Abstract.
The main contribution of our approach is to apply the Hilbert-Huang Transform (which consists of two parts: (a) Empirical Mode Decomposition (EMD), and (b) the Hilbert spectral analysis) to texture analysis. The EMD is locally adaptive and suitable for analysis of non-linear or non-stationary processes. This one-dimensional decomposition technique extracts a finite number of oscillatory components or “well-behaved” AM-FM functions, called Intrinsic Mode Function (IMF), directly from the data. Firstly, we extend the EMD to 2D-data (i.e. images), the so called bidimensional EMD (BEMD), the process being called 2D-sifting process. The 2D-sifting process is performed in two steps: extrema detection by neighboring window or morphological operators and surface interpolation by radial basis functions or multigrid B-splines. Secondly, we analyse each 2D-IMF obtained by BEMD by studying local properties (amplitude, phase, isotropy and orientation) extracted from the monogenic signal of each one of them. The monogenic signal is a 2D-generalization of the analytic signal, where the Riesz Transform replaces the Hilbert Transform. The performance of this texture analysis method, using the BEMD and Riesz Transform, is demonstrated with both synthetic and natural images.
Similar content being viewed by others
References
Amidror I (2002) Scattered data interpolation methods for electronic imaging systems: a survey. J Elect Imag 11(2):157-176
Barnhill R (1977) Representation and Approximation of Surfaces. In: Rice JR (ed) Mathematical Software III. Academic Press, New York, pp 68-119
Barthels RH, Beatty JC, Barsky BA (1987) An introduction to splines for use in Computer Graphics and Geometric Modeling. Morgan Kaufmann Publishers
Beucher S, Meyer F (1993) The morphological approach to segmentation: The watershed transformation. In: Dougherty ER (ed) Mathematical Morphology in Image Processing. Marcel Dekker, Inc., New York, NY, Chap 12, pp 433-481
Beucher S (2001) Geodesic reconstruction, saddle zones and hierarchical segmentation. Image Anal Stereol 20:137-141
Bovik AC, Clark M, Geisler WS (1990) Multichannel texture analysis using localized spatial filters. IEEE Trans Pattern Anal Mach Intell 12(1):55-73
Brodatz P (1966) Textures: a photographic album for artists and designers. Dover, New York
Buhmann MD (2000) Radial Basis Functions. Acta Numerica, pp 1-38
Bülow T (1999) Hypercomplex Spectral Signal Representations for the Processing and Analysis of Images. Thesis, Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik
Bülow T, Sommer G (2001) Hypercomplex signals: a novel extension of the analytic signal to the multidimensional case. IEEE Trans Signal Process 49(11):2844-2852
Carr JC, FrightWR, Beatson RK (1997) Surface Interpolation with Radial Basis Functions for Medical Imaging. J IEEE Trans on Medical Imag 16(1):96-107
Cesmeli E, Wang DL (1997) Texture segmentation using Gaussian Markov random fields and LEGION. The 1997 IEEE International Conference on Neural Networks, vol 3, Houston, Tex., 9-12 June. Institute of Electrical and Electronics Engineers, New York
Chen CC, DaponteJS, Fox MD (1989) Fractal feature analysis and classification in medical imaging. IEEE Trans Med Imag 8(2):133-142
Daehlen M, Skyth V (1989) Modelling Non-rectangular Surfaces using Box-splines. In: Handscomb DC (ed) Mathematics of Surfaces III, pp 287-300
Daugman J (1988) Complete discrete 2D Gabor transform by neural networks for image analysis and compression. IEEE Trans Acoust Speech Signal Process 36:1169-1179
Deléchelle E, Nunes JC, Lemoine J (2003) Empirical Mode Decomposition synthesis of fractional processes in 1D and 2D dimensions. Image and Vision Computing (submitted)
