Progress in Artificial Intelligence

, Volume 6, Issue 2, pp 121–132 | Cite as

Baddeley’s Delta metric for local contrast computation in hyperspectral imagery

  • C. Lopez-Molina
  • D. Ayala-Martini
  • A. Lopez-Maestresalas
  • H. Bustince
Regular Paper


Recent years have brought a quick decay in prize of hyperspectral imagery equipment. As a consequence, new applications have appeared, a relevant example being the analysis of agro-food materials. Such applications need to be grounded on dedicated image processing operators, which fully accomplish with (and exploit) the characteristics of hyperspectral imagery. In this regard, we study the quantitative comparison of spectra, which can be further used to produce a variety of image processing operators. Specifically, we propose the use of Baddeley’s Delta metric for the comparison of spectra. Our method has theoretical advantages over classical bandwise comparison measures, which are often inconsistent with human perception of dissimilarity between spectra. Our proposal is put to the test in the context of local contrast computation, with application to item segmentation of in-laboratory imagery.


Hyperspectral imagery Comparison measures Baddeley’s Delta metric Local contrast Image segmentation 



This research was supported by the National Institute for Agricultural and Food Research and Technology (INIA) through the Project RTA2013-00006-C03-03 and also by the Spanish Ministry of Science (Project TIN-2016-77356-P).


