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Characterizing first and second-order patches using geometry-limited diffusion

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Information Processing in Medical Imaging (IPMI 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 687))

Abstract

I propose a diffusion process that operates on the jet-space of an image. This process uses variable conductance diffusion as an alternative to Gaussian scale in order to smooth differential measurements in a manner that preserves structures of interest. The process is presented within a general framework that suggests a wide range of possibilities for segmenting images on the basis of homogeneity of local shape. Previous work has shown how first-order geometry is used to locate ridges and valleys in greyscale objects. In this paper I use apply these principles to first and second-order geometry in order to find boundaries and skeletons of objects. Examples of first and second-order segmentations of medical images are given. This method appears to offer a reliable and accurate means of segmenting images and is shown to preserve the orthogonal group properties of properly constructed geometric invariants.

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References

  1. J. Blom. Topological and Geometrical Aspects of Image Structure. PhD thesis, University of Utrecht, 1992.

    Google Scholar 

  2. J. Canny. A computational approach to edge detection. IEEE PAMI, 8(6):679–698, 1987.

    Google Scholar 

  3. N. G. Cooper and G. B. West. Scale and Dimension, pages 4–21. Cambridge University Press, 1988.

    Google Scholar 

  4. J. M. Gauch. A multiresolution intensity axis of symmetry and its application to image segmentation. Technical Report TR89-047, Department of Computer Science, University of North Carolina, Chapel Hill, North Carolina 27599–3175, 1989.

    Google Scholar 

  5. G. Gerig, O. Kubler, R. Kikinis, and F.A Jolesz. Nonlinear anistropic filtering of MRI data. Technical Report BIWI-TR-124, Institute for Communication Technology, Image Science Division, ETH-Zentrum, Surich, Switzerland, 1991.

    Google Scholar 

  6. S. Grossberg. Neural dynamics of brightness perception: Features, boundaries, diffusion, and resonance. Percpetion and Psychophysics, 36(5):428–456, 1984.

    Google Scholar 

  7. J. J. Koenderink. The structure of images. Biol. Cybern., 50:363–370, 1984.

    Article  PubMed  Google Scholar 

  8. J. J. Koenderink. Solid Shape. MIT press, Cambridge, Mass, 1990.

    Google Scholar 

  9. J. J. Koenderink and A. J. Van Doorn. Receptive field families. Biol. Cybern., 63:291–298, 1990.

    Article  Google Scholar 

  10. T. Lindeberg. A scale-space for descrete signals. IEEE PAMI, 12(3):234–245, 1990.

    Google Scholar 

  11. N. Nordstrom. Biased anisotropic diffusion — a unified regularization and diffusion approach to edge detection. Image and Visual Comp, 8(4):318–327, 1990.

    Article  Google Scholar 

  12. P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis Machine Intelligence, 12:629–639, 1990.

    Article  Google Scholar 

  13. S. M. Pizer, J.M. Gauch, T. J. Cullip, and R. E. Fredericksen. Descriptions of intensity structure via scale and symmetry. In Proceedings First Conference on Visualization in Boimedical Computing, pages 94–101, 1990.

    Google Scholar 

  14. P. L. Rosin, A. C. F. Colchester, and D. J. Hawkes. Early image representation using regions defined by maximum gradient profiles between singular points. To appear in Pattern Recognition, 1991.

    Google Scholar 

  15. Bart ter Haar Romeny and Luc Florack. A multiscale geometric approach to human vision. In B. Hendee and P. N. T. Wells, editors, Perception of Visual Information. Springer Verlag, Berlin, 1991.

    Google Scholar 

  16. B.M. ter Haar Romeny and L.M.J. Florack. Scale space; its natural operators and differential invariants. In A. C. F. Colchester and D. J. Hawkes, editors, Lecture Notes in Computer Science, volume 511, pages 239–255. Springer-Verlag, 1991. Springer-Verlag, 1991, pp..

    Google Scholar 

  17. R. T. Whitaker. Geometry-limited diffusion in the characterization of geometric patches in images. CVGIP: Image Understanding, 57(1):111–120, January 1993.

    Article  Google Scholar 

  18. R. T. Whitaker and S. M. Pizer. Geometry-based image segmentation using anisotropic diffusion. In Ying-Lie O, A. Toet, H.J.A.M Heijmans, D.H. Foster, and P. Meer, editors, Shape in Picture: The mathematical description of shape in gerylevel images. Springer Verlag, Heidelberg, 1993.

    Google Scholar 

  19. R. T. Whitaker and S. M. Pizer. A multi-scale approach to nonuniform diffusion. CVGIP: Image Understanding, 57(1):99–110, January 1993.

    Article  Google Scholar 

  20. R. A. Young. Simulation of human retinal function with the Gaussian derivative model. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1986.

    Google Scholar 

  21. R. A. Young. The Gaussian derivative model for spatial vision: I. Retinal mechanisms. Spatial Vision, 2(4):273–293, 1987.

    PubMed  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of North Carolina at Chapel Hill, 27599-3175, Chapel Hill, North Carolina

    Ross T. Whitaker

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  1. Ross T. Whitaker
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Harrison H. Barrett A. F. Gmitro

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© 1993 Springer-Verlag Berlin Heidelberg

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Whitaker, R.T. (1993). Characterizing first and second-order patches using geometry-limited diffusion. In: Barrett, H.H., Gmitro, A.F. (eds) Information Processing in Medical Imaging. IPMI 1993. Lecture Notes in Computer Science, vol 687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013786

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  • DOI: https://doi.org/10.1007/BFb0013786

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56800-1

  • Online ISBN: 978-3-540-47742-6

  • eBook Packages: Springer Book Archive

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