/s00348-005-0048-y

    Article  Google Scholar 

  • Dalziel SB, Hughes GO, Sutherland BR (1998) Synthetic schlieren. In: Proceedings of the 8th international symposium on flow visualization, Sorrento, pp 62.1–62.6

  • Dalziel SB, Hughes GO, Sutherland BR (2000) Whole field density measurements by synthetic schlieren. Exp Fluids 28:322–335. doi:10.1007/s003480050391

    Article  Google Scholar 

  • Elder J (1967a) Steady free convection in a porous medium heated from below. J Fluid Mech 27:29–48. doi:10.1017/S0022112067000023

    Article  Google Scholar 

  • Elder J (1967b) Transient convection in a porous medium. J Fluid Mech 27:609–623. doi:10.1017/S0022112067000576

    Article  Google Scholar 

  • Emami-Meybodi H, Hassanzadeh H, Green CP, Ennis-King J (2015) Convective dissolution of \(\text{CO}_2\) in saline aquifers: progress in modeling and experiments. Int J Greenh Gas Control. doi:10.1016/j.ijggc.2015.04.003

    Google Scholar 

  • Gibson J (1950) The perception of visual surfaces. Am J Psychol 63(3):367–384

    Article  Google Scholar 

  • Gibson J (1966) The problem of temporal order in stimulation and perception. J Psychol 62(2):141–149

    Article  MathSciNet  Google Scholar 

  • Gojani AB, Obayashi S (2012) Assesment of some experimental and image analysis factors for background oriented schlieren measurements. Appl Opt 51:7554–7559. doi:10.1364/AO.51.007554

    Article  Google Scholar 

  • Gojani AB, Kamishi B, Obayashi S (2013) Measurement sensitivity and resolution for background oriented schlieren during image recording. J Vis 16:201–207. doi:10.1007/s12650-013-0170-5

    Article  Google Scholar 

  • Gupta SN, Prince JL (1996) Stochastic models for DIV-CURL optical flow methods. IEEE Signal Process Lett 3:32–34

    Article  Google Scholar 

  • Hartline BK, Lister RB (1977) Thermal convection in a Hele-Shaw cell. J Fluid Mech 79:379–389. doi:10.1017/S0022112077000202

    Article  MATH  Google Scholar 

  • Horn B, Schunck B (1981) Determining optical flow. Artif Intell 17:185–203. doi:10.1016/0004-3702(81)90024-2

    Article  Google Scholar 

  • Horne RN, O’Sullivan MJ (1974) Oscillatory convection in a porous medium heated from below. J Fluid Mech 66:339–352. doi:10.1017/S0022112074000231

    Article  MATH  Google Scholar 

  • Koster JN (1983) Interferometric investigation of convection in plexiglass boxes. Exp Fluids 1:121–128. doi:10.1007/BF00272010

    Google Scholar 

  • Koster JN, Muller U (1982) Free convection in vertical gaps. J Fluid Mech 125:429–451. doi:10.1017/S0022112082003425

    Article  Google Scholar 

  • Kumar P, Muralidhar K (2012) Schlieren and shadowgraph methods in heat and mass transfer. Springer, New York. doi:10.1007/978-1-4614-4535-7

    Google Scholar 

  • Lee S, Kim S (2004) Application of holographic interferometry and 2D PIV for HSC convective flow diagnostics. Meas Sci Technol 15:664. doi:10.1088/0957-0233/15/4/008

    Article  Google Scholar 

  • Liberzon A, Gurka R, Taylor Z (2009) Openpiv home page. [Online]. http://www.openpiv.net

  • Lucas B, Kanade T (1981) An iterative image registration technique with an application to stereo vision. In: Proceedings of seventh international joint conference on artificial intelligence, Vancouver, pp 674–679

  • Meinhardt-Llopis E, Sánchez J, Kondermann D (2013) Horn–Schunck optical flow with a multi-scale strategy. Image Process On Line 3:151–172. doi:10.5201/ipol.2013.20

