Experiments in Fluids

, 57:41 | Cite as

Shearlet-based detection of flame fronts

  • Rafael Reisenhofer
  • Johannes KieferEmail author
  • Emily J. King
Research Article


Identifying and characterizing flame fronts is the most common task in the computer-assisted analysis of data obtained from imaging techniques such as planar laser-induced fluorescence (PLIF), laser Rayleigh scattering (LRS), or particle imaging velocimetry (PIV). We present Complex Shearlet-Based Ridge and Edge Measure (CoShREM), a novel edge and ridge (line) detection algorithm based on complex-valued wavelet-like analyzing functions—so-called complex shearlets—displaying several traits useful for the extraction of flame fronts. In addition to providing a unified approach to the detection of edges and ridges, our method inherently yields estimates of local tangent orientations and local curvatures. To examine the applicability for high-frequency recordings of combustion processes, the algorithm is applied to mock images distorted with varying degrees of noise and real-world PLIF images of both OH and CH radicals. Furthermore, we compare the performance of the newly proposed complex shearlet-based measure to well-established edge and ridge detection techniques such as the Canny edge detector, another shearlet-based edge detector, and the phase congruency measure.


Particle Imaging Velocimetry Edge Detector Flame Front Local Curvature Canny Edge Detector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abdou I, Pratt W (1979) Quantitative design and evaluation of enhancement/thresholding edge detectors. Proc IEEE 67(5):753–763CrossRefGoogle Scholar
  2. Aldén M, Bood J, Li Z, Richter M (2011) Visualization and understanding of combustion processes using spatially and temporally resolved laser diagnostic techniques. Proc Combust Inst 33:69–97CrossRefGoogle Scholar
  3. Bayley AE, Hardalupas Y, Taylor AMKP (2012) Local curvature measurements of a lean, partially premixed swirl-stabilised flame. Exp Fluids 52:963–983CrossRefGoogle Scholar
  4. Candès EJ, Donoho DL (2004) New tight frames of curvelets and optimal representations of objects with piecewise \(C^2\) singularities. Commun Pure Appl Math 57(2):219–266MathSciNetCrossRefzbMATHGoogle Scholar
  5. Candès EJ, Guo F (2002) New multiscale transforms, minimum total variation synthesis: applications to edge-preserving image reconstruction. Signal Process 82(11):1519–1543CrossRefzbMATHGoogle Scholar
  6. Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 8(6):679–698CrossRefGoogle Scholar
  7. Danielsson PE (1990) Machine vision for three-dimensional scenes. Academic Press, chap Generalized and Separable Sobel OperatorsGoogle Scholar
  8. Daubechies I (1992) Ten lectures on wavelets, CBMS-NSF regional conference series in applied mathematics, vol 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PAGoogle Scholar
  9. Do MN, Vetterli M (2003) Contourlets. In: Welland GV (ed) Beyond wavelets, studies in computational mathematics, vol 10. Academic Press/Elsevier Science, San Diego, CA, pp 1–27Google Scholar
  10. Donoho DL (1999) Wedgelets: nearly minimax estimation of edges. Ann Stat 27(3):859–897MathSciNetCrossRefzbMATHGoogle Scholar
  11. Duda RO, Hart PE (1972) Use of the Hough transformation to detect lines and curves in pictures. Commun ACM 15:11–15CrossRefzbMATHGoogle Scholar
  12. Dyer MJ, Crosley DR (1982) Two-dimensional imaging of OH laser-induced fluorescence in a flame. Opt Lett 7:382–384CrossRefGoogle Scholar
  13. Fourguette DC, Zurn RM, Long MB (1986) Two-dimensional Rayleigh scattering thermometry in a turbulent nonpremixed methane-hydrogen flame. Combust Sci Technol 44:307–317CrossRefGoogle Scholar