Duchon J (1977) Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: Schempp W, Zeller K (eds) Constructive Theory of functions of several variables. Springer, Berlin, pp 85-100
Duits R, Florack LMJ, de Graaf J, ter Haar Romeny BM (2004) On the Axioms of scale-space theory. J Imag Vis 20(3):267-298
Dunn D, Higgins WE, Wakeley J (1994) Texture segmentation using 2-D Gabor elementary functions. IEEE Trans Pattern Anal Mach Intell 16(2):130-149
Eom KB (1999) Segmentation of monochrome and color textures using moving average modeling approach. Image Vision Comput 17(3):231-242
Felsberg M, Sommer G (2001) The monogenic signal. IEEE Trans Signal Process 49, December
Felsberg M, Sommer G (2001) Structure multivector for local analysis of images. In: Klette R, Huang T, Gimelfarb G (eds) Multi-image analysis, vol 2032 of LNCS. Proc. Dagstuhl Workshop on Theoretical Foundations of Computer Vision, Springer-Verlag, Berlin, pp 93-104
Felsberg M, Sommer G (2002) The poisson scale-space: A unified approach to phase-based image processing in scale-space. Technical Report Number 0208, Christian-Albrechts-Universität zu Kiel, Institut für Informatik und Praktische Mathematik, August
Felsberg M, Sommer G (2004) The monogenic scale-space: A unifying approach to phase-based image processing in scale-space. J Math Imag Vis 21:5-26
Felsberg M (2002) Low-Level Image Processing with the Structure Multivector. PhD thesis, Institute of Computer Science and Applied Mathematics Christian-Albrechts-University of Kiel, TR no. 0203, available at http://www.informatik.uni-kiel.de/reports/2002/0203.html
Flandrin P, Gonçalvés P (2004) Empirical Mode Decompositions as a Data-Driven Wavelet-Like Expansions. Int J Wavelets, Multires Info Proc (to appear)
Flandrin P, Gonçalvés P, Rilling G (2004) Empirical Mode Decomposition as Filter Bank. IEEE Sig Proc Lett 11(2):112-114
Forsey DR, Bartels RH (1995) Surface Fitting with Hierarchical Splines. ACM Trans Graph 14(2):134-161
Franke R, Nielson GM (1991) Scattered Data Interpolation and Applications: A Tutorial and Survey. In: Hagen H, Roller D (eds) Geometric Modelling: Methods and Their Application. Springer, Berlin, pp 131-160
Glassner A (1995) Principles of Digital Image Synthesis. Morgan Kaufmann, San Francisco, 1995
Gimel’farb G (1999) Image textures and Gibbs random fields. Kluwer Academic, Dordrecht
Granlund GH, Knutsson H (1995) Signal Processing for Computer Vision. Kluwer Academic Publishers, Dordrecht
Hahn SL (1996) Hilbert transforms in signal processing Artech. House, Boston, London
Hahn SL (1992) Multidimensional complex signals with single-orthant spectra Proc. IEEE, vol. 80, pp 1287-1300
Hansen M (1998) Stereosehen - ein verhaltensbasierter Ansatz. PhD thesis, Inst. f. Inf. u. Prakt. Math. der Christian-Albrechts-Universität Kiel
Haralick R (1979) Statistical and structural approaches to texture. IEEE Proc 67(5):786-804
Haralick RM, Shanmugam K, Dinstein I (1973) Textural features for image classification. IEEE Trans Syst Man Cybern 3(6):610-621
Hardy RL (1971) Multiquadratic equations of topography and other irregular surfaces. J Geophys Res 76(8):1905-1915
Hoppe H, DeRose T, Duchamp T, Halstead M, Jin M, McDonald J, Schweitzer J, Stuetzle W (1994) Piecewise Smooth Surface Reconstruction. Computer Graphics (SIGGRAPH ‘94 Conf. Proc.), pp 295-302
Hormigo J, Cristóbal G (1998) High resolution spectral analysis of images using the pseudo-Wigner distribution. IEEE Trans Signal Process 46(6):1757-1763
Hoschek J, Lasser D (1993) Computer Aided Geometric Design. A.K. Peters, Ltd., Wellesley, Mass.
Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen N-C, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis. Proc Roy Soc Lond, Ser. A 454:903-995
Huang NE, Shen Z, Long SR (1999) A new view of nonlinear water waves: the Hilbert spectrum. Annu Rev Fluid Mech 31:417-457
Huang NE, Wu ML, Qu W, Long SR, Shen SSP (2003) Applications of Hilbert-Huang transform to non-stationary financial time series analysis. Appl Stoch Models Business Ind 19:245-268
Jain AK, Farrokhnia F (1991) Unsupervised texture segmentation using Gabor filters. Pattern Recogn 24(12):1167-1186
Jähne B (1997) Digitale Bildverarbeitung. Springer, Berlin, 1997
Julesz B, Bergen JR (1983) Textons, the fundamental elements in preattentive vision and perception of textures. Bell Syst Tech J 62(6):1619-1645
Kovesi P (1999) Image Features From Phase Congruency. Videre: A Journal of Computer Vision Research MIT Press. Volume 1, Number 3, Summer
Kovesi P (1996) Invariant Measures of Image Features from Phase Information. PhD thesis, University of Western Australia
Laine A, Fan J (1993) An adaptive approach for texture segmentation by multi-channel wavelet frames. Technical report TR-93-025, Center for Computer Vision and Visualization, University of Florida
Lee S, Wolberg G, Shin SS (1997) Scattered data interpolation with multilevel B-plines. IEEE Trans Vis Comp Graph 3(3)
Linderhed A (2002) 2D empirical mode decompositions in the spirit of image compression. Wavelet and Independent Component Analysis Applications IX, SPIE Proceedings Vol. 4738, April 2002, pp 1-8
Linderhed A (2004) Image compression based on empirical mode decomposition. Uppsala, March 11-12, Proc. of SSAB 04 Symp. on Image Analysis, pp 110-113
Linderhed A (2004) Variable Sampling of the Empirical Mode Decomposition of Two-Dimensional Signals. Special issue on “Sampling and Frames in Wavelet Theory and Time-Frequency Analysis” of the International Journal of Wavelets, Multiresolution and Information Processing, preprint
Liu X, Wang D (2000) Texture classification using spectral histograms. Electronic report 25 (OSU-CISRC-7/2000-TR17). http://citeseer.nj.nec.com/liu00texture.html. Cited 12 September 2002
Liu Z, Peng S (2004) Estimation of Image Fractal Dimension Based on Empirical Mode Decomposition. Advanced Concepts for Intelligent Vision Systems (ACIVS), Aug. 31-Sept., Brussels, Belgium
Liu Z, Peng S (2004) Texture segmentation using directional Empirical Mode Decomposition. IEEE International Conference on Image Processing (ICIP) October 24-27, Singapore
Livens S, Van de Wouwer G (1997) Wavelets for texture analysis: an overview. Proceedings of the sixth international conference on Image Processing and its Applications (IPA’97), Dublin, Ireland
Mallat S (1996) Wavelets for a vision. Proc IEEE 84(4):604-614
Materka A, Strzelecki M (1998) Texture analysis methods: a review. COST B11 report, Technical University of Lodz
Meyer Y (1993) Wavelets: algorithms and applications. SIAM Press, Philadelphia
Nielson GM (1993) Scattered data modeling. IEEE Computer Graphics and Applications, pp 60-70
Nunes JC (2003) Analyse multiéchelle d’images. Application á l’angiographie rétinienne et á la DMLA. Thesis, Université Paris 12, France
Nunes JC, Bouaoune Y , Deléchelle E, Niang O, Bunel P (2003) Image analysis by bidimensional empirical mode decomposition. Image Vis Comput 21:1019-1026
Nunes JC, Niang O, Bouaoune Y, Deléchelle E, Bunel P (2003) Texture analysis based on the Bidimensional Empirical Mode Decomposition with Gray-Level Co-occurrence models. ISSPA’2003 Seventh International Symposium on Signal Processing and its Applications, (Paris, France), 1-4 July
Nunes JC, Niang O, Bouaoune Y, Deléchelle E, Bunel P (2003) Bidimensional Empirical Mode Decomposition modified for texture analysis. SCIA’2003 13th Scandinavian Conference on Image Analysis, (Göteborg, Sweden), June 29-July 2 2003
Nunes JC, Niang O, Bouaoune Y, Deléchelle E, Bunel P (2003) Décomposition Empirique Multimodale Bidimensionnelle Modifiée pour l’analyse d’images. GRETSI’2003 - 19éme Colloque GRETSI sur le traitement du signal et des images, (Paris, France), 8-11 septembre
Oonincx PJ (2002) Empirical mode decomposition: a new tool for S-wave detection. CWI Reports of Probability, Networks and Algorithms (PNA), PNA-R0203
Osten W (1991) Digitale Verarbeitung und Auswertung von Interferenzbildern. Akademie Verlag, Berlin, 1991
