Skip to main content

Koordinatentransformationen und geometrische Operatoren

  • Chapter
Handbuch der Operatoren für die Bildbearbeitung
  • 125 Accesses

Zusammenfassung

Bei verschiedenen Bildoperatoren besteht das Ziel weniger in einer Veränderung der Bildwerte, sondern vordergründig in einer bestimmten geometrischen Abbildung eines gegebenen Bildes oder Bildausschnittes in die Bildebene. Diese Abbildung kann z.B. eine Verkleinerung, eine Verschiebung (Translation), eine Drehung (Rotation), eine Spiegelung (Inversion), eine geometrische Anpassung zweier Bilder (etwa um die Deckungsgleichheit der dargestellten Bildstrukturen zu erreichen) oder eine Aneinanderfügung benachbarter Bildausschnitte sein. Dabei wird i.a. auch eine gewisse Korrektur oder Angleichung von Bildwerten erforderlich sein. Das Wesen dieser geometrischen Operatoren ist jedoch durch (i.a. relativ einfache) Koordinatentransformationen K ausgezeichnet. Ein Pixel (x, y, f(x, y)) wird gemäß der gewählten Koordinatentransformation auf ein Pixel (K(x, y) f(x, y)) abgebildet, d.h. der Bildpunkt K(x, y) = (r, s) ist die neue Position des (alten) Bildwertes f(x, y).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. Ahrens, J.H., Dieter, U.: Extension of Forsythe’s method for random sampling from the normal distribution. Mathematics of Computation, Vol. 27, Oct. 1973, S. 927–937.

    MathSciNet  MATH  Google Scholar 

  2. Arce, G.R., McLoughlin, M.P.: Theoretical analysis of the max/median filter, IEEE Trans., Vol. ASSP-35, Jan. 1987, S. 60–69.

    Google Scholar 

  3. Arcelli, C., Cordelia, L., Levialdi, S.: Parallel thinning of binary pictures, Electronic Letters, Vol. 11, 1975, N. 7, S. 148–149.

    Article  Google Scholar 

  4. Arcelli, C., Cordelia, L., Levialdi, S.: More about a thinning algorithm, Electronic Letters, Vol. 16, 1980, N. 2, S. 51–53.

    Article  Google Scholar 

  5. Arcelli, C., Sanniti di Baja, G.: A width-independent fast thinning algorithm, IEEE Trans., Vol. PAMI-7, July 1985, S. 463–474.

    Google Scholar 

  6. Bednar, J.B., Watt, T.L.: Alpha-trimmed means and their relationship to median filters, IEEE Trans, Vol. ASSP-32, Feb. 1984, S. 145–153.

    Google Scholar 

  7. Bolon, P., Fruttaz, J.L.: Adaptive order filters: application to edge enhancement of noisy images, in: Lagunas, M.A. et al. (Hrsg.): Signal Processing V: Theories and Applications, Elsevier, Amsterdam, 1990, S. 817–820.

    Google Scholar 

  8. Bolon, P., Raji, A., Lambert, P., Mouhoub, M.: Symmetrical recursive median filters application to noise reduction and edge detection, in: Lagunas, M.A. et al. (Hrsg.), Signal Processing V: Theories and Applications, Elsevier, Amsterdam, 1990, S. 813–816.

    Google Scholar 

  9. Boukharouba, S., Rebordao, J.M., Wendel, P.L.: An amplitude segmentation method based on the distribution function of an image. Computer Vision, Graphics and Image Processing, Vol. 29, 1985, S. 47–59.

    Article  Google Scholar 

  10. Bourbakis, N.G., A parallel-symmetric thinning algorithm, Pattern Recognition, Vol. 22, 1989, N. 4, S. 387–396.

    Article  Google Scholar 

  11. Burt, P.J., Adelson, E.H.: The laplacian pyramid as a compact image code, IEEE Trans., Vol. COM-31, April 1983, S. 532–540.

    Article  Google Scholar 

  12. Cai, Y.L., Chen, C.S.: An edge preserving smoothing filter based on the robust estimate, Proc. 8th ICPR, Paris, 1986, S. 206–208.

