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On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor

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Visualization and Processing of Tensor Fields

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

As a step towards a local analysis of local image features, the position, peak value, and covariance matrix of an isolated, noise-free multivariate Gaussian are determined in closed form from four ‘observables’, computed by gaussian-weighted averaging first and second powers of (up to second order) partial derivatives of a digitized greyvalue distribution.

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References

  1. Brox Th., van den Boomgaard R., Lauze F., van de Weijer J., Weickert J., Mrázek P., Kornprobst P. (2004) Adaptive Structure Tensors and their Applications. (This volume)

    Google Scholar 

  2. Chomat O., Colin de Verdière V., Hall D., Crowley J.L. (2000) Local Scale Selection for Gaussian Based Description Techniques. In: Vernon D. (Ed.) Proc. ECCV-2000 (Part I) at Dublin, Ireland, June 26–July 1, 2000. LNCS 1842 Springer, Berlin Heidelberg, 117–133

    Google Scholar 

  3. Duda R.O., Hart P.E., Storck D.G. (2001) Pattern Classification. 2nd edn. John Wiley & Sons, New York

    MATH  Google Scholar 

  4. Förstner W.A. (1994) A Framework for Low-Level Feature Extraction. In: Eklundh J.-O. (Ed.), Proc. ECCV-1994 (Part II) at Stockholm, Sweden, May 2–6, 1994. LNCS 801 Springer, Berlin Heidelberg, 383–394

    Google Scholar 

  5. Förstner W.A., Gülch E. (1987) A Fast Operator for Detection and Precise Location of Distinct Points, Corners and Centers of Circular Features. In: Proc. Workshop of the Intern. Soc. for Photogrammetry & Remote Sensing at Interlaken, Switzerland, June 1987, 281–305

    Google Scholar 

  6. Gelb, A. (Ed.) (1974) Applied Optimal Estimation. The MIT Press, Cambridge and London

    Google Scholar 

  7. Kadir T., Brady M. (2001) Saliency, Scale and Image Description. Intern. J. Computer Vision 45(2):83–105

    Article  MATH  Google Scholar 

  8. Koenderink J.J. (1984) The Structure of Images. Biolog. Cybernetics 50:363–370.

    Article  MathSciNet  MATH  Google Scholar 

  9. Koenderink J.J., van Doorn A.J. (1992) Generic Neighborhood Operators. IEEE Trans. Pattern Analysis Machine Intelligence PAMI-14(6):597–605.

    Article  Google Scholar 

  10. Koenderink J.J., van Doorn A.J. (2002) Image Processing Done Right. In: Heyden A., Sparr G., Nielsen M., Johansen P. (Eds.) Proc. ECCV-2002 (Part I) at Copenhagen, Denmark, May 28–31, 2002. LNCS 2350 Springer, Berlin Heidelberg, 158–172

    Google Scholar 

  11. Köthe U. (2004) Low-Level Feature Detection Using the Boundary Tensor. (This volume)

    Google Scholar 

  12. Lindeberg T. (1998) Feature Detection with Automatic Scale Selection. Intern. J. Computer Vision 30(2):79–116

    Article  Google Scholar 

  13. Lindeberg T. (2002) Time-Recursive Velocity-Adapted Spatio-Temporal Scale-Space Filters. In: Heyden A., Sparr G., Nielsen M., Johansen P. (Eds.) Proc. ECCV-2002 (Part I) at Copenhagen, Denmark, May 28–31, 2002. LNCS 2350 Springer, Berlin Heidelberg, 52–67

    Google Scholar 

  14. Middendorf M. (2003) Zur Auswertung lokaler Grauwertstrukturen (in German). Dissertation, Fakultät für Informatik der Universität Karlsruhe (TH), Juli 2003. Norderstedt, ISBN 3-8334-1175-9

    Google Scholar 

  15. Middendorf M., Nagel H.-H. (2002) Empirically Convergent Adaptive Estimation of Greyvalue Structure Tensors. In: Van Gool L. (Ed.) Proc. 24th DAGM Symposium 2002 at Zurich, Switzerland, September 16–20, 2002. LNCS 2449 Springer, Berlin Heidelberg, 66–74

    Google Scholar 

  16. Spies H., Scharr H. (2001) Accurate Optical Flow in Noisy Image Sequences. In: Proc. ICCV-2001 (Vol. I) at Vancouver, BC, July 9–12, 2001. 587–592.

    Google Scholar 

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Nagel, HH. (2006). On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor. In: Weickert, J., Hagen, H. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31272-2_3

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