A TV flow based local scale estimate and its application to texture discrimination

Journal of Visual Communication and Image Representation

Volumn 17, Issue 5, 2006, Pages 1053-1073

  Brox, Thomas ^a   Weickert, Joachim ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

Nonlinear diffusion; Scale; Segmentation; Texture

Indexed keywords

ESTIMATION; INFORMATION DISSEMINATION; OPTICAL FILTERS; QUALITY CONTROL; SIGNAL PROCESSING; TEXTURES;

GABOR FILTERS; LOCAL SCALE ESTIMATE; NONLINEAR DIFFUSION; TEXTURE DISCRIMINATION; TEXTURE SEGMENTATION;

MECHANICAL VARIABLES CONTROL;

EID: 33748605303     PISSN: 10473203     EISSN: 10959076     Source Type: Journal    
DOI: 10.1016/j.jvcir.2005.06.001     Document Type: Article

References (52)

1. Julesz B. Textons, the elements of texture perception, and their interactions. Nature 290 (1981) 91-97
2. Julesz B. Texton gradients: the texton theory revisited. Biol. Cybernet. 54 (1986) 245-251
3. S.-C. Zhu, C. Guo, Y. Wu, W. Wang, What are textons? in: A. Heyden, G. Sparr, M. Nielsen, P. Johansen (Eds.), Computer Vision-ECCV 2002, vol. 2353 of Lecture Notes in Computer Science, Springer, Copenhagen, Denmark, 2002, pp. 793-807.
4. Gabor D. Theory of communication. J. Institut. Electr. Eng. 93 (1946) 429-457
5. Marcelja S. Mathematical description of the response of simple cortical cells. J. Opt. Soc. Am. 70 (1980) 1297-1300
6. Daugman J. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. J. Opt. Soc. Am. A 2 7 (1985) 1160-1169
7. Field D.J. Relation between the statistics of natural images and the response properties of cortical cells. J. Opt. Soc. Am. A 4 (1987) 2379-2394
8. Bovik A.C., Clark M., and Geisler W.S. Multichannel texture analysis using localized spatial filters. IEEE Trans. Pattern Anal. Mach. Intell. 12 1 (1990) 55-73
9. Dunn D., Higgins W.E., and Wakeley J. Texture segmentation using 2-D Gabor elementary functions. IEEE Trans. Pattern Anal. Mach. Intell. 16 2 (1994) 130-149
10. C. Sagiv, N.A. Sochen, Y.Y. Zeevi, Geodesic active contours applied to texture feature space, in: M. Kerckhove (Ed.), Scale-Space and Morphology in Computer Vision, vol. 2106 of Lecture Notes in Computer Science, Springer, Berlin, 2001, pp. 344-352.
11. Paragios N., and Deriche R. Geodesic active regions and level set methods for supervised texture segmentation. Internat. J. Comput. Vis. 46 3 (2002) 223-247
12. W. Förstner, E. Gülch, A fast operator for detection and precise location of distinct points, corners and centres of circular features, in: Proc. ISPRS Intercommission Conference on Fast Processing of Photogrammetric Data, Interlaken, Switzerland, 1987, pp. 281-305.
13. Rao A.R., and Schunck B.G. Computing oriented texture fields. CVGIP: Graph. Models Image Process. 53 (1991) 157-185
14. Bigün J., Granlund G.H., and Wiklund J. Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Trans. Pattern Anal. Mach. Intell. 13 8 (1991) 775-790
15. Jeong H., and Kim I. Adaptive determination of filter scales for edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 14 5 (1992) 579-585
16. Lindeberg T. Scale-Space Theory in Computer Vision (1994), Kluwer, Boston
17. Lindeberg T. Principles for automatic scale selection. In: Jähne B., Haußecker H., and Geißler P. (Eds). Handbook on Computer Vision and Applications vol. 2 (1999), Academic Press, Boston, USA 239-274
18. Elder J.H., and Zucker S.W. Local scale control for edge detection and blur estimation. IEEE Trans. Pattern Anal. Mach. Intell. 20 7 (1998) 699-716
19. J. Sporring, C.I. Colios, P.E. Trahanias, Generalized scale-selection, Tech. Rep. 264, Foundation for Research and Technology-Hellas, Crete, Greece (Dec. 1999).
20. G. Gómez, J.L. Marroquín, L.E. Sucar, Probabilistic estimation of local scale, in: Proc. International Conference on Pattern Recognition, vol. 3, Barcelona, Spain, 2000, pp. 798-801.
21. M. Galun, E. Sharon, R. Basri, A. Brandt, Texture segmentation by multiscale aggregation of filter responses and shape elements, in: Proc. IEEE International Conference on Computer Vision, Nice, France, 2003, pp. 716-723.
22. Andreu F., Ballester C., Caselles V., and Mazón J.M. Minimizing total variation flow. Diff. Integral Equat. 14 3 (2001) 321-360
23. Rudin L.I., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Phys. D 60 (1992) 259-268
24. Acar R., and Vogel C.R. Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems 10 (1994) 1217-1229
25. T. Brox, M. Welk, G. Steidl, J. Weickert, Equivalence results for TV diffusion and TV regularisation, in: L.D. Griffin, M. Lillholm (Eds.), Scale-Space Methods in Computer Vision, vol. 2695 of Lecture Notes in Computer Science, Springer, Berlin, 2003, pp. 86-100.
26. Steidl G., Weickert J., Brox T., Mrázek P., and Welk M. On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs. SIAM J. Numer. Anal. 42 2 (2004) 686-713
27. D.M. Strong, J.-F. Aujol, T.F. Chan, Scale recognition, regularization parameter selection, and Meyer's G norm in total variation regularization, Tech. Rep. CAM-05-02, Department of Mathematics, University of California at Los Angeles, CA, USA (Jan. 2005).
28. Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, vol. 22 of University Lecture Series, AMS, Providence, 2001.
29. T. Brox, J. Weickert, A TV flow based local scale measure for texture discrimination, in: T. Pajdla, J. Matas (Eds.), Computer Vision-Proc. 8th European Conference on Computer Vision, vol. 3022 of Lecture Notes in Computer Science, Springer, Prague, Czech Republic, 2004.
30. Strong D.M., and Chan T.F. Edge-preserving and scale-dependent properties of total variation regularization. Inverse Problems 19 (2003) 165-187
31. Mammen E., and van de Geer S. Locally adaptive regression splines. Ann. Stat. 25 1 (1997) 387-413
32. A.M. Yip, F. Park, Solution dynamics, causality, and critical behaviour of the regularization parameter in total variation denoising problems, Tech. Rep. CAM-03-59, Department of Mathematics, University of California at Los Angeles, CA, USA (Oct. 2003).
33. Pollak I., Willsky A.S., and Huang Y. Nonlinear evolution equations as fast and exact solvers of estimation problems. IEEE Trans. Signal Process. 53 2 (2005) 484-498
34. N. J. Diff. Equat. 184 2 (2002) 475-525
35. Andreu F., Caselles V., Diaz J.I., and Mazón J.M. Qualitative properties of the total variation flow. J. Funct. Anal. 188 2 (2002) 516-547
36. Weickert J., ter Haar Romeny B.M., and Viergever M.A. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans. Image Process. 7 3 (1998) 398-410
37. Tai X.-C. Global extrapolation with a parallel splitting method. Numer. Algorithms 3 4 (1992) 427-440
38. Koepfler G., Lopez C., and Morel J.M. A multiscale algorithm for image segmentation by variational method. SIAM J. Numer. Anal. 31 1 (1994) 282-299
39. D. Mumford, J. Shah, Boundary detection by minimizing functionals, I, in: Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Computer Society Press, San Francisco, CA, 1985, pp. 22-26.
40. Morel J.-M., and Solimini S. Variational Methods in Image Segmentation (1994), Birkhäuser, Basel
41. Malik J., Belongie S., Leung T., and Shi J. Contour and texture analysis for image segmentation. Internat. J. Comput. Vis. 43 1 (2001) 7-27
42. J. Weickert, T. Brox, Diffusion and regularization of vector- and matrix-valued images, in: M.Z. Nashed, O. Scherzer (Eds.), Inverse Problems, Image Analysis, and Medical Imaging, vol. 313 of Contemporary Mathematics, AMS, Providence, 2002, pp. 251-268.
43. T. Brox, J. Weickert, B. Burgeth, P. Mrázek, Nonlinear structure tensors, Tech. Rep. 113, Dept. of Mathematics, Saarland University, Saarbrücken Germany (Oct. 2004).
44. Rousson M., Brox T., and Deriche R. Active unsupervised texture segmentation on a diffusion based feature space. Proc. 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2003), IEEE Computer Society Press, Madison, WI 99-704
45. R. van den Boomgaard, J. van de Weijer, Robust estimation of orientation for texture analysis, in: S. karthik (Ed.), Proc. Texture 2002, 2nd International Workshop on Texture Analysis and Synthesis, Copenhagen, 2002.
46. D. Tschumperlé, R. Deriche, Diffusion tensor regularization with constraints preservation, in: Proc. 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, IEEE Computer Society Press, Kauai, HI, 2001, pp. 948-953.
47. Gerig G., Kübler O., Kikinis R., and Jolesz F.A. Nonlinear anisotropic filtering of MRI data. IEEE Trans. Med. Imag. 11 (1992) 221-232
48. Unser M. Texture classification and segmentation using wavelet frames. IEEE Trans. Image Process. 4 11 (1995) 1549-1560
49. Portilla J., Navarro R., Nestares O., and Tabernero A. Texture synthesis-by-analysis based on a multiscale early-vision model. Opt. Eng. 35 (1996) 2403-2417
50. Chan T., Sandberg B., and Vese L. Active contours without edges for vector-valued images. J. Vis. Commun. Image Represent. 11 (2000) 130-141
51. Paragios N., and Deriche R. Geodesic active regions: a new paradigm to deal with frame partition problems in computer vision. J. Vis. Commun. Image Represent. 13 1/2 (2002) 249-268
52. T. Brox, M. Rousson, R. Deriche, J. Weickert, Unsupervised segmentation incorporating colour, texture, and motion, in: N. Petkov, M.A. Westenberg (Eds.), Computer Analysis of Images and Patterns, vol. 2756 of Lecture Notes in Computer Science, Springer, Berlin, 2003, pp. 353-360.