Abstract

The application of nonlinear anisotropic diffusion filtering to reduce noise and enhance contours in images obtained by two-dimensional planar laser-induced fluorescence (PLIF) spectroscopy is presented. In this process the diffusion coefficient is locally adapted, becoming negligible as object boundaries are approached. Noise is efficiently removed, and object contours are strongly enhanced. The technique is demonstrated with PLIF images obtained from the OH radical recorded in turbulent flames. We show that nonlinear diffusion is suitable as a preprocessing step, before image segmentation becomes possible, and we demonstrate how the technique is applied for the quantitative extraction of flame reaction boundaries from PLIF data.

© 2000 Optical Society of America

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  1. R. K. Hanson, “Combustion diagnostics: planar imaging techniques,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1986), Vol. 21, pp. 1677–1691.
  2. B. Yip, J. K. Lam, M. Winter, M. B. Long, “Time resolved three-dimensional concentration measurements in a gas jet,” Science 235, 1209–1211 (1987).
    [CrossRef] [PubMed]
  3. A. Orth, V. Sick, J. Wolfrum, R. Maly, M. Zahn, “Simultaneous 2D single-shot imaging of OH concentrations and temperature fields in an SI engine simulator,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1994), Vol. 25, pp. 143–150.
  4. I. van Cruyningen, A. Lozano, R. K. Hanson, “Planar imaging of concentration by planar laser induced fluorescence,” Exp. Fluids 10, 41–49 (1990).
    [CrossRef]
  5. C. F. Kaminski, J. Engström, M. Aldén, “Quasi instantaneous 2 dimensional temperature measurements in a spark ignition engine using 2-line atomic fluorescence,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1998), Vol. 27, pp. 85–93.
  6. A. C. Eckbreth, Laaser Diagnostics for Combustion Temperature and Species, Vol. 3 of Combustion Science and Technology Book Series (Gordon & Breach, Amsterdam, 1996).
  7. J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).
  8. C. F. Kaminski, J. Hult, M. Aldén, “High repetition rate planar laser induced fluorescence of OH in a turbulent non-premixed flame,” Appl. Phys. B 68, 757–760 (1999).
    [CrossRef]
  9. P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
    [CrossRef]
  10. H. Malm, “Multiscale image analysis and image enhancement based on partial differential equations,” Master’s thesis (Lund Institute of Technology, Lund, 1998).
  11. J. Weickert, “Anisotropic diffusion in image processing,” Ph.D. dissertation (Universität Kaiserslautern, Kaiserslautern, 1996).
  12. F. Catté, P.-L. Lions, J.-M. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182–193 (1992).
    [CrossRef]
  13. G. Gerig, O. Klüber, R. Kikinis, F. A. Jolesz, “Nonlinear anisotropic filtering of MRI data,” IEEE Trans. Med. Imaging 11, 221–232 (1992).
    [CrossRef] [PubMed]
  14. A. Handlovicova, K. Mikula, F. Sgallari, “Numerical methods for nonlinear diffusion equations arising in image processing,” Preprint No. 1 (Slovak University of Technology, Bratislava, 1999).
  15. J. Weickert, B. M. ter Haar Romeny, M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. Image Process. 7, 398–410 (1998).
    [CrossRef]
  16. J. Weickert, K. J. Zuiderveld, B. M. ter Haar Romeny, W. J. Niessen, “Parallel implementation of AOS schemes: A fast way of nonlinear diffusion filtering,” in Proceedings of the 1997 International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 396–399.
  17. C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.
  18. A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
    [CrossRef]
  19. T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.
  20. C. F. Kaminski, X. S. Bai, J. Hult, A. Dreizler, S. Lindenmaier, L. Fuchs, “Flame growth and wrinkling in a turbulent flow,” Appl. Phys. B (to be published).

2000 (1)

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

1999 (1)

C. F. Kaminski, J. Hult, M. Aldén, “High repetition rate planar laser induced fluorescence of OH in a turbulent non-premixed flame,” Appl. Phys. B 68, 757–760 (1999).
[CrossRef]

1998 (1)

J. Weickert, B. M. ter Haar Romeny, M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. Image Process. 7, 398–410 (1998).
[CrossRef]

1992 (2)

F. Catté, P.-L. Lions, J.-M. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

G. Gerig, O. Klüber, R. Kikinis, F. A. Jolesz, “Nonlinear anisotropic filtering of MRI data,” IEEE Trans. Med. Imaging 11, 221–232 (1992).
[CrossRef] [PubMed]

1990 (2)

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

I. van Cruyningen, A. Lozano, R. K. Hanson, “Planar imaging of concentration by planar laser induced fluorescence,” Exp. Fluids 10, 41–49 (1990).
[CrossRef]

1987 (1)

B. Yip, J. K. Lam, M. Winter, M. B. Long, “Time resolved three-dimensional concentration measurements in a gas jet,” Science 235, 1209–1211 (1987).
[CrossRef] [PubMed]

Aldén, M.

