The monogenic scale-space: A unifying approach to phase-based image processing in scale-space

Journal of Mathematical Imaging and Vision

Volumn 21, Issue 1, 2004, Pages 5-26

  Felsberg, Michael ^a   Sommer, Gerald ^b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b UNIVERSITY OF KIEL   (Germany)

Author keywords

Analytic signal; Local phase; Monogenic signal; Poisson kernel; Riesz transform; Scale space

Indexed keywords

ANALYTIC SIGNAL; LOCAL PHASE; MONOGENIC SIGNAL; POISSON KERNEL; RIESZ TRANSFORM; SCALE-SPACE;

ATTENUATION; EDGE DETECTION; FEATURE EXTRACTION; IMAGE RECONSTRUCTION; MATHEMATICAL TRANSFORMATIONS; VECTORS;

IMAGE ANALYSIS;

EID: 3543071716     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JMIV.0000026554.79537.35     Document Type: Article

References (52)

1. J. Babaud, A.P. Witkin, M. Baudin, and R.O. Duda, "Uniqueness of the Gaussian kernel for scale-space filtering," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 8, No. 1, pp. 26-33, 1986.
2. J. Behar, M. Porat, and Y.Y. Zeevi. "Image reconstruction from localized phase," IEEE Transactions on Signal Processing, Vol. 40, No. 4, pp. 736-743, 1992.
3. R.N. Bracewell, The Fourier Transform and its Applications, Mcgraw Hill, 1986.
4. R.N. Bracewell, Two-Dimensional Imaging, Prentice Hall Signal Processing Series. Prentice Hall, Englewood Cliffs, 1995.
5. F. Brackx, R. Delanghe, and F. Sommen, Clifford Analysis, Pitman: Boston, 1982.
6. I. Bronstein, K. Semendjajew, G. Musiol, and H. Mühlig, Taschenbuch der Mathematik, Verlag Harri Deutsch, Frankfurt, 1993.
7. K. Burg, H. Haf, and F. Wille, Höhere Mathematik für Ingenieure, Band V Funktionalanalysis und Partielle Differential-gleichungen, Teubner Stuttgart, 1993.
8. K. Burg, H. Haf, and F. Wille, Höhere Mathematik für Ingenieure, Band IV Vektoranalysis und Funktionentheorie, Teubner Stuttgart, 1994.
9. P.J. Burt and E.H. Adelson, "The Laplacian pyramid as a compact image code," IEEE Trans. Communications, Vol. 31, No. 4, pp. 532-540, 1983.
10. F. Carte, P.-L. Lions, J.-M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Analysis, Vol. 32, pp. 1895-1909, 1992.
11. R. Duits, L.M.J. Florack, J. de Graaf, and B.M. ter Haar Romeny, "On the axioms of scale space theory," Journal of Mathematical Imaging and Vision, 2002 (accepted).
12. R. Duits, L.M.J. Florack, B. M. ter Haar Romeny, and J. de Graaf, "Scale-space axioms critically revisited," in Signal and Image Processing, N. Younan (Ed.), IASTED, ACTA Press, Kauai, August 2002, pp. 304-309.
13. M. Evans, N. Hastings, and J.B. Peacock, Statistical Distributions, 3rd. ed., Wiley-Interscience, 2000.
14. M. Felsberg, "Disparity from monogenic phase," in 24. DAGM Symposium Mustererkennung, Zurich, L.V. Gool (Ed.), Vol. 2449 of Lecture Notes in Computer Science, Springer, Heidelberg, 2002, pp. 248-256.
15. M. Felsberg, Low-Level Image Processing with the Structure Multivector, Ph.D. thesis, Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel, 2002. TR no. 0203, available at http://www.informatik.unikiel.de/reports/2002/0203.html.
16. M. Felsberg, R. Duits, and L. Florack, "The monogenic scale space on a bounded domain and its applications," in Scale Space Conference, 2003 (accepted).
17. M. Felsberg and G. Sommer, "A new extension of linear signal processing for estimating local properties and detecting features," in 22. DAGM Symposium Mustererkennung, G. Sommer, N. Krüger, and C. Perwass (Eds.), Springer, Heidelberg, Kiel, 2000, pp. 195-202.
18. M. Felsberg and G. Sommer, "The monogenic signal," IEEE Transactions on Signal Processing, Vol. 49, No. 12, pp. 3136-3144, 2001.
19. M. Felsberg and G. Sommer, "Scale adaptive filtering derived from the Laplace equation," in 23. DACM Symposium Mustererkeimung, B. Radig and S. Florczyk (Eds.), Vol. 2191 of Lecture Notes in Computer Science, Springer, Heidelberg, München, 2001, pp. 124-131.
20. M. Felsberg and G. Sommer, "The Poisson scale-space: A unified approach to phase-based image processing in scale-space," Tech. Rep. LiTH-ISY-R-2453, Dept. EE, Linköping University, SE-581 83 Linköping, Sweden, 2002.
21. M. Felsberg and G. Sommer, "The structure multivector," in Applied Geometrical Algebras in Computer Science and Engineering, Birkhäuser, Boston, 2002, pp. 437-448.
22. L. Florack, Image Structure, Vol. 10 of Computational Imaging and Vision, Kluwer Academic Publishers, 1997.
23. L. Florack and A. Kuijper, "The topological structure of scale-space images," Journal of Mathematical Imaging and Vision, Vol. 12, No. 1, pp. 65-79, 2000.
24. G.H. Granlund, "In search of a general picture processing operator," Computer Graphics and Image Processing, Vol. 8, pp. 155-173, 1978.
25. G.H. Granlund and H. Knutsson, Signal Processing for Computer Vision, Kluwer Academic Publishers: Dordrecht, 1995.
26. S.L. Hahn, Hilbert Transforms in Signal Processing, Artech House: Boston, London, 1996.
27. D. Hestenes, "Multivector calculus," J. Math. Anal. and Appl., Vol. 24, No. 2, pp. 313-325, 1968.
28. R.A. Hummel, "Representations based on zero-crossings in scale space," in Proc. IEEE Comp. Soc. Conf. Computer Vision and Pattern Recognition, Miami Beach, 1986, pp. 204-209.
29. T. Iijima, "Basic theory of pattern observation," in Papers of Technical Group on Automata and Automatic Control, IECE, Japan, December 1959.
30. T. Iijima, "Basic theory on normalization of pattern (In case of a typical one-dimensional pattern)," Bulletin of the Electrotechnical Laboratory, Vol. 26, pp. 368-388, 1962.
31. T. Iijima, "Observation theory of two-dimensional visual patterns," in Papers of Technical Group on Automata and Automatic Control, IECE, Japan, October 1962.
32. B. Jähne, Digitale Bildverarbeitung, Springer: Berlin, 1997.
33. J.J. Koenderink, "The structure of images," Biological Cybernetics, Vol. 50, pp. 363-370, 1984.
34. P. Kovesi, "Image features from phase information," Videre: Journal of Computer Vision Research, Vol. 1, No. 3, 1999.
35. S.G. Krantz, Handbook of Complex Variables, Birkhäuser: Boston, 1999.
36. G. Krieger and C. Zetzsche, "Nonlinear image operators for the evaluation of local intrinsic dimensionality," IEEE Transactions on Image Processing, Vol. 5, No. 6, pp. 1026-1041, 1996.
37. T. Lindeberg, Scale-Space Theory in Computer Vision, The Kluwer International Series in Engineering and Computer Science. Kluwer Academic Publishers: Boston, 1994.
38. T. Lindeberg, "Linear spatio-temporal scale-space," in ScaleSpace Theory in Compuler Vision, Vol. 1252 of Lecture Notes in Computer Science, Springer: Utrecht, Netherlands, 1997.
39. T. Lindeberg, On the Axiomatic Foundations of Linear Scale-Space: Combining Semi-Croup Structure with Causality vs. Scale Invariance, Ch. 6, Kluwer Academic, 1997.
40. A.Papoulis, The Fourier Integralandits Applications, McGraw-Hill: New York, 1962.
41. A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 1965.
42. E.J. Pauwels, L.J. Van Gool, P. Hddelaers, and T. Moons, "An extended class of scale-invariant and recursive scale space filters," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 7, pp. 691-701, 1995.
43. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 12, No. 7, pp. 629-639, 1990.
44. D. Reisfeld, "The constrained phase congruency feature detector: Simultaneous localization, classification and scale determination," Pattern Recognition Letters, Vol. 17, pp. 1161-1169, 1996.
45. J.L. Schiff, The Laplace Transform, Undergraduate Texts in Mathematics. Springer: New York, 1999.
46. N. Sochen, R. Kimmel, and R. Malladi, "A geometrical framework for low level vision," IEEE Trans. on Image Processing, Special Issue on PDE Based Image Processing, Vol. 7, No. 3, pp. 310-318, 1998.
47. E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press: New Jersey, 1971.
48. J. Weickert, "Anisotropic siffusion in image processing," Ph.D. thesis, Faculty of Mathematics, University of Kaiserslautern, 1996.
49. J. Weickert, "A review of nonlinear diffusion filtering," in Scale-Space Theory in Computer Vision, B. ter Haar Romeny, L. Florack, J. Koenderink, and M. Viergever (Eds.), Vol. 1252 of LNCS, Springer: Berlin, 1997, pp. 260-271.
50. J. Weickert, S. Ishikawa, and A. Imiya, "Scale-space has first been proposed in Japan," Mathematical Imaging and Vision, Vol. 10, pp. 237-252, 1999.
51. A.P. Witkin, "Scale-space filtering," in Proc. 8th Int. Joint Conf. An. Intell., 1983, pp. 1019-1022.
52. A.L. Yuille and T. Poggio, "Scaling theorems for zerocrossings," IEEE Trans. Pattern Analysis and Machine Intell., Vol. 8, pp. 15-25, 1986.