Pentland AP (1984) Fractal-based description of natural scenes. IEEE Trans Pattern Anal Mach Intell 6:661-674
Pickett RM (1970) Visual analyses of texture in the detection and recognition of objects. Lipkin BS, Rosenfeld A (eds) Picture processing and psychopictorics. Academic Press, New York
Pichler O, Teuner A, Hosticka BJ (1996) A comparison of texture feature extraction using adaptive Gabor filtering pyramidal and tree structured wavelet transforms. Pattern Recogn 29(5):733-742
Qin H, Terzopoulos D (1996) D-NURBS: A Physics-Based Framework for Geometric Design. IEEE Transactions on Visualization and Computer Graphics 2(1):85-96
Randen T, Husoy JH (1999) Filtering for texture classification: a comparative study. IEEE Trans Pattern Anal Mach Intell 21:291-310
Reed TR, Wechesler H (1990) Segmentation of textured images and Gestalt organization using spatial/spatial-frequency representations. IEEE Trans Pattern Anal Mach Intell 12:1-12
Reisfeld D (1996) Constrained phase congruency: simultaneous detection of interest points and of their scales. Computer Vision and Pattern Recognition, 1996. Proceedings CVPR ‘96, IEEE Computer Society
Sarkar N, Chaudhuri BB (1992) An efficient approach to estimate fractal dimension of textural images. Pattern Recogn 25(9):1035-1041
Schmitt FJM, Barsky BB, Du W (1986) An Adaptive Subdivision Method for Surface-Fitting from Sampled Data. Computer Graphics (SIGGRAPH ‘86 Conf. Proc.), pp 179-188
Schumaker L (1976) Fitting Surfaces to Scattered Data. In: Chui C, Schumaker L, Lorentz G (eds) Approximation Theory II, Wiley, New York, pp 203-268
http://www.ks.informatik.uni-kiel.de/~visatec
Shepard D (1968) A two dimensional interpolation function for irregularly spaced data. Proceedings of ACM 23rd National Conference, pp 517-524
Sommer G, Bülow T, Pallek D (2000) Riesz transforms for the isotropic estimation of the local phase of moire interferograms. In: Perwass Ch, Sommer G, Krüger N (eds) 22. Symposium für Mustererkennung, DAGM 2000, pp 333-340. Springer, Kiel, 2000
Stark H (1971) An extension of the Hilbert transform product theorem. Proc IEEE 59:1359-1360
Stein E, Weiss G (1971) Introduction to Fourier analysis on euclidian spaces. Princeton University Press, New Jersey, 1971
Tomita F, Tsuji S (1990) Computer analysis of visual textures. Kluwer Academic, Boston.
Tuceryan M, Jain AK (1998) Texture analysis. In: Chen CH, Pau LF, Wang PSP (eds) The handbook of pattern recognition and computer vision, 2nd edn. World Scientific Publishing, Singapore
Unser M (1999) Splines: a perfect fit for signal and image processing. IEEE Signal Processing Magazine (11):22-38
Unser M (1995) Texture classification and segmentation using wavelet frames. IEEE Trans Image Process 4(11):1549-1560
Unser M, Aldroubi A, Eden M (1993) B-Spline Signal Processing: Part I - Theory. IEEE Trans Signal Process 41(2):821-833
Unser M, Aldroubi A, Eden M (1993) B-Spline Signal Processing: Part II-Efficient Design and Applications. IEEE Trans Signal Process 41(2):821-833
Vincent L (1993) Morphological grayscale reconstruction in image analysis: applications and efficient algorithms. Technical report 91-16, Harvard Robotics Laboratory, November 1991. IEEE Trans Image Process 2(2):176-201
Wickerhauser MV (1994) Adapted wavelet analysis from theory to software. IEEE Press, Los Alamitos
Yang Z, Qi D, Yang L (2004) Signal Period Analysis Based on Hilbert-Huang Transform and Its Application to Texture Analysis (Preprint). http://www.ims.nus.edu.sg/preprints/2004-38.pdf
Zhang W, Tang Z, Li J (1998) Adaptive Hierarchical B-Spline Surface Approximation of Large-Scale Scattered Data. In Proc. Pacific Graphics ‘98, pp 8-16
Zhou J, Patrikalakis NM, Tuohy ST, Ye X (1997) Scattered Data Fitting with Simplex Splines in Two and Three Dimensional Spaces. The Vis Comput 13(7):295-315
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 6 November 2002, Accepted: 15 November 2004, Published online: 25 February 2005
Rights and permissions
About this article
Cite this article
Nunes, J.C., Guyot, S. & Deléchelle, E. Texture analysis based on local analysis of the Bidimensional Empirical Mode Decomposition. Machine Vision and Applications 16, 177–188 (2005). https://doi.org/10.1007/s00138-004-0170-5
Issue Date:
DOI: https://doi.org/10.1007/s00138-004-0170-5