Multiscale Texture Extraction with Hierarchical (BV,G p ,L 2) Decomposition
Tóm tắt
In this paper, we first present a hierarchical (BV,G
p
,L
2) variational decomposition model and then use it to achieve multiscale texture extraction which offers a hierarchical, separated representation of image texture in different scales. The starting point is the use of the variational (BV,G
p
,L
2) decomposition; a given image f∈L
2(Ω) is decomposed into a sum of u
0+v
0+r
0, where (u
0,v
0)∈(BV(Ω),G
p
(Ω)) is the minimizer of an energy functional E(f,λ
0;u,v) and r
0 is the residual (i.e. r
0=f−u
0−v
0). In this decomposition, v
0 represents the fixed scale texture of f, which is measured by the parameter λ
0. To achieve a multiscale representation, we proceed to capture essential textures of f which have been absorbed by the residuals. Such a goal can be achieved by iterating a refinement decomposition to the residual of the previous step, i.e. r
i
=u
i+1+v
i+1+r
i+1, where (u
i+1,v
i+1) is the minimizer of E(r
i
,λ
0/2
i+1;u,v). In this manner, we can obtain a hierarchical representation of f. In addition, we discuss some theoretical properties of the hierarchical (BV,G
p
,L
2) decomposition and give its numerical implementation. Finally, we apply this hierarchical decomposition to the multiscale texture extraction. The performance of this method is demonstrated with both synthetic and real images.
Tài liệu tham khảo
Abbadeni, N.: Texture representation and retrieval using the causal autoregressive model. J. Vis. Commun. Image Represent. 21(7), 651–664 (2010)
Arunachalam, N., Ramamoorthy, B.: Fourier transform based texture measures for grinding wheel condition monitoring using machine vision. Int. J. Manuf. Technol. Manag. 21, 112–121 (2010)
Ashish, B.K., Kumar, A., Padhy, P.K.: Satellite image processing using discrete cosine transform and singular value decomposition. Adv. Digit. Image Process. Inf. Sci. 205(1), 277–290 (2011)
Aubert, G., Aujol, J.: Modeling very oscillating signals. Application to image processing. Appl. Math. Optim. 51, 163–182 (2003)
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing. Springer, New York (2001)
Aujol, J., Aubert, G., Blanc-Féraud, L., Chambolle, A.: Image decomposition application to SAR images. Scale Space Methods Comput. Vis. 2695, 297–312 (2003)
Aujol, J., Aubert, G., Blanc-Féraud, L., Chambolle, A.: Image decomposition into a bounded variation component and an oscillating component. J. Math. Imaging Vis. 22(1), 71–88 (2005)
Athavale, P., Tadmor, E.: Integro-differential equations based on (BV,L 1) image decomposition. SIAM J. Imaging Sci. 4(1), 300–312 (2011)
Bovik, A.C., Clark, M., Geisler, W.S.: Multichannel texture analysis using localized spatial filters. IEEE Trans. Pattern Anal. Mach. Intell. 12(1), 55–73 (1990)
Buades, A., Le, T., Morel, J., Vese, L.: Fast cartoon + texture image filters. IEEE Trans. Image Process. 19, 1978–1986 (2010)
Cesmeli, E., Wang, D.L.: Texture segmentation using Gaussian Markov random fields and neural oscillator networks. IEEE Trans. Neural Netw. 12(2), 394–404 (2001)
Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20, 89–97 (2004)
Chan, T., Shen, J., Vese, L.: Variational PDE models in image processing. Not. Am. Math. Soc. 50, 14–26 (2003)
Chan, T., Esedoglua, S., Park, F.: Image decomposition combining staircase reduction and texture extraction. J. Vis. Commun. Image Represent. 18, 464–486 (2007)
Chan, T., Esedoglua, S., Park, F.: Fourth order dual method for staircase reduction in texture extraction and image restoration problems. In: 17th IEEE International Conference on Image Processing (ICIP), 2010, vol. 26–29, pp. 4137–4140 (2010)
Chen, C.C., Daponte, J.S., Fox, M.D.: Fractal feature analysis and classification in medical imaging. IEEE Trans. Med. Imaging 8(2), 133–142 (1989)
Coburn, C.A., Roberts, A.C.B.: A multiscale texture analysis procedure for improved forest stand classification. Int. J. Remote Sens. 25(20), 4287–4308 (2004)
Daugman, J.: Complete discrete 2D Gabor transform by neural networks for image analysis and compression. IEEE Trans. Acoust. Speech Signal Process. 36, 1169–1179 (1988)
Fauzi, M.F.A., Lewis, P.H.: A multiscale approach to texture-based image retrieval. PAA Pattern Anal. Appl. 11, 141–157 (2008)
Gimelfarb, G.: Image Textures and Gibbs Random Fields. Kluwer Academic, Dordrecht (1999)
Haralick, R.M.: Statistical and structural approaches to texture. Proc. IEEE 67(5), 786–804 (1979)
Haralick, R.M., Shanmugam, K., Dinstein, I.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973)
Hay, G.J., Niemann, K.O.: Visualizing 3-D texture: A three-dimensional structural approach to model forest texture. Can. J. Remote Sens. 20, 90–101 (1994)
Hormigo, J., Cristobal, G.: High resolution spectral analysis of images using the pseudo-Wigner distribution. IEEE Trans. Signal Process. 46(6), 1757–1763 (1998)
Jain, A.K., Farrokhnia, F.: Unsupervised texture segmentation using Gabor filters. Pattern Recognit. 24(12), 1167–1186 (1991)
Julesz, B., Bergen, J.R.: Textons, the fundamental elements in preattentive vision and perception of textures. Bell Syst. Tech. J. 62(6), 1619–1645 (1983)
Le, T., Vese, L.: Image decomposition using total variation and div(BMO). Multiscale Model. Simul. 4, 390–423 (2005)
Liang, K.H., Tjahjadi, T.: Adaptive scale fixing for multiscale texture segmentation. IEEE Trans. Image Process. 15(1), 249–256 (2006)
Liu, X., Wang, D.: Texture classification using spectral histograms. IEEE Trans. Image Process. 12(6), 661–670 (2003)
Mallat, S.: Wavelets for a vision. Proc. IEEE 84(4), 604–614 (1996)
Mao, J.C., Jain, A.K.: Texture classification and segmentation using multi-resolution simultaneous autoregressive models. Pattern Recognit. 25(2), 173–188 (1992)
Materka, A., Strzelecki, M.: Texture analysis methods—a review. COST B11 report, Technical University of Lodz (1998)
Meyer, Y.: Wavelets: Algorithms and Applications. SIAM, Philadelphia (1993)
Meyer, Y.: Oscillating patterns in image processing and nonlinear evolution equations. In: Univ. Lecture Ser., vol. 22. AMS, Providence (2001)
Michael, D.: Wavelet features for color image classification. In: Annual Conference Imaging and Geospatial Information Society, Orlando (2000)
Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program., Ser. A 103, 127–152 (2005)
Nunes, J.C., Guyot, S., Delechelle, E.: Texture analysis based on local analysis of the bidimensional empirical mode decomposition. Mach. Vis. Appl. 16, 177–188 (2005)
Osher, S., Solé, A., Vese, L.: Image decomposition and restoration using total variation minimization and the H −1 norm. Multiscale Model. Simul. 1(3), 349–370 (2003)
Pentland, A.P.: Fractal-based description of natural scenes. IEEE Trans. Pattern Anal. Mach. Intell. 6, 661–674 (1984)
Pichler, O., Teuner, A., Hosticka, B.J.: A comparison of texture feature extraction using adaptive Gabor filtering pyramidal and tree structured wavelet transforms. Pattern Recognit. 29(5), 733–742 (1996)
Pu, Y.F., Zhou, J.L.: A novel approach for multi-scale texture segmentation based on fractional differential. Int. J. Comput. Math. 88(1), 58–78 (2011)
Reed, T.R., Wechesler, H.: Segmentation of textured images and Gestalt organization using spatial/spatial-frequency representations. IEEE Trans. Pattern Anal. Mach. Intell. 12, 1–12 (1990)
Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Sarkar, N., Chaudhuri, B.B.: An efficient approach to estimate fractal dimension of textural images. Pattern Recognit. 25(9), 1035–1041 (1992)
Shen, J.: Inpainting and the fundamental problem of image processing. SIAM News 36 (2003)
Starck, J., Elad, M., Donoho, D.: Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans. Image Process. 14, 1570–1582 (2005)
Tadmor, E., Athavale, P.: Multiscale image representation using integro-differential equations. Inverse Probl. Imaging 3(4), 693–710 (2009)
Tadmor, E., Nezzar, S., Vese, L.: A multiscale image representation using hierarchical (BV;L 2) decompositions. Multiscale Model. Simul. 2(4), 554–579 (2003)
Tadmor, E., Nezzar, S., Vese, L.: Multiscale hierarchical decomposition of images with applications to deblurring, denoising and segmentation. Commun. Math. Sci. 6(2), 281–307 (2008)
Tuceryan, M., Jain, A.K.: Texture analysis. In: Handbook of Pattern Recognition and Computer Vision, pp. 235–276 (1993)
Vese, L., Osher, S.: Modeling textures with total variation minimization and oscillating patterns in image processing. J. Sci. Comput. 19, 553–572 (2003)
Vese, L., Osher, S.: Image denoising and decomposition with total variation minimization and oscillatory functions. J. Math. Imaging Vis. 20, 7–18 (2004)
Weiss, P., Aubert, G., Blanc-Féraud, L.: Efficient schemes for total variation minimization under constraints in image processing. SIAM J. Sci. Comput. 31(3), 2047–2080 (2009)