  1. 1.
    Abul Hasnat, M., Alata, O., Trémeau, A.: Joint color-spatial-directional clustering and region merging (JCSD-RM) for unsupervised RGB-D image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 38(11), 2255–2268 (2016)CrossRefGoogle Scholar
  2. 2.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33, 898–916 (2011)CrossRefGoogle Scholar
  3. 3.
    Baddeley, A.J.: An error metric for binary images. In: Förstner, W., Ruwiedel, S. (eds.) Robust Comput Vision: Qual Vision Algorithms, pp. 59–78. Wichmann Verlag, Karlsruhe (1992)Google Scholar
  4. 4.
    Baddeley, A.J.: Errors in binary images and an \(L^p\) version of the Hausdorff metric. Nieuw Archief voor Wiskunde 10, 157–183 (1992)MathSciNetMATHGoogle Scholar
  5. 5.
    Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners, Studies in Fuzziness and Soft Computing, vol. 221. Springer (2007)Google Scholar
  6. 6.
    Blanton, H., Jaccard, J.: Arbitrary metrics in psychology. Am. Psychol. 61(1), 27 (2006)CrossRefGoogle Scholar
  7. 7.
    Bustince, H., Barrenechea, E., Pagola, M.: Restricted equivalence functions. Fuzzy Sets Syst. 157(17), 2333–2346 (2006)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986)CrossRefGoogle Scholar
  9. 9.
    Cheng, J.H., Sun, D.W.: Hyperspectral imaging as an effective tool for quality analysis and control of fish and other seafoods: current research and potential applications. Trends Food Sci. Technol. 37(2), 78–91 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Comaniciu, D., Meer, P.: Mean shift: a robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24(5), 603–619 (2002)CrossRefGoogle Scholar
  11. 11.
    Coquin, D., Bolon, P.: Application of Baddeley’s distance to dissimilarity measurement between gray scale images. Pattern Recognit. Lett. 22(14), 1483–1502 (2001)CrossRefMATHGoogle Scholar
  12. 12.
    Coquin, D., Bolon, P., Onea, A.: Objective metric for colour image comparison. In: European Signal Processing Conference, pp. 1–4 (2000)Google Scholar
  13. 13.
    De Miguel, L., Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.: Unbalanced interval-valued OWA operators. Progress in Artificial Intelligence pp. 1–8 (2016)Google Scholar
  14. 14.
    De Miguel, L., Bustince, H., Pekala, B., Bentkowska, U., Da Silva, I., Bedregal, B., Mesiar, R., Ochoa, G.: Interval-valued atanassov intuitionistic OWA aggregations using admissible linear orders and their application to decision making. IEEE Trans. on Fuzzy Systems (2017, in press)Google Scholar
  15. 15.
    Di Gesu, V., Starovoitov, V.: Distance-based functions for image comparison. Pattern Recognit. Lett. 20(2), 207–214 (1999)CrossRefMATHGoogle Scholar
  16. 16.
    ElMasry, G., Kamruzzaman, M., Sun, D.W., Allen, P.: Principles and applications of hyperspectral imaging in quality evaluation of agro-food products: a review. Crit. Rev. Food Sci. Nutr. 52(11), 999–1023 (2012)CrossRefGoogle Scholar
  17. 17.
    ElMasry, G., Sun, D.W.: Principles of hyperspectral imaging technology. In: D.W., Sun (ed.) Hyperspectral Imaging for Food Quality Analysis and control, pp. 3–43. Academic press, San Diego, CA, USA (2010)Google Scholar
  18. 18.
    ElMasry, G., Wang, N., ElSayed, A., Ngadi, M.: Hyperspectral imaging for nondestructive determination of some quality attributes for strawberry. J. Food Eng. 81(1), 98–107 (2007)CrossRefGoogle Scholar
  19. 19.
    ElMasry, G., Wang, N., Vigneault, C., Qiao, J., ElSayed, A.: Early detection of apple bruises on different background colors using hyperspectral imaging. LWT-Food Sci. Technol. 41(2), 337–345 (2008)CrossRefGoogle Scholar
  20. 20.
    Evans, A., Liu, X.U.: A morphological gradient approach to color edge detection. IEEE Trans. Image Process. 15(6), 1454–1463 (2006)CrossRefGoogle Scholar
  21. 21.
    KERMIT Research Unit, Ghent University: The Kermit Image Toolkit (KITT).
  22. 22.
    Goetz, A., Vane, G., Solomon, J., Rock, B.: Imaging spectrometry for earth remote sensing. Science 228(4704), 1147–1152 (1985)CrossRefGoogle Scholar
  23. 23.
    Gómez, D., Yáñez, J., Guada, C., Rodríguez, J.T., Montero, J., Zarrazola, E.: Fuzzy image segmentation based upon hierarchical clustering. Knowl. Based Syst. 87, 26–37 (2015)CrossRefGoogle Scholar
  24. 24.
    González-Hidalgo, M., Massanet, S.: A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing. Soft Comput. 18(11), 1–15 (2013)Google Scholar
  25. 25.
    Gowen, A., O’Donnell, C., Cullen, P., Downey, G., Frias, J.: Hyperspectral imaging-an emerging process analytical tool for food quality and safety control. Trends Food Sci. Technol. 18(12), 590–598 (2007)CrossRefGoogle Scholar
  26. 26.
    Guada, C., Gómez, D., Rodríguez, J., Yáñez, J., Montero, J.: Classifying image analysis techniques from their output. Int. J. Comput. Intell. Syst. 9, 43–68 (2016)CrossRefGoogle Scholar
  27. 27.
    Image and Visual Representation Lab (IVRL), École Polytechnique Fédérale de Lausanne: SLIC superpixel project.
  28. 28.
    Keresztes, J.C., Goodarzi, M., Saeys, W.: Real-time pixel based early apple bruise detection using short wave infrared hyperspectral imaging in combination with calibration and glare correction techniques. Food Control 66, 215–226 (2016)CrossRefGoogle Scholar