    Article  Google Scholar 

  • Nagamo K, Mochida T, Ochifuji K (2002) Influence of natural convection on forced horizontal flow in saturated porous media for aquifer thermal energy storage. Appl Therm Eng 22:1299–1311. doi:10.1016/S1359-4311(02)00056-X

    Article  Google Scholar 

  • Neufeld J, Hesse M, Riaz A, Hallworth M, Tchelepi H, Huppert H (2010) Convective dissolution of carbon dioxide in saline aquifers. Geophys Res Lett 37(L22):404. doi:10.1029/2010GL044728

    Google Scholar 

  • Nield D, Bejan A (2006) Convection in porous media, 3rd edn. Springer, New York. doi:10.1007/978-1-4614-5541-7

    MATH  Google Scholar 

  • Otero J, Dontcheva L, Jonhston H, Worthing R, Kurganov A, Petrova G, Doering C (2004) High-Rayleigh-number convection in a fluid-saturated porous layer. J Fluid Mech 500:263–281. doi:10.1017/S0022112003007298

    Article  MathSciNet  MATH  Google Scholar 

  • Ozawa M, Muller U, Kimura I (1992) Flow and temperature measurement of natural convection in a Hele-Shaw cell using a thermo-sensitive liquid-crystal tracer. Exp Fluids 12:213–222. doi:10.1007/BF00187298

    Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes 3rd edition: the art of scientific computing, 3rd edn. Cambridge University Press, New York

    Google Scholar 

  • Raffel M (2015) Background-oriented schlieren (BOS) techniques. Exp Fluids 56:1–17. doi:10.1007/s00348-015-1927-5

    Article  Google Scholar 

  • Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry. A practical guide, 2nd edn. Springer, Berlin. doi:10.1007/978-3-540-72308-0

    Book  Google Scholar 

  • Randolph JB, Saar MO (2011) Coupling carbon dioxide sequestration with geothermal energy capture in naturally permeable, porous geologic formations: Implications for \(\text{CO}_2\) sequestration. Energy Procedia 4:2206–2213. doi:10.1016/j.egypro.2011.02.108

    Article  Google Scholar 

  • Richard H, Raffel M (2001) Principle and applications of the background oriented schlieren BOS method. Meas Sci Technol 12:1576. doi:10.1088/0957-0233/12/9/325

    Article  Google Scholar 

  • Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60:259–268. doi:10.1016/0167-2789(92)90242-F

    Article  MathSciNet  MATH  Google Scholar 

  • Ruhnau P, Schnorr C (2007) Optical Stokes flow estimation: an imaging-based control approach. Exp Fluids 42:61–78. doi:10.1007/s00348-006-0220-z

    Article  Google Scholar 

  • Ruhnau P, Gutter C, Schnorr C (2005a) A variational approach for particle tracking velocimetry. Meas Sci Technol 16:1449–1458. doi:10.1088/0957-0233/16/7/007

    Article  Google Scholar 

  • Ruhnau P, Kohlberger T, Schnorr C, Nobach H (2005b) Variational optical flow estimation for particle image velocimetry. Exp Fluids 38:21–32. doi:10.1007/s00348-004-0880-5

    Article  Google Scholar 

  • Sanchez J, Meinhardt-Llopis E, Facciolo G (2013) TV-\(\textit{L}_1\) optical flow estimation. Image Process On Line 3:137–150. doi:10.5201/ipol.2013.26

    Article  Google Scholar 

  • Stark M (2013) Optical flow PIV: improving the accuracy and applicability of particle image velocimetry. ETH, Department of Mechanical and Process Engineering. https://books.google.cl/books?id=p92MnQEACAAJ

  • Strong DM, Chan TF (2003) Edge-preserving and scale-dependent properties of total variation regularization. Inverse Probl 19:165–187. doi:10.1088/0266-5611/19/6/059

    Article  MathSciNet  Google Scholar 

  • Sun T, Teja A (2004) Density, viscosity and thermal conductivity of aqueous solutions of propylene glycol, dipropylene glycol, and tripropylene glycol between 290 K and 460 K. J Chem Eng Data 49:1311–1317. doi:10.1021/je049960h

    Article  Google Scholar 

  • Suter D (1994) Vector splines in computer vision. In: Proceedings of Australasian workshop thin plates, Sydney

  • Sutherland BR, Dalziel SB, Hughes GO, Linden PF (1999) Visualization and measurement of intertial waves by synthetic schlieren: part 1. Vertically oscillating cylinder. J Fluid Mech 390:93–126. doi:10.1017/S0022112099005017

    Article  MATH  Google Scholar 

  • Tokgoz S, Geisler R, van Bokhoven LJA, Wieneke B (2012) Temperature and velocity measurements in a fluid layer using background-oriented schlieren and PIV methods. Meas Sci Technol 23(115):302. doi:10.1088/0957-0233/23/11/115302

    Google Scholar 

  • Turan J, Ovsenik L, Benca M (2002) Laboratory equipment type fiber optic refractometer. Radioengineering 11:27–32

    Google Scholar 

  • Wang Z, Bovik AC (2009) Mean squared error: love it or leave it? A new look at signal fidelity measures. IEEE Signal Proc Mag 26:98–117. doi:10.1109/MSP.2008.930649

    Article  Google Scholar 

  • Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13:600–612. doi:10.1109/TIP.2003.819861

    Article  Google Scholar 

  • Wedel A, Cremers D (2011) Stereo scene flow for 3D motion analysis, 1st edn. Springer, London. doi:10.1007/978-0-85729-965-9

    Book  Google Scholar 

  • Wedel A, Pock T, Zach C, Cremers D, Bischof H (2008) An improved algorithm for TV-\(\textit{L}_1\) optical flow. In: Proceedings of the Dagstuhl motion workshop, Dagstuhl Castle

  • Wildeman S, Lhuissier H, Sun C, Lohse D (2012) Inside a kettle. arXiv:12103693

  • Zach C, Pock T, Bischof H (2007) A duality based approach for realtime TV-\(\textit{L}_1\) Optical Flow. In: Hamprecht A, Schnorr C, Jahne B (eds) Pattern Recognition, chap 22, Springer, Berlin, pp 214–223

Download references

Acknowledgments

The authors gratefully acknowledge support from the Chilean National Commission for Scientific and Technological Research (CONICYT) through Beca Nacional de Doctorado #21110836 and the National Fund for Scientific and Technological Development (FONDECYT) projects #1111012 and #1110168. The project number PFB03-CMM is also acknowledged. This work is a contribution from the FONDAP-CONICYT #15090013 project Centro de Excelencia en Geotermia de los Andes (CEGA).

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Authors and Affiliations

  1. Departamento de Ingeniería Civil, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2002, Santiago de Chile, Chile

    Juvenal A. Letelier & Paulo Herrera

  2. Centro de Excelencia en Geotermia de los Andes (CEGA), Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago de Chile, Chile

    Juvenal A. Letelier & Paulo Herrera

  3. Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago de Chile, Chile

    Nicolás Mujica

  4. Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Beauchef 851, Santiago de Chile, Chile

    Jaime H. Ortega

  5. Centro de Modelamiento Matemático UMI 2807 CNRS, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Beauchef 851, Santiago de Chile, Chile

    Jaime H. Ortega

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  1. Juvenal A. Letelier
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Correspondence to Juvenal A. Letelier.

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Letelier, J.A., Herrera, P., Mujica, N. et al. Enhancement of synthetic schlieren image resolution using total variation optical flow: application to thermal experiments in a Hele-Shaw cell. Exp Fluids 57, 18 (2016). https://doi.org/10.1007/s00348-015-2109-1

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