http://iet.metastore.ingenta.com
1887

Levellings based on spatially adaptive scale spaces using local image features

Levellings based on spatially adaptive scale spaces using local image features

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Image Processing — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The authors propose here to overcome lacks of robustness against noise and adaptability to image features for which classical morphological operators suffer from. For doing this, they propose to deal with partial differential equations (PDEs) for generalised Cauchy problems, and they show that the proposed PDEs are equivalent to impose both robustness and adaptability to structuring functions of the corresponding sup-inf operators. This allows them to introduce spatially adaptability in levellings, and it turns out that the proposed approach constitutes a PDE formulation and a generalisation of a larger class of levellings, the so-called extended levellings, for which one of them are characterised by quasi-flat zones. They show the efficiency of the proposed approach on synthetic, grey, and colour images with different types of noises.

References

    1. 1)
      • 1. Xu, Y., Géraud, T., Najman, L.: ‘Hierarchical image simplification and segmentation based on Mumford–Shah-salient level line selection’, Pattern Recognit. Lett., 2016, 83, pp. 278286.
    2. 2)
      • 2. Soille, P.: ‘Morphological image analysis’ (Springer-Verlag, Berlin, 1999).
    3. 3)
      • 3. Serra, J.: ‘Image analysis and mathematical morphology: theoretical advances’, vol. II, (AP, London, 1988).
    4. 4)
      • 4. Heijmans, H.J.A.M.: ‘Morphological image operators’ (Academic Press, Boston, 1994).
    5. 5)
      • 5. Angulo, J.: ‘Chapter 1 – convolution in (max, min)-algebra and its role in mathematical morphology’, in: Hawkes, P.W. (Ed.): ‘Advances in imaging and electron physics’, vol. 203, (Elsevier, London, 2017), pp. 166.
    6. 6)
      • 6. Alvarez, L., Lions, P.L., Morel, J.M.: ‘Image selective smoothing and edge detection by nonlinear diffusion. ii’, SIAM J. Numer. Anal., 1992, 29, (3), pp. 845866.
    7. 7)
      • 7. Alvarez, L., Guichard, F., Lions, P.L., et al: ‘Axioms and fundamental equations of image processing’, Arch. Ration. Mech. Anal., 1993, 123, pp. 199257.
    8. 8)
      • 8. Brockett, R.W., Maragos, P.: ‘Evolution equation for continuous-scale morphology’. IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP), San Francisco, CA, USA, 1992, pp. 14.
    9. 9)
      • 9. Brockett, R.W., Maragos, P.: ‘Evolution equations for continuous-scale morphological filtering’, IEEE Trans. Signal Process., 1994, 42, (12), pp. 33773386.
    10. 10)
      • 10. van den Boomgaard, R., Smeulders, A.: ‘Towards a morphological scale-space theory’, in: O, Y.L., Toet, A., Foster, D., et al (Eds.): ‘Proceedings of the NATO advanced research workshop ‘shape in picture’’, (Springer-Verlag, Berlin, 1992), pp. 631640.
    11. 11)
      • 11. van den Boomgaard, R., Smeulders, A.: ‘The morphological structures of images: the differential equations of morphological scale-space’, IEEE Trans. Pattern Anal. Mach. Intell., 1994, 16, (11), pp. 11011113.
    12. 12)
      • 12. Beucher, S., Blosseville, J.M., Lenoir, F.: ‘Traffic spatial measurements using video image processing’. Proc. SPIE on Intelligent Robots and Computer Vision, Cambridge, Massachusetts, USA, 1987, vol. 848, pp. 18.
    13. 13)
      • 13. Cuisenaire, O.: ‘Locally adaptable mathematical morphology using distance transformations’, Pattern Recognit., 2006, 39, (3), pp. 405416.
    14. 14)
      • 14. Lerallut, R., Decencière, E., Meyer, F.: ‘Image filtering using morphological amoebas’, Image Vis. Comput., 2007, 25, pp. 395404.
    15. 15)
      • 15. Grazzini, J., Soille, P.: ‘Edge-preserving smoothing using a similarity measure in adaptive geodesic neighbourhoods’, Pattern Recognit., 2009, 42, pp. 23062316.
    16. 16)