  14. Frank J, Kaiser S, Long M (2005) Multiscalar imaging in partially premixed jet flames with argon dilution. Combust Flame 143:507–523CrossRefGoogle Scholar
  15. Grohs P, Keiper S, Kutyniok G, Schäfer M (2016) \(\alpha\)-Molecules. Appl Comput Harmon Anal. doi: 10.1016/j.acha.2015.10.009
  16. Guo K, Kutyniok G, Labate D (2006) Sparse multidimensional representations using anisotropic dilation und shear operators. In: Lai MJ, Chen G (eds) Wavelets und splines. Nashboro Press, Nashville, pp 189–201Google Scholar
  17. Haar A (1909) Zur Theorie der orthogonalen Funktionensysteme. Ph.D. thesis, University of GöttingenGoogle Scholar
  18. Haar A (1910) Zur Theorie der orthogonalen Funktionensysteme. Math Ann 69(3):331–371MathSciNetCrossRefzbMATHGoogle Scholar
  19. Haq MZ, Sheppard CGW, Wooley R, Greenhalgh DA, Lockett RD (2002) Wrinkling and curvature of laminar and turbulent premixed flames. Combust Flame 131:1–15CrossRefGoogle Scholar
  20. Kiefer J, Li ZS, Zetterberg J, Bai XS, Alden M (2008) Investigation of local flame structures and statistics in partially premixed turbulent jet flames using simultaneous single-shot CH and OH planar laser-induced fluorescence imaging. Combust Flame 154:802–818CrossRefGoogle Scholar
  21. King EJ, Reisenhofer R, Kiefer J, Lim WQ, Li Z, Heygster G (2015) Shearlet-based edge detection: flame fronts and tidal flats. In: Tescher AG (ed) Applications of digital image processing XXXVIII, society of photo-optical instrumentation engineers (SPIE) conference series, vol 9599Google Scholar
  22. Kingsbury N (1999) Image processing with complex wavelets. Philos Trans R Soc Lond 357(1760):2543–2560CrossRefzbMATHGoogle Scholar
  23. Kovesi P (1999) Image features from phase congruency. Videre J Comput Vis Res 1(3):1–26Google Scholar
  24. Kovesi P (2000) Phase congruency: a low-level image invariant. Psychol Res 64:136–148CrossRefGoogle Scholar
  25. Kovesi PD (2015) MATLAB and Octave functions for computer vision and image processing. Centre for Exploration Targeting, School of Earth and Environment, The University of Western Australia. pk/research/matlabfns/. Accessed 2015
  26. Kutyniok G, Labate D (2009) Resolution of the wavefront set using continuous shearlets. Trans Am Math Soc 361(5):2719–2754MathSciNetCrossRefzbMATHGoogle Scholar
  27. Kutyniok G, Labate D, Lim WQ, Weiss G (2005) Sparse multidimensional representation using shearlets. In: Papadakis M, Laine, Unser (eds) Wavelets XI, society of photo-optical instrumentation engineers (SPIE) conference series, vol 5914, pp 254–262Google Scholar
  28. Kutyniok G, Lemvig J, Lim WQ (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J Math Anal 44(4):2962–3017MathSciNetCrossRefzbMATHGoogle Scholar
  29. Kutyniok G, Lim WQ, Reisenhofer R (2016) ShearLab 3D: faithful digital shearlet transforms based on compactly supported shearlets. ACM Trans Math Softw 42(1):5MathSciNetCrossRefGoogle Scholar
  30. Lindeberg T (1998) Edge detection and ridge detection with automatic scale selection. Int J Comput Vis 30(2):117–154CrossRefGoogle Scholar
  31. Mallat S, Hwang WL (1992) Singularity detection and processing with wavelets. IEEE Trans Inf Theory 38(2):617–643MathSciNetCrossRefzbMATHGoogle Scholar
  32. Mallat S, Zhong S (1992) Characterization of signals from multiscale edges. IEEE Trans Pattern Anal Mach Intell 14(7):710–732CrossRefGoogle Scholar
  33. Malm H, Sparr G, Hult J, Kaminski CF (2000) Nonlinear diffusion filtering of images obtained by planar laser-induced fluorescence spectroscopy. J Opt Soc Am A 17:2148–2156CrossRefGoogle Scholar
  34. McMillin BK, Palmer JL, Hanson RK (1993) Temporally resolved, two-line fluorescence imaging of NO temperature in a transverse jet in a supersonic cross flow. Appl Opt 32(36):7534–7545CrossRefGoogle Scholar