  29. 29.
    Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. Int. J. Comput. Vision 30(2), 117–156 (1998)CrossRefGoogle Scholar
  30. 30.
    López-Maestresalas, A., Keresztes, J.C., Goodarzi, M., Arazuri, S., Jarén, C., Saeys, W.: Non-destructive detection of blackspot in potatoes by Vis-NIR and SWIR hyperspectral imaging. Food Control 70, 229–241 (2016)CrossRefGoogle Scholar
  31. 31.
    Lopez-Molina, C., Barrenechea, E., Bustince, H., De Baets, B.: Multichannel gradient fusion based on ordered weighted aggregation operators. In: Proceedings of the Eurofuse Workshop, (2013)Google Scholar
  32. 32.
    Lopez-Molina, C., Bustince, H., De Baets, B.: Separability criteria for the evaluation of boundary detection benchmarks. IEEE Trans. Image Process. 25(3), 1047–1055 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Lopez-Molina, C., De Baets, B., Bustince, H.: Quantitative error measures for edge detection. Pattern Recognit. 46(4), 1125–1139 (2013)CrossRefGoogle Scholar
  34. 34.
    Lopez-Molina, C., Galar, M., Bustince, H., De Baets, B.: Extending the upper–lower edge detector by means of directional masks and OWA operators. Prog. Artif. Intell. 1, 267–276 (2012)CrossRefGoogle Scholar
  35. 35.
    Lu, R., Peng, Y.: Hyperspectral scattering for assessing peach fruit firmness. Biosyst. Eng. 93(2), 161–171 (2006)CrossRefGoogle Scholar
  36. 36.
    Marco-Detchart, C., Cerron, J., De Miguel, L., Lopez-Molina, C., Bustince, H., Galar, M.: A framework for radial data comparison and its application to fingerprint analysis. Appl. Soft Comput. 46, 246–259 (2016)CrossRefGoogle Scholar
  37. 37.
    Marr, D.: Vision. MIT Press, Cambridge, MA, USA (1982)Google Scholar
  38. 38.
    Marr, D., Hildreth, E.: Theory of edge detection. Proc. R. Soc. Lond. 207(1167), 187–217 (1980)CrossRefGoogle Scholar
  39. 39.
    Monteiro, S.T., Minekawa, Y., Kosugi, Y., Akazawa, T., Oda, K.: Prediction of sweetness and amino acid content in soybean crops from hyperspectral imagery. ISPRS J. Photogramm. Remote Sens. 62(1), 2–12 (2007)CrossRefGoogle Scholar
  40. 40.
    Odet, C., Belaroussi, B., Benoit-Cattin, H.: Scalable discrepancy measures for segmentation evaluation. In: Proceedings of the International Conference on Image Processing, vol. 1, pp. 785–788 (2002)Google Scholar
  41. 41.
    Otsu, N.: Threshold selection method for gray-level histograms. IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Pantofaru, C.: Studies in using image segmentation to improve object recognition. Ph.D. thesis, The Robotics Institute, Carnegie Mellon University (2008)Google Scholar
  43. 43.
    Qin, J., Burks, T.F., Kim, M.S., Chao, K., Ritenour, M.A.: Citrus canker detection using hyperspectral reflectance imaging and PCA-based image classification method. Sens. Instrum. Food Qual. Saf. 2(3), 168–177 (2008)CrossRefGoogle Scholar
  44. 44.
    Rajkumar, P., Wang, N., EImasry, G., Raghavan, G., Gariepy, Y.: Studies on banana fruit quality and maturity stages using hyperspectral imaging. J. Food Eng. 108(1), 194–200 (2012)CrossRefGoogle Scholar
  45. 45.
    Ren, X., Malik, J.: Learning a classification model for segmentation. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 10–17 (2003)Google Scholar
  46. 46.
    Santini, S., Jain, R.: Similarity measures. IEEE Trans. Pattern Anal. Mach. Intell. 21(9), 871–883 (1999)CrossRefGoogle Scholar
  47. 47.
    Smith, S.M., Brady, J.M.: SUSAN—a new approach to low level image processing. Int. J. Comput. Vision 23, 45–78 (1997)CrossRefGoogle Scholar
  48. 48.
    Tversky, A., Gati, I.: Similarity, separability, and the triangle inequality. Psychol. Rev. 89(2), 123 (1982)CrossRefGoogle Scholar
  49. 49.
    Tversky, A., Krantz, D.H.: The dimensional representation and the metric structure of similarity data. J. math. psychol. 7(3), 572–596 (1970)MathSciNetCrossRefMATHGoogle Scholar
  50. 50.
    Wilson, D.L., Baddeley, A.J., Owens, R.A.: A new metric for grey-scale image comparison. Int. J. Comput. Vision 24, 5–17 (1997)CrossRefGoogle Scholar
  51. 51.
    Xuecheng, L.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52(3), 305–318 (1992)MathSciNetCrossRefMATHGoogle Scholar
  52. 52.
    Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)CrossRefMATHGoogle Scholar
  53. 53.
    Yao, H., Lewis, D.: Spectral preprocessing and calibration techniques. In: D.W., Sun (ed.) Hyperspectral Imaging For Food Quality Analysis and Control, pp. 45–78. (2010)Google Scholar
  54. 54.
    Zadeh, L.A.: Fuzzy logic= Computing with words. IEEE Trans. Fuzzy Syst. 4(2), 103–111 (1996)CrossRefGoogle Scholar
  55. 55.
    Zamperoni, P., Starovoitov, V.: On measures of dissimilarity between arbitrary gray-scale images. Int. J. Shape Model. 2(02–03), 189–213 (1996)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • C. Lopez-Molina
    • 1
  • D. Ayala-Martini
    • 2
  • A. Lopez-Maestresalas
    • 2
  • H. Bustince
    • 1
  1. 1.Dpto. Automatica y ComputacionUniversidad Publica de NavarraPamplonaSpain
  2. 2.Dpto. Proyectos e Ing. RuralUniversidad Publica de NavarraPamplonaSpain

Personalised recommendations