      • 16. Angulo, J.: ‘Morphological bilateral filtering and spatially variant adaptive structuring functions’. Int. Symp. Mathematical Morphology (ISMM), Italy, 2011 (LNCS, 6671), pp. 212223.
    17. 17)
      • 17. Verdú Monedero, R., Angulo, J., Serra, J.: ‘Anisotropic morphological filters with spatially variant structuring elements based on image-dependent gradient fields’, IEEE Trans. Image Process., 2011, 20, (1), pp. 200212.
    18. 18)
      • 18. Vachier, C., Meyer, F.: ‘News form viscousland’. Int. Symp. Mathematical Morphology (ISMM), Rio de Janeiro, Brazil, 2007, pp. 189200.
    19. 19)
      • 19. Maragos, P., Vachier, C.: ‘A PDE formulation For viscous morphological operators with extensions to intensity-adaptive operators’. IEEE Int. Conf. Image Processing (ICIP), San Diego, CA, 2008, pp. 22002203.
    20. 20)
      • 20. Legaz Aparicio, Á.G., Verdú Monedero, R., Angulo, J.: ‘Adaptive morphological filters based on a multiple orientation vector field dependent on image local features’, J. Comput. Appl. Math., 2017, 330, pp. 965981.
    21. 21)
      • 21. Breuß, M., Benedi, B., Weickert, J.: ‘Anisotropic continuous-scale morphology’. Pattern Recognition and Image Analysis, Berlin, Germany, 2007 (LNCS, 4486), pp. 515522.
    22. 22)
      • 22. Diop, E.H.S., Angulo, J.: ‘Robust nonlinear PDEs for multiscale morphological image analysis’. 83rd GAMM, Darmstadt, Germany, 2012, pp. 12.
    23. 23)
      • 23. Diop, E.H.S., Angulo, J.: ‘Spatially adaptive PDEs for robust image sharpening’. IEEE Int. Conf. Image Processing (ICIP), Orlando, FL, 2012, pp. 949952.
    24. 24)
      • 24. Maragos, P., Vachier, C.: ‘Overview of adaptive morphology: trends and perspectives’. IEEE Int. Conf. Image Processing (ICIP), Cairo, Egypt, 2009, pp. 22412244.
    25. 25)
      • 25. Ćurić, V., Landström, A., Thurley, M.J., et al: ‘Adaptive mathematical morphology – a survey of the field’, Pattern Recognit. Lett., 2014, 47, (Suppl. C), pp. 1828.
    26. 26)
      • 26. Roerdink, J.B.T.M.: ‘Adaptivity and group invariance in mathematical morphology’. IEEE Int. Conf. Image Processing (ICIP), Cairo, Egypt, 2009, pp. 22532256.
    27. 27)
      • 27. Matheron, G.: ‘Les nivellements’. Centre de Morphologie Mathématique, 1997.
    28. 28)
      • 28. Meyer, F.: ‘The levelings’, in: Heijmans, H., Roerdink, J. (Eds.): ‘Mathematical morphology and its applications to image and signal processing’, (Kluwer Academic, Dordrecht/Norwell, MA, 1998), pp. 199207.
    29. 29)
      • 29. Meyer, F., Maragos, P.: ‘Nonlinear scale-space representation with morphological levelings’, J. Vis. Commun. Image Represent., 2000, 11, pp. 245265.
    30. 30)
      • 30. Pesaresi, M., Benediktsson, J.A.: ‘A new approach for the morphological segmentation of high-resolution satellite imagery’, IEEE Trans. Geosci. Remote Sens., 2001, 39, (2), pp. 309320.
    31. 31)
      • 31. Meyer, F.: ‘Levelings and morphological segmentation’. Proc. SIBGRAPI ‘98 Int. Symp. Computer Graphics, Image Processing, and Vision, Rio de Janeiro, Brazil, 1998, pp. 2835.
    32. 32)
      • 32. Vincent, L.: ‘Morphological grayscale reconstruction in image analysis: applications and efficient algorithms’, IEEE Trans. Image Process., 1993, 2, (2), pp. 176201.
    33. 33)
      • 33. Salembier, P., Serra, J.: ‘Flat zones filtering, connected operators, and filters by reconstruction’, IEEE Trans. Image Process., 1995, 4, (8), pp. 11531160.
    34. 34)
      • 34. Alves, W.A.L., Morimitsu, A., Hashimoto, R.F.: ‘Scale-Space representation based on levelings through hierarchies of level sets’. Int. Symp. Mathematical Morphology (ISMM 2015), Reykjavik, Iceland, 2015, pp. 265276.
    35. 35)
      • 35. Xu, Y., Géraud, T., Najman, L.: ‘Connected filtering on tree-based shape-spaces’, IEEE Pattern Anal. Mach. Intell., 2016, 38, (6), pp. 11261140.
    36. 36)
      • 36. Alves, W.A.L., Hashimoto, R.F., Marcotegui, B.: ‘Ultimate levelings’, Comput. Vis. Image Underst., 2017, 165, pp. 6074.