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

C. F. Kaminski, J. Hult, M. Aldén, “High repetition rate planar laser induced fluorescence of OH in a turbulent non-premixed flame,” Appl. Phys. B 68, 757–760 (1999).
[CrossRef]

C. F. Kaminski, J. Engström, M. Aldén, “Quasi instantaneous 2 dimensional temperature measurements in a spark ignition engine using 2-line atomic fluorescence,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1998), Vol. 27, pp. 85–93.

T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.

C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.

Bai, X. S.

C. F. Kaminski, X. S. Bai, J. Hult, A. Dreizler, S. Lindenmaier, L. Fuchs, “Flame growth and wrinkling in a turbulent flow,” Appl. Phys. B (to be published).

Catté, F.

F. Catté, P.-L. Lions, J.-M. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Coll, T.

F. Catté, P.-L. Lions, J.-M. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Dibble, R. W.

J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).

Ding, T.

T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.

Dreizler, A.

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.

C. F. Kaminski, X. S. Bai, J. Hult, A. Dreizler, S. Lindenmaier, L. Fuchs, “Flame growth and wrinkling in a turbulent flow,” Appl. Phys. B (to be published).

Eckbreth, A. C.

A. C. Eckbreth, Laaser Diagnostics for Combustion Temperature and Species, Vol. 3 of Combustion Science and Technology Book Series (Gordon & Breach, Amsterdam, 1996).

Engström, J.

C. F. Kaminski, J. Engström, M. Aldén, “Quasi instantaneous 2 dimensional temperature measurements in a spark ignition engine using 2-line atomic fluorescence,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1998), Vol. 27, pp. 85–93.

Fuchs, L.

C. F. Kaminski, X. S. Bai, J. Hult, A. Dreizler, S. Lindenmaier, L. Fuchs, “Flame growth and wrinkling in a turbulent flow,” Appl. Phys. B (to be published).

Gerig, G.

G. Gerig, O. Klüber, R. Kikinis, F. A. Jolesz, “Nonlinear anisotropic filtering of MRI data,” IEEE Trans. Med. Imaging 11, 221–232 (1992).
[CrossRef] [PubMed]

Golombok, M.

T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.

Handlovicova, A.

A. Handlovicova, K. Mikula, F. Sgallari, “Numerical methods for nonlinear diffusion equations arising in image processing,” Preprint No. 1 (Slovak University of Technology, Bratislava, 1999).

Hanson, R. K.

I. van Cruyningen, A. Lozano, R. K. Hanson, “Planar imaging of concentration by planar laser induced fluorescence,” Exp. Fluids 10, 41–49 (1990).
[CrossRef]

R. K. Hanson, “Combustion diagnostics: planar imaging techniques,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1986), Vol. 21, pp. 1677–1691.

Hult, J.

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

C. F. Kaminski, J. Hult, M. Aldén, “High repetition rate planar laser induced fluorescence of OH in a turbulent non-premixed flame,” Appl. Phys. B 68, 757–760 (1999).
[CrossRef]

C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.

T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.

C. F. Kaminski, X. S. Bai, J. Hult, A. Dreizler, S. Lindenmaier, L. Fuchs, “Flame growth and wrinkling in a turbulent flow,” Appl. Phys. B (to be published).

Jolesz, F. A.

G. Gerig, O. Klüber, R. Kikinis, F. A. Jolesz, “Nonlinear anisotropic filtering of MRI data,” IEEE Trans. Med. Imaging 11, 221–232 (1992).
[CrossRef] [PubMed]

Kaminski, C. F.

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

C. F. Kaminski, J. Hult, M. Aldén, “High repetition rate planar laser induced fluorescence of OH in a turbulent non-premixed flame,” Appl. Phys. B 68, 757–760 (1999).
[CrossRef]

C. F. Kaminski, J. Engström, M. Aldén, “Quasi instantaneous 2 dimensional temperature measurements in a spark ignition engine using 2-line atomic fluorescence,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1998), Vol. 27, pp. 85–93.