    Google Scholar 

  13. Campbell, T.G., du Buf, J.M.: A quantitative comparison of median-based filters, in: Kunt, M. (Hrsg.), Proc. SPIE Conf. on Visual Communications and Image Processing, Lausanne, 1990, S. 176–187.

    Google Scholar 

  14. Chavez, P.: Simple high-speed digital image processing to remove quasi-coherent noise patterns, U.S. Geological Survey Computer Center Division, interner Bericht.

    Google Scholar 

  15. Chen, J.S., Huertas, A., Medioni, G.: Fast convolution with Laplacian-of-Gaussian masks, IEEE Trans., Vol. PAMI-9, July 1987, S. 584–590.

    Google Scholar 

  16. Chin, R.T., Wan, H.K., Stover, D.L., Iverson, R.D.: A one-pass thinning algorithm and its parallel implementation, Computer Vision, Graphics, and Image Processing, Vol. 40, 1987, S. 30–40.

    Article  Google Scholar 

  17. Davis, L.S.: A survey of edge detection techniques, Computer Graphics and Image Processing, Vol. 4, 1975, S. 248–270.

    Article  Google Scholar 

  18. Delia Giustina, D.: Progetto nel dominio della frequenza di filtri LoG per Vestrazione dei contorni, Diplomarbeit Nr. 197/90, Dipartimento di Elettro-nica e Informatica, Università di Padova, 1990.

    Google Scholar 

  19. Dillencourt, M.B., Samet, H.: Connected-component labeling of binary images, Technical Report CS-TR-2303, University of Maryland, 1989.

    Google Scholar 

  20. Eckhardt, U., Maderlechner, G.: Parallel reduction of digital sets, Siemens Forsch.- u. Entwickl.-Berichte, Bd. 17, 1988, N. 4, S. 184–189.

    MathSciNet  MATH  Google Scholar 

  21. Fahnestock, J.D., Schowengerdt, R.A.: Spatially variant contrast enhancement using local range modification, Optical Engineering, Vol. 22, N. 3, 1983, S. 378–381.

    Google Scholar 

  22. Haralick, R.M., Shapiro, L.G.: Glossary of computer vision terms, Pattern Recognition, Vol. 24, 1991, S. 69–93.

    Article  Google Scholar 

  23. Haralick, R.M., Sternberg, S.R., Zhuang, X.: Image analysis using mathematical morphology, IEEE Trans., Vol. PAMI-9, July 1987, S. 532–550.

    Google Scholar 

  24. Haralick, R.M.: Edge and region analysis for digital image data, Computer Graphics and Image Processing, Vol. 12, 1980, S. 60–73.

    Article  Google Scholar 

  25. Huertas, A., Medioni, G.: Detection of intensity changes with subpixel accuracy using Laplacian-of-Gaussian masks, IEEE Trans., Vol. PAMI-8, Sept. 1986, S. 651–664.

    Google Scholar 

  26. Itoh, K., Ichioka, Y., Minami, T.: Nearest-neighbor median filter, Applied Optics, Vol. 27, 1988, N. 16, S. 3445–3450.

    Article  Google Scholar 

  27. Kim, V., Yaroslavskii, L.: Rank algorithms for picture processing, Computer Vision, Graphics, and Image Processing, Vol. 35, 1986, S. 234–258.

    Article  Google Scholar 

  28. Klette, R.: Algorithmen und Programme, in: Autbild 85/3, Wissenschaftliche Beiträge der Friedrich-Schiller-Universität, Jena, 1985, S. 7–61.

    Google Scholar 

  29. Klette, R.: Entwurf und Analyse effizienter Algorithmen, in: Autbild′87, Wissenschaftliche Beiträge der Friedrich-Schiller-Universität, Jena, 1987, S. 114–153.

    Google Scholar 

  30. Kovalevsky, V.A.: Finite topology as applied to image analysis, Computer Vision, Graphics and Image Processing, Vol. 46, 1989, S. 141–161.

    Article  Google Scholar 

  31. Lee, J.S., Haralick, R.M., Shapiro, L.G.: Morphologic edge detection, Proc. 8th International Conference on Pattern Recognition, Paris, 1986, S. 369–373.

    Google Scholar 

  32. Lee, J.S.: Digital image smoothing and the sigma filter, Computer Vision, Graphics, and Image Processing, Vol. 24, 1983, S. 255–269.