  35. Morrone MC, Owens RA (1987) Feature detection from local energy. Pattern Recogn Lett 6:303–313CrossRefGoogle Scholar
  36. Morrone MC, Ross J, Burr DC, Owens R (1986) Mach bands are phase dependent. Nature 324(6094):250–253CrossRefGoogle Scholar
  37. Negi P, Labate D (2012) 3-D discrete shearlet transform and video processing. Image Process IEEE Trans 21(6):2944–2954MathSciNetCrossRefGoogle Scholar
  38. Pennec EL, Mallat S (2005) Bandelet image approximation and compression. SIAM J Multiscale Model Simul 4:2005MathSciNetCrossRefzbMATHGoogle Scholar
  39. Pfadler S, Beyrau F, Löffler M, Leipertz A (2006) Application of a beam homogenizer to planar laser diagnostics. Opt Express 14(22):10,171–10,180CrossRefGoogle Scholar
  40. Pfadler S, Beyrau F, Leipertz A (2007) Flame front detection using conditioned particle image velocimetry (CPIV). Opt Express 15:15,444–15,456CrossRefGoogle Scholar
  41. Prewitt JMS (1970) Object enhancement and extraction. In: Lipkin BS, Rosenfeld A (eds) Picture processing and psychopictorics, vol 75. Elsevier, PhiladelphiaGoogle Scholar
  42. Reisenhofer R (2014) The complex shearlet transform and applications to image quality assessment. Master’s thesis, Technische Universität BerlinGoogle Scholar
  43. Roberts LG (1963) Machine perception of three-dimensional solids. Ph.D. thesis, Massachusetts Institute of TechnologyGoogle Scholar
  44. Seitzman J, Hanson R, DeBarber P, Hess C (1994) Application of quantitative two-line OH planar laser-induced fluorescence for temporally resolved planar thermometry in reacting flows. Appl Opt 33(18):4000–4012CrossRefGoogle Scholar
  45. Selesnick IW (2001) Hilbert transform pairs of wavelet bases. IEEE Signal Process Lett 8(6):170–173CrossRefGoogle Scholar
  46. Selesnick IW, Abdelnour AF (2004) Symmetric wavelet tight frames with two generators. Appl Comput Harmon Anal 17(2):211–225MathSciNetCrossRefzbMATHGoogle Scholar
  47. Slabaugh CD, Pratt AC, Lucht RP (2015) Simultaneous 5 kHz OH-PLIF/PIV for the study of turbulent combustion at engine conditions. Appl Phys B 118:109–130CrossRefGoogle Scholar
  48. Sobel I, Feldman G (1968) A \(3\times 3\) isotropic gradient operator for image processing. In: Presentation at the Stanford Artificial Intelligence ProjectGoogle Scholar
  49. Staal J, Abràmoff MD, Niemeijer M, Viergever MA, van Ginneken B (2004) Ridge-based vessel segmentation in color images of the retina. IEEE Trans Med Imaging 23(4):501–509CrossRefGoogle Scholar
  50. Storath M (2013) Amplitude and sign decompositions by complex wavelets-theory and applications to image analysis. Ph.D. thesis, Technische Universität MünchenGoogle Scholar
  51. Sweeney M, Hochgreb S (2009) Autonomous extraction of optimal flame fronts in OH planar laser-induced fluorescence images. Appl Opt 48:3866–3877CrossRefGoogle Scholar
  52. Thurow B, Jiang N, Lempert W (2013) Review of ultra-high repetition rate laser diagnostics for fluid dynamic measurements. Meas Sci Technol 24(012):002Google Scholar
  53. van Deemter JH, Buf JMHD (2000) Simultaneous detection of lines and edges using compound Gabor filters. Int J Pattern Recogn 14(6):757–777CrossRefGoogle Scholar
  54. Yi S, Labate D, Easley GR, Krim H (2009) A shearlet approach to edge analysis and detection. IEEE Trans Image Process 18(5):929–941MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Rafael Reisenhofer
    • 1
  • Johannes Kiefer
    • 2
    Email author
  • Emily J. King
    • 1
  1. 1.Computational Data Analysis, Fachbereich 3Universität BremenBremenGermany
  2. 2.Technische Thermodynamik, Fachbereich 4Universität BremenBremenGermany

Personalised recommendations