T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.

C. F. Kaminski, X. S. Bai, J. Hult, A. Dreizler, S. Lindenmaier, L. Fuchs, “Flame growth and wrinkling in a turbulent flow,” Appl. Phys. B (to be published).

C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.

Kikinis, R.

G. Gerig, O. Klüber, R. Kikinis, F. A. Jolesz, “Nonlinear anisotropic filtering of MRI data,” IEEE Trans. Med. Imaging 11, 221–232 (1992).
[CrossRef] [PubMed]

Klüber, O.

G. Gerig, O. Klüber, R. Kikinis, F. A. Jolesz, “Nonlinear anisotropic filtering of MRI data,” IEEE Trans. Med. Imaging 11, 221–232 (1992).
[CrossRef] [PubMed]

Lam, J. K.

B. Yip, J. K. Lam, M. Winter, M. B. Long, “Time resolved three-dimensional concentration measurements in a gas jet,” Science 235, 1209–1211 (1987).
[CrossRef] [PubMed]

Lindenmaier, S.

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.

C. F. Kaminski, X. S. Bai, J. Hult, A. Dreizler, S. Lindenmaier, L. Fuchs, “Flame growth and wrinkling in a turbulent flow,” Appl. Phys. B (to be published).

Lions, P.-L.

F. Catté, P.-L. Lions, J.-M. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Long, M. B.

B. Yip, J. K. Lam, M. Winter, M. B. Long, “Time resolved three-dimensional concentration measurements in a gas jet,” Science 235, 1209–1211 (1987).
[CrossRef] [PubMed]

Lozano, A.

I. van Cruyningen, A. Lozano, R. K. Hanson, “Planar imaging of concentration by planar laser induced fluorescence,” Exp. Fluids 10, 41–49 (1990).
[CrossRef]

Maas, U.

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.

J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).

Malik, J.

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Malm, H.

H. Malm, “Multiscale image analysis and image enhancement based on partial differential equations,” Master’s thesis (Lund Institute of Technology, Lund, 1998).

Maly, R.

A. Orth, V. Sick, J. Wolfrum, R. Maly, M. Zahn, “Simultaneous 2D single-shot imaging of OH concentrations and temperature fields in an SI engine simulator,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1994), Vol. 25, pp. 143–150.

Mikula, K.

A. Handlovicova, K. Mikula, F. Sgallari, “Numerical methods for nonlinear diffusion equations arising in image processing,” Preprint No. 1 (Slovak University of Technology, Bratislava, 1999).

Morel, J.-M.

F. Catté, P.-L. Lions, J.-M. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Niessen, W. J.

J. Weickert, K. J. Zuiderveld, B. M. ter Haar Romeny, W. J. Niessen, “Parallel implementation of AOS schemes: A fast way of nonlinear diffusion filtering,” in Proceedings of the 1997 International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 396–399.

Orth, A.

A. Orth, V. Sick, J. Wolfrum, R. Maly, M. Zahn, “Simultaneous 2D single-shot imaging of OH concentrations and temperature fields in an SI engine simulator,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1994), Vol. 25, pp. 143–150.

Perona, P.

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Sgallari, F.

A. Handlovicova, K. Mikula, F. Sgallari, “Numerical methods for nonlinear diffusion equations arising in image processing,” Preprint No. 1 (Slovak University of Technology, Bratislava, 1999).

Sick, V.

A. Orth, V. Sick, J. Wolfrum, R. Maly, M. Zahn, “Simultaneous 2D single-shot imaging of OH concentrations and temperature fields in an SI engine simulator,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1994), Vol. 25, pp. 143–150.

ter Haar Romeny, B. M.

J. Weickert, B. M. ter Haar Romeny, M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. Image Process. 7, 398–410 (1998).
[CrossRef]

J. Weickert, K. J. Zuiderveld, B. M. ter Haar Romeny, W. J. Niessen, “Parallel implementation of AOS schemes: A fast way of nonlinear diffusion filtering,” in Proceedings of the 1997 International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 396–399.

van Cruyningen, I.

I. van Cruyningen, A. Lozano, R. K. Hanson, “Planar imaging of concentration by planar laser induced fluorescence,” Exp. Fluids 10, 41–49 (1990).
[CrossRef]

van der Meer, Th. H.

T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.

Versluis, M.