    37. 37)
      • 37. Breuß, M., Hoeltgen, L., Kleefeld, A.: ‘Matrix-valued levelings for colour images’. Int. Symp. Mathematical Morphology (ISMM), Fontainebleau, France, 2017, pp. 296308.
    38. 38)
      • 38. Burgeth, B., Kleefeld, A.: ‘Morphology for color images via Loewner order for matrix fields’. Int. Symp. Mathematical Morphology (ISMM), Uppsala, Sweden, 2013, pp. 243254.
    39. 39)
      • 39. Matheron, G.: ‘Random sets and integral geometry’ (John Wiley & Sons, New York, 1975).
    40. 40)
      • 40. Serra, J.: ‘Image analysis and mathematical morphology’, vol. I, (Academic Press, England, 1982).
    41. 41)
      • 41. Rockafellar, R.T.: ‘Convex analysis’ (Princeton University Press, Princeton, 1970).
    42. 42)
      • 42. Catté, F., Dibos, F., Koepfler, G.: ‘A morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets’, SIAM J. Numer. Anal., 1995, 32, pp. 18951909.
    43. 43)
      • 43. Cao, F.: ‘Partial differential equations and mathematical morphology’, J. Math. Pures Appl., 1998, 77, pp. 909941.
    44. 44)
      • 44. van den Boomgaard, R., Dorst, L.: ‘The morphological equivalent of Gaussian scale-space’, in Sporring, J., Nielsen, M., Florack, L., et al (Eds.): ‘Gaussian scale-space theory, of computational imaging and vision’, vol. 8, (Springer, Dordrecht, 1997), pp. 203220.
    45. 45)
      • 45. Dorst, L., van den Boomgaard, R.: ‘Morphological signal processing and the slope transform’, Signal Process., 1994, 38, pp. 7998.
    46. 46)
      • 46. Maragos, P.: ‘Slope transforms: theory and application to nonlinear signal processing’, IEEE Trans. Signal Process., 1995, 43, (4), pp. 864877.
    47. 47)
      • 47. Sapiro, G., Kimmel, R., Shaked, D., et al: ‘Implementing continuous-scale morphology via curve evolution’, Pattern Recognit., 1993, 26, (9), pp. 13631372.
    48. 48)
      • 48. Crandall, M.G., Ishii, H., Lions, P.L.: ‘User's guide to viscosity solutions of second order partial differential equations’, Bull. New Ser. Am. Math. Soc., 1992, 27, (1), pp. 167.
    49. 49)
      • 49. Lions, P.L.: ‘Generalized solutions of Hamilton–Jacobi equations’ (Pitman Advanced Publishing Program, London, 1982).
    50. 50)
      • 50. Bardi, M., Evans, L.C.: ‘On HOPF's formulas for solutions of Hamilton–Jacobi equations’, Nonlinear Anal. Theory Methods Appl., 1984, 8, (11), pp. 13731381.
    51. 51)
      • 51. Maragos, P., Meyer, F.: ‘Nonlinear PDEs and numerical algorithms for modeling levelings and reconstruction filters’. Scale-Space Theories in Computer Vision, Corfu, Greece, 1999, pp. 363374.
    52. 52)
      • 52. Rudin, L.I., Osher, S.: ‘Feature-oriented image enhancement with shock filters’ (Caltech, Los Angeles, CA, 1989), Caltech-CS-TR-89-3.
    53. 53)
      • 53. Schavemaker, J.G.M., Reinders, M.J.T., Gerbrands, J.J., et al: ‘Image sharpening by morphological filtering’, Pattern Recognit., 2000, 33, pp. 9971012.
    54. 54)
      • 54. Ta, V.T., Elmoataz, A., Lézoray, O.: ‘Nonlocal morphological levelings by partial differential equations over weighted graphs’. IEEE Int. Conf. Pattern Recognition, FL, USA, 2008, pp. 14.
    55. 55)
      • 55. Lions, P.L., Souganidis, P.E., Vásquez, J.L.: ‘The relation between the porous medium and the eikonal equations in several space dimensions’, Rev. Mat. Iberoam., 1987, 3, (3 Y 4), pp. 275340.
    56. 56)
      • 56. Bresson, X., Chan, T.F.: ‘Fast dual minimization of the vectorial total variation norm and applications to color image processing’, Inverse Probl. Imaging, 2008, 2, (4), pp. 184455.
    57. 57)
      • 57. Strekalovskiy, E., Chambolle, A., Cremers, D.: ‘A convex representation for the vectorial Mumford–Shah functional’. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), Providence, RI, 2012, pp. 17121719.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-ipr.2018.5151
Loading

Related content

content/journals/10.1049/iet-ipr.2018.5151
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address