    Article  Google Scholar 

  33. Lee, Y.H., Fam, A.T.: An edge gradient enhancing adaptive order statistic filter, IEEE Trans., Vol. ASSP-35, May 1987, S. 680–695.

    Google Scholar 

  34. Lee, Y.H., Kassam, S.A.: Generalized median filtering and related nonlinear filtering techniques, IEEE Trans., Vol. ASSP-33, June 1985, S. 672–683.

    Google Scholar 

  35. Magid A., Rotman, S.R., Weiss, A.M.: Comment on “Picture thresholding using an iterative selection method”, IEEE Trans., Vol. SMC-20, Sept./Oct. 1990, S. 1238–1239.

    Google Scholar 

  36. McDonnell, M.J.: Box-filtering techniques, Computer Graphics and Image Processing, Vol. 17, 1981, S. 65–70.

    Article  Google Scholar 

  37. Nagao, M., Matsuyama, T.: Edge preserving smoothing, Computer Graphics and Image Processing, Vol. 9, 1979, S. 394–407.

    Article  Google Scholar 

  38. Nieminen, A., Heinonen, P., Neuvo, Y.: A new class of detail-preserving filters for image processing, IEEE Trans., Vol. PAMI-9, Jan. 1987, S. 74–90.

    Google Scholar 

  39. Pavlidis, T.: A thinning algorithm for discrete binary images, Computer Graphics and Image Processing, Vol. 13, 1980, S. 142–157.

    Article  Google Scholar 

  40. Piper, J.: Efficient implementation of skeletonisation using interval coding, Pattern Recognition Letters, Vol. 3, 1985, S. 389–397.

    Article  Google Scholar 

  41. Pitas, I., Venetsanopoulos, A.N.: Nonlinear order statistic filters for image filtering and edge detection, Signal Processing, Vol. 10, 1986, S. 395–413.

    Article  Google Scholar 

  42. Presetnik F.F., Filipovic, M.: Adaptive median filtering of images degraded by speckle noise, in: Lacoume, J.L. et al. (Hrsg.), Signal Processing IV: Theories and Applications, Elsevier, Amsterdam, 1988, S. 651–654.

    Google Scholar 

  43. Raji, A., Bolon, P.: Streaking effects of recursive median filters and symmetrical recursive median filters, in: Cappellini, V. (Hrsg.), Proc. Intern. Conf. on Digital Signal Processing, Firenze, Sept. 1991.

    Google Scholar 

  44. Restrepo, A., Bovik, A.C.: Adaptive trimmed mean filters for image restoration, IEEE Trans., Vol. ASSP-36, Aug. 1988, S. 1326–1337.

    Google Scholar 

  45. Ridler, T.W., Calvard, S.: Picture thresholding using an iterative selection method, IEEE Trans., Vol. SMC-8, Aug. 1978, S. 630–632.

    Google Scholar 

  46. Rosenfeld, A., Pfaltz, J.L.: Distance functions on digital pictures, Pattern Recognition, Vol. 1, 1968, S. 33–61.

    Article  MathSciNet  Google Scholar 

  47. Sahoo, P.K., Soitani, S., Wong, A.K.: A survey of thresholding techniques, Computer Vision, Graphics, and Image Processing, Vol. 41, 1988, S. 233–260.

    Article  Google Scholar 

  48. Scher, A., Dias Velasco, F.R., Rosenfeld, A.: Some new image smoothing techniques, IEEE Trans., Vol. SMC-10, March 1980, S. 153–158.

    Google Scholar 

  49. Schöniger, I.: Die Erkennung von Bodenerosionsschäden in digitalisierten Luftbildern mit Hilfe von Regionenwachstumsverfahren, Diplomarbeit, Institut für Geographie, Technische Universität Braunschweig, 1988.

    Google Scholar 

  50. Sezan, M.I.: A peak detection algorithm and its application to histogram-based image data reduction, Computer Vision, Graphics, and Image Processing, Vol. 49, 1990, S. 36–51.

    Article  Google Scholar 

  51. Siohan, P., Pelé, D., Ouvrard, V.: Two design techniques for 2-D LoG-Filters, in: Kunt, M. (Hrsg.), Proc. SPIE Conf. on Visual Communications and Image Processing, Lausanne, 1990, S. 970–981.