T. Ding, Th. H. van der Meer, M. Versluis, M. Golombok, J. Hult, M. Aldén, C. F. Kaminski, “Time-resolved PLIF measurements in turbulent diffusion flames,” in Third International Symposium on Turbulence, Heat and Mass Transfer, Y. Nagano, K. Hanjalic, T. Tsuji, eds. (Aichi Shuppan, Tokyo, 2000), pp. 857–864.

Viergever, M. A.

J. Weickert, B. M. ter Haar Romeny, M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. Image Process. 7, 398–410 (1998).
[CrossRef]

Warnatz, J.

J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).

Weickert, J.

J. Weickert, B. M. ter Haar Romeny, M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. Image Process. 7, 398–410 (1998).
[CrossRef]

J. Weickert, “Anisotropic diffusion in image processing,” Ph.D. dissertation (Universität Kaiserslautern, Kaiserslautern, 1996).

J. Weickert, K. J. Zuiderveld, B. M. ter Haar Romeny, W. J. Niessen, “Parallel implementation of AOS schemes: A fast way of nonlinear diffusion filtering,” in Proceedings of the 1997 International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 396–399.

Winter, M.

B. Yip, J. K. Lam, M. Winter, M. B. Long, “Time resolved three-dimensional concentration measurements in a gas jet,” Science 235, 1209–1211 (1987).
[CrossRef] [PubMed]

Wolfrum, J.

A. Orth, V. Sick, J. Wolfrum, R. Maly, M. Zahn, “Simultaneous 2D single-shot imaging of OH concentrations and temperature fields in an SI engine simulator,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1994), Vol. 25, pp. 143–150.

Yip, B.

B. Yip, J. K. Lam, M. Winter, M. B. Long, “Time resolved three-dimensional concentration measurements in a gas jet,” Science 235, 1209–1211 (1987).
[CrossRef] [PubMed]

Zahn, M.

A. Orth, V. Sick, J. Wolfrum, R. Maly, M. Zahn, “Simultaneous 2D single-shot imaging of OH concentrations and temperature fields in an SI engine simulator,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1994), Vol. 25, pp. 143–150.

Zuiderveld, K. J.

J. Weickert, K. J. Zuiderveld, B. M. ter Haar Romeny, W. J. Niessen, “Parallel implementation of AOS schemes: A fast way of nonlinear diffusion filtering,” in Proceedings of the 1997 International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 396–399.

Appl. Phys. B (2)

C. F. Kaminski, J. Hult, M. Aldén, “High repetition rate planar laser induced fluorescence of OH in a turbulent non-premixed flame,” Appl. Phys. B 68, 757–760 (1999).
[CrossRef]

A. Dreizler, S. Lindenmaier, U. Maas, J. Hult, M. Aldén, C. F. Kaminski, “Characterization of a spark ignition system by planar laser induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations,” Appl. Phys. B 70, 287–294 (2000).
[CrossRef]

Exp. Fluids (1)

I. van Cruyningen, A. Lozano, R. K. Hanson, “Planar imaging of concentration by planar laser induced fluorescence,” Exp. Fluids 10, 41–49 (1990).
[CrossRef]

IEEE Trans. Image Process. (1)

J. Weickert, B. M. ter Haar Romeny, M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. Image Process. 7, 398–410 (1998).
[CrossRef]

IEEE Trans. Med. Imaging (1)

G. Gerig, O. Klüber, R. Kikinis, F. A. Jolesz, “Nonlinear anisotropic filtering of MRI data,” IEEE Trans. Med. Imaging 11, 221–232 (1992).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Science (1)

B. Yip, J. K. Lam, M. Winter, M. B. Long, “Time resolved three-dimensional concentration measurements in a gas jet,” Science 235, 1209–1211 (1987).
[CrossRef] [PubMed]

SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. (1)

F. Catté, P.-L. Lions, J.-M. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Other (12)

R. K. Hanson, “Combustion diagnostics: planar imaging techniques,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1986), Vol. 21, pp. 1677–1691.

A. Orth, V. Sick, J. Wolfrum, R. Maly, M. Zahn, “Simultaneous 2D single-shot imaging of OH concentrations and temperature fields in an SI engine simulator,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 1994), Vol. 25, pp. 143–150.

A. Handlovicova, K. Mikula, F. Sgallari, “Numerical methods for nonlinear diffusion equations arising in image processing,” Preprint No. 1 (Slovak University of Technology, Bratislava, 1999).

J. Weickert, K. J. Zuiderveld, B. M. ter Haar Romeny, W. J. Niessen, “Parallel implementation of AOS schemes: A fast way of nonlinear diffusion filtering,” in Proceedings of the 1997 International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 396–399.

C. F. Kaminski, J. Hult, M. Aldén, S. Lindenmaier, A. Dreizler, U. Maas, “Spark ignition of turbulent methane/air mixtures revealed by time resolved planar laser induced fluorescence and direct numerical simulations,” in Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28.

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Figures (13)

Fig. 1
Fig. 1

Schematic setup of planar laser light-scattering techniques.

Fig. 2
Fig. 2

A, Photograph of line-of-sight flame emission from a turbulent nonpremixed flame. The area imaged by the PLIF experiments is indicated by the white box, corresponding to 24 mm × 23 mm, starting 40 mm above the burner nozzle B, PLIF raw image showing two-dimensional OH-radical concentrations in a cut through the flame. C, PLIF image after nonlinear diffusion filtering. The position of the flame front is strongly enhanced.

Fig. 3
Fig. 3

Sharpening of an edge by nonlinear anisotropic diffusion. The plot shows the evolution of a noisy, blurred step function during 25 computational iterations. Clearly the edge is strongly enhanced, while noise fluctuations are effectively smoothed out by the process.

Fig. 4
Fig. 4

Graph displaying the diffusive flow g(|u|)u for three different diffusivity functions g as a function of the edge strengths u/λ in the image. The functions are, a, the function used in this paper [Eq. (5)], g(s)=1-exp[-Cm/(s/λ)8] and, b and c, two functions originally proposed by Perona and Malik, g(s)=1/[1+(|s|/λ)2] and g(s)=exp[-(|s|/λ)2], respectively. All three curves are normalized to unity area with maximum flow occurring at u=λ.

Fig. 5
Fig. 5

Behavior of an edge propagating through the diffusion filtering process. The evolutions of A, u; B, u; and C, tu are shown for n equal to 1, 10, and 100 iteration steps, respectively.

Fig. 6
Fig. 6

Illustration of the gradient-selective behavior of the diffusion process. A, Unprocessed periodic function u; B, its gradient u. Function u contains a large range of gradients, successively decreasing for each period. C, Filtered function ufil; D, its gradient ufil. It can be seen that the peak with the lowest gradient (the rightmost peak on in graph A) is not retained in the filtered image. All other gradients are strongly enhanced.

Fig. 7
Fig. 7

Filtering of periodic structures with increasing degrees of white noise added and consequently decreasing signal-to-noise ratios. A, Unfiltered function u; B, its gradient. C, After filtering, the features of the original periodic function are restored and enhanced (ufil); D, the corresponding gradient.

Fig. 8
Fig. 8

A, Gradients u of an unperturbed periodic structure u; C, gradients ∇(u + noise) of the same structure with increasing levels of noise added (analogous to Fig. 7); E, gradients (ufil) of the filtered structure. B, D, and F, Corresponding histograms of the gradient distributions. The magnitude of the flow |g(u)u| as a function of u is superimposed on the histogram to help visualize which gradients are preserved by the process.

Fig. 9
Fig. 9

Effects of the contrast parameter λ on the retainment of image structure during nonlinear diffusion filtering. The line profile shown corresponds to the pixel row indicated in white in Fig. 2B. A, Raw intensity profile; B, C, and D, filtered profile for λ equal to 3, 5, and 7, respectively.

Fig. 10
Fig. 10

Three-dimensional plots of, A, the original PLIF image and, B, the nonlinear-diffusion-filtered image.

Fig. 11
Fig. 11

Original PLIF raw image with the identified flame fronts superimposed as white outlines.

Fig. 12
Fig. 12

Dependence of the circumference to area ratio, η, as a function of different filter parameters. A, Dependence on λ; B, on σ; C, on n; D on m.

Fig. 13
Fig. 13

Circumference to area ratio, η, as a function of the noise level in an artificially generated test image.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

Gσ(x) :=12πσ2exp(-|x|2/2σ2),
tu=div(du),
tu=div[g(|u|)u].
div[g(|u|)u]=g(|u|)uξξ+Φ(|u|)uηη,
g(s)=1-exp-Cm(s/λ)m.
tu=div[g(|(Gσ * u)|)u].
xui,j=ui+1,j-ui-1,j2,
yui,j=ui,j+1-ui,j-12
X=120-100010-100010000000-100010N×N,
Y=1201000-101000-100000001000-10M×M.
un=un-1+Δt[(g·xun-1)X+Y(g·yun-1)].

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