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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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
Duda R.O., Hart P.E., Storck D.G. (2001) Pattern Classification. 2nd edn. John Wiley & Sons, New York
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
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
Gelb, A. (Ed.) (1974) Applied Optimal Estimation. The MIT Press, Cambridge and London
Kadir T., Brady M. (2001) Saliency, Scale and Image Description. Intern. J. Computer Vision 45(2):83–105
Koenderink J.J. (1984) The Structure of Images. Biolog. Cybernetics 50:363–370.
Koenderink J.J., van Doorn A.J. (1992) Generic Neighborhood Operators. IEEE Trans. Pattern Analysis Machine Intelligence PAMI-14(6):597–605.
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
Köthe U. (2004) Low-Level Feature Detection Using the Boundary Tensor. (This volume)
Lindeberg T. (1998) Feature Detection with Automatic Scale Selection. Intern. J. Computer Vision 30(2):79–116
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
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
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
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/3-540-31272-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25032-6
Online ISBN: 978-3-540-31272-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)