    Google Scholar 

  52. Sotak, G.E., Boyer, K.L.: The Laplacian-of-Gaussion kernel: a formal analysis and design procedure for fast, accurate convolution and full-frame output, Computer Vision, Graphics, and Image Processing, Vol. 48, 1989, S. 147–189.

    Article  Google Scholar 

  53. Suzuki, S., Abe, K.: Binary picture thinning by an iterative parallel two-subcicle operation, Pattern Recognition, Vol. 20, 1987, N. 3, S. 297–307.

    Article  Google Scholar 

  54. Tamura, H.: A comparison of line thinning algorithms from digital geometry viewpoint, Proc. 4th IJCPR, Kyoto, 1978, S. 715–719.

    Google Scholar 

  55. Trussell, H.J.: Comments on “Picture thresholding using an iterative selection method”, IEEE Trans., Vol. SMC-9, May 1979, S. 311.

    Google Scholar 

  56. Tyan, S.G.: Median filtering, deterministic properties, in: Huang, T.S. (Hrsg.), Two-dimensional digital signal processing II. Transforms and median filters, Springer, Berlin, 1981.

    Google Scholar 

  57. van den Boomgaard, R.: Threshold logic and mathematical morphology, in: Cantoni, V. et al. (Hrsg.): Progress in image analysis and processing, World Scientific Publishing, Singapore, 1990, S. 111–118.

    Google Scholar 

  58. Voss, K.: Shadingkorrektur in der automatischen Bildverarbeitung, Bild und Ton, Bd. 36, 1983, H. 6, S. 170–172.

    Google Scholar 

  59. Wang, D., Vagnucci, A.H., Li, C.C.: Gradient inverse smoothing scheme and the evaluation of its performance, Computer Graphics and Image Processing, Vol. 15, 1981, S. 167–181.

    Article  Google Scholar 

  60. Wang, D., Wang, Q.: A weighted averaging method for image smoothing, Proc. 8th ICPR, Paris, 1988, S. 981–983.

    Google Scholar 

  61. Wang, X., Wang, D.: On the max/median filter, IEEE Trans., Vol. ASSP-38, Aug. 1990, S. 1473–1475.

    Google Scholar 

  62. Xia, Y.: Skeletonization via the realization of the fire front’s propagation and extinction in digital binary shapes, IEEE Trans., Vol. PAMI-11, Oct. 1989, S. 1076–1086.

    Google Scholar 

  63. Yokoi S., Toriwaki, J., Fukumura, T.: An analysis of topological properties of digitized binary pictures using local features, Computer Graphics and Image Processing, Vol. 4, 1975, S. 63–73.

    Article  MathSciNet  Google Scholar 

  64. Zamperoni, P.: An agglomerative approach to modeling and segmentation of aerial views, in: Proc. MARI-87, Paris, Mai 1987, S. 426–431.

    Google Scholar 

  65. Zamperoni, P.: An automatic low-level segmentation procedure for remote sensing images, Multidimensional Systems and Signal Processing, Vol. 3, 1992, S. 29–44.

    Article  Google Scholar 

  66. Zamperoni, P.: Feature extraction by rank-order filtering for image segmentation, International Journal of Pattern Recognition and Artificial Intelligence, Vol. 2, 1988, N. 2, S. 301–319.

    Article  Google Scholar 

  67. Zamperoni, P.: Variations on the rank-order filtering theme for grey-tone and binary image enhancement, in: Proc. ICASSP′89, Glasgow, Mai 1989, S. 1401–1404.

    Google Scholar 

  68. Hufnagl, P., Schlosser, A., Voss, K.: Ein Algorithmus zur Konstruktion von Voronoidiagramm und Delaunaygraph, Bild und Ton 38 (1985), Heft 8, S. 241–245.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig / Wiesbaden

About this chapter

Cite this chapter

Klette, R., Zamperoni, P. (1992). Koordinatentransformationen und geometrische Operatoren. In: Handbuch der Operatoren für die Bildbearbeitung. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-90612-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-90612-0_4

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-06431-0

  • Online ISBN: 978-3-322